Fourth National Incidence Study of 

Child Abuse and Neglect (NIS–4) 

Supplementary Analyses 

of Race Differences in 

Child Maltreatment Rates 

in the NIS–4 

Authors: 

Andrea J. Sedlak 

Karla McPherson 

Barnali Das 

March 2010 

Prepared for: 

Office of Planning, Research, and Evaluation (OPRE) 

and the Children’s Bureau 

Administration for Children and Families (ACF) 

U.S. Department of Health and Human Services (DHHS) 

Washington, DC 

Prepared by: 

Westat, Inc. 

1650 Research Boulevard 

Rockville, MD 

Contract No. GS23F8144H, Order # HHSP233200400058U 
 

 


 


 


 


 


 

TABLE OF CONTENTS 

Chapter.................................................................................................................................................... Page
 

EXECUTIVE SUMMARY.................................................................................................... 1 

1. INTRODUCTION............................................................................................ 3 

1.1 Race Findings in the NIS–4 ................................................................ 4 

1.2 Understanding the Discrepant Findings of the ...............................
 

NIS–3 and the NIS–4........................................................................... 4 

2. RATIONALE, BACKGROUND, AND PURPOSE OF 

MULTI-FACTOR ANALYSES OF NIS–4 DATA .................................... 12 

2.1 Rationale................................................................................................. 12 

2.2 Background............................................................................................ 13 

2.3 Purpose................................................................................................... 15 

3. METHODOLOGY........................................................................................... 16 

3.1 Construction of the Synthetic Database............................................ 16 

3.2 Model-building Procedures ................................................................. 20 

3.3 Follow-up Analyses............................................................................... 23
 

4. MULTI-FACTOR MODELS .......................................................................... 25 

4.1 Harm Standard Maltreatment.............................................................. 26 

4.2 Endangerment Standard Maltreatment.............................................. 33
 

5. DISCUSSION..................................................................................................... 46 

5.1 Differences Between NIS–3 and NIS–4 ........................................... 46 

5.2 Race Differences in the NIS–4 Isolated from Other, 

Correlated Risk Factors........................................................................ 47 

5.3 Limitations ............................................................................................. 52 

5.4 Conclusions............................................................................................ 53
 

i 
LIST OF TABLES 

Table Page 

Table 1–1 Differences in Percentages of White and Black Children With Specific 

Family Risk Conditions, 1993 and 2006 ....................................................... 8 

Table 3–1 Measures in the NIS–4 Synthetic Database................................................... 18

Table 4–1 Multi-Factor Model Predicting All Harm Standard Maltreatment for 

All Black and White Children ........................................................................... 27 

Table 4–2 Multi-factor Model Predicting Harm Standard Physical Abuse for All 

Black and White Children.................................................................................. 28 

Table 4–3 Multi-factor Model Predicting Harm Standard Physical Abuse for 

Black and White Children Living With Parents ............................................. 30 

Table 4–4 Multi-factor Model Predicting Harm Standard Sexual Abuse for All 

Black and White Children.................................................................................. 31 

Table 4–5 Multi-factor Model Predicting Harm Standard Emotional Maltreatment 

for All Black and White Children..................................................................... 32 

Table 4–6 Multi-factor Model Predicting Harm Standard Physical Neglect for All 

Black and White Children.................................................................................. 32 

Table 4–7 Multi-factor Model Predicting All Endangerment Standard Maltreatment 

for All Black and White Children .................................................................... 34 

Table 4–8 Multi-factor Model Predicting Endangerment Standard Physical Abuse 

for All Black and White Children..................................................................... 37 

Table 4–9 Multi-factor Model Predicting Endangerment Standard Sexual Abuse for 

All Black and White Children ........................................................................... 40 

Table 4–10 Multi-factor Model Predicting Endangerment Standard Emotional 

Maltreatment for All Black and White Children............................................ 41

Table 4–11 Multi-factor Logistic Model Predicting Endangerment Standard Physical 

Neglect for All Black and White Children ...................................................... 44 

LIST OF FIGURES 

Figure Page 

Figure 1–1 Estimated Rates of all Harm Standard Maltreatment for White and 

Black Children in the NIS–3 and NIS–4, With Their 95-percent 

 Confidence Intervals ............................................................................................... 6

Figure 1–2 Estimated Rates of Harm Standard Physical Abuse for White and 

Black Children in the NIS–3 and NIS–4, With Their 95-percent 

 Confidence Intervals ............................................................................................... 7

Figure 1–3 Percentages of White Children and of Black Children Who Were 
 

Living in Households With Different Incomes in 1993 and in 2006............... 10 

Figure 1–4 Changes in Median Income for Families With Children 

(derived from data in Table F-9, U.S. Census Bureau, 2009)............................ 11 


 

ii 
 

Figure 2–1 Percentage of Children in Low SES Households by Their Family 

 Structure .................................................................................................................... 13 

Figure 2–2 Percentage of Black Children and White Children Living in Different 

 Family Structures ..................................................................................................... 13

Figure 4–1 Model-based Marginal Probabilities of Harm Standard Physical Abuse 

(and Approximate Confidence Intervals) by Child’s Race and SES ................ 29 

Figure 4–2 Model-based Marginal Probabilities of All Endangerment Standard 

Maltreatment (and Approximate Confidence Intervals) by Child’s Race 

and Socioeconomic Status...................................................................................... 35 

Figure 4–3 Model-based Marginal Probabilities of All Endangerment Standard 

Maltreatment (and Approximate Confidence Intervals) by Child’s Race 

and Family Structure ............................................................................................... 36 

Figure 4–4 Model-based Marginal Probabilities of Endangerment Standard Physical 

Abuse (and Approximate Confidence Intervals) by Race and SES ................. 38 

Figure 4–5 Model-based Marginal Probabilities of Endangerment Standard Physical 

Abuse (and Approximate Confidence Intervals) by Child’s Race and 

 Family St.................................................................................................................... 39 

Figure 4–6 Model-based Marginal Probabilities of Endangerment Standard 

Emotional Maltreatment (and Approximate Confidence Intervals) 

by Child’s Race and SES......................................................................................... 42 

Figure 4–7 Model-based Marginal Probabilities of Endangerment Standard 

Emotional Maltreatment (and Approximate Confidence Intervals) 

by Child’s Race and Family Structure ................................................................... 43 

Figure 4–8 Model-based Marginal Probabilities of Endangerment Standard Physical 

Neglect (and Approximate Confidence Intervals) by Child’s Race 

 and SES ..................................................................................................................... 44 

REFERENCES ....................................................................................................... 55

iii 
APPENDICES 

A Confidence Intervals for NIS–3 and NIS–4 Maltreatment Estimates 

for Black and White Children ................................................................................ A–1 

B Imputation of Missing Demographic Data Items............................................... B–1 

C Construction of the Synthetic Database for Use in Building Multi-factor 

 Logistic Models ........................................................................................................ C–1

D Procedures for Generating Marginal Probabilities from Final 

 Logistic Models ........................................................................................................ D–1

E Final Logistic Regression Models for All Maltreatment Categories................. E–1 

F Model-Based Marginal Probabilities and 95%-Confidence Intervals for 

Race-Related Findings for all Black and White Children................................... F–1 

iv 

 

EXECUTIVE SUMMARY 

For the first time in the history of the National Incidence Study of Child Abuse and 

Neglect, the most recent cycle, the NIS–4, found race differences in maltreatment rates, with Black 

children experiencing maltreatment at higher rates than White children in several categories. The 

efforts described in this report attempted to understand this finding by considering possible reasons 

why the NIS–4 results diverged from the findings in earlier cycles and by using multi-factor logistic 

modeling to reanalyze the NIS–4 data in order to isolate whether and how race contributed to 

maltreatment risk independent of the other important risk factors that correlated with race. 

The authors examined two possible explanations for why the NIS–4 found statistically 

reliable race differences in rates of some categories of child maltreatment, in contrast to the findings 

of previous NIS cycles. They concluded that the finding is at least partly a consequence of the 

greater precision of the NIS–4 estimates and partly due to the enlarged gap between Black and 

White children in economic well-being. Income, or socioeconomic status, is the strongest predictor 

of maltreatment rates, but since the time of the NIS–3, incomes of Black families have not kept pace 

with the incomes of White families. 

Race correlates with a number of other predictors of maltreatment, so it was important 

to take the effects of these other correlated predictors into account when evaluating the effects of 

race. The authors attempted to do this by building multi-factor models that incorporated all the 

statistically reliable predictors of maltreatment in the category. The final multi-factor models 

revealed that race did have effects on risk in certain maltreatment categories, even after the effects of 

other important predictors were considered. 

Black children were at significantly greater risk than White children of experiencing 

physical abuse under both the Harm and Endangerment Standards, but in both cases, this race 

difference depended on SES. The race difference was small or nonexistent among children living in 

low SES households, but it was notably larger for children in not-low SES households. 

In two maltreatment categories, Endangerment Standard emotional maltreatment and 

overall Endangerment Standard maltreatment, race differences depended on SES and family 

structure. There were no race differences among children in low SES households, but the 

maltreatment risk for Black children in not-low SES households was two or more times greater than 

1
 

 

the risk for White children in this condition. Black children were also at comparatively elevated risk 

when living with unmarried parents or a single parent with a partner in the household, whereas the 

risk for White children in those circumstances was considerably lower. At the same time, White 

children appeared to have somewhat higher risk than Black children when living with married 

parents who were not both biologically related to them and when living with a single parent who had 

no cohabiting partner. 

White children had significantly higher risk for Endangerment Standard physical 

neglect, but this race difference appeared only among children in low SES households. This pattern 

resembled the earlier findings of multi-factor analyses of the NIS–3 data, which applied in more 

maltreatment categories in that study (Sedlak and Schultz, 2005). 

The present findings are qualified by the limitations of the predictors that were available 

for the NIS–4 multi-factor analyses, which comprised only general demographic characteristics of 

the children and their families. The key measure of SES was less than ideal in two respects—the 

large amount of missing data that required imputation and the fact race differences that emerged in 

the not-low SES condition could, in part, actually reflect the underlying income differences. 

Independent evidence indicates that Black and White children very probably have different 

underlying SES distributions within the NIS–4 non-low SES category, with the not-low SES Black 

children less well off than the not-low SES White children. If the economic resources of Black and 

White children had been equivalent in this condition, then the observed pattern of higher risk for 

Black children under non-low SES conditions may not have emerged. For these reasons, the race 

differences observed in the not-low SES condition in this report must be interpreted with caution. 

2
 
 

 


 

1. INTRODUCTION 

The National Incidence Study of Child Abuse and Neglect (NIS) is a periodic federal 

effort that provides estimates of the number of children who are abused and neglected in the United 

States. NIS gathers data from both (1) child protective service agencies and (2) community 

professionals who encounter maltreated children during the course of their work in a variety of 

agencies, including schools, hospitals, law enforcement, day care, and shelters. The NIS integrates 

the cases obtained from the multiple sources, generating national estimates of the numbers of 

abused and neglected children that include both those who receive the attention of CPS agencies 

and those who do not (Sedlak & Schultz, 2005; Sedlak, Mettenburg, Basena, Petta, McPherson, 

Greene, and Li, 2010). 

The NIS has been implemented four times, providing national estimates for children 

abused and neglected in 1980, 1986, 1993, and 2005-2006 (National Center on Child Abuse and 

Neglect, 1981; Sedlak, 1991; Sedlak & Broadhurst, 1996; Sedlak et al., 2010). The most recent 

implementation, NIS–4, was the first time that the study detected race differences in rates of child 

maltreatment. This paper reports the NIS–4 research team’s efforts to understand these unexpected 

and unprecedented race differences, by examining potential reasons why the findings on race in the 

NIS–4 diverged from those in earlier NIS cycles and by conducting further analyses of the NIS–4 

data to determine whether other risk factors that differentially affect Black and White children could 

account for the observed findings.1 

This introductory chapter summarizes the NIS–4 findings on race and examines 

potential explanations for why they diverge from those of earlier NIS cycles. Chapter 2 presents the 

rationale for the multi-factor analyses of the NIS–4 data and describes similar analyses of the NIS–3 

data, which serve as historical background for the present analyses. In order to conduct the multifactor analyses, it was necessary to develop a special database that integrated the NIS–4 data on 

maltreated children with Census data on the general child population. Chapter 3 describes the 

methodology used to develop this synthetic database and build the multi-factor models to account 

for risk of maltreatment. Chapter 4 reports on the results of the model-building efforts. Chapter 5 

summarizes the conclusions of these efforts, discussing their limitations and implications. 

1 For this report, the analyses of race differences in the NIS–4 included only the Black children and White children because maltreatment rates for 

these groups differed in nearly all categories where race differences emerged, while the maltreatment rates for Hispanic children nearly always 

resembled the rates for White children. 

3
 
 

 


 

1.1 Race Findings in the NIS–4 

In contrast to all the earlier NIS cycles, which found no race differences in rates of 

maltreatment, the NIS–4 found statistically reliable race differences in several maltreatment 

categories, with Black children having higher rates than White children (Sedlak et al., 2010).2 The 

NIS uses two standards to define maltreatment, the Harm Standard and the Endangerment 

Standard.3 The NIS–4 findings, given in the Report to Congress (Sedlak et al., 2010), indicated that, 

under both definitional standards, Black children experienced a significantly higher rate of physical 

abuse, overall abuse, and overall maltreatment. Under the Endangerment Standard, Black children 

also had significantly higher rates of emotional neglect and overall neglect. Statistically marginal race 

differences emerged in rates of sexual abuse and overall neglect under the Harm Standard and in 

rates of physical neglect under the Endangerment Standard.4 

1.2 Understanding the Discrepant Findings of the NIS–3 and the NIS–45 

The fact that the NIS–4 found statistically significant differences between Black and 

White rates of child maltreatment, contrary to the findings of the first three NIS cycles, warrants 

further explanation. The NIS–4 research team examined two possible explanations. First, the NIS–4 

used much larger samples and generated estimates that were more precise than those of the NIS–3. 

The greater precision of the NIS–4 estimates may have allowed this latest study to detect race 

differences in maltreatment rates, even if the underlying patterns of risk and resulting maltreatment 

have not changed. Second, it is possible that the distribution of risk factors changed in some way. 

That is, changes in the socioeconomic circumstances of Black and White children during the interval 

between the two NIS cycles may have contributed to changes in their maltreatment rates. These two 

explanations are not mutually exclusive. 

2 Following the practice in the Census, the NIS–4 data forms allowed respondents to indicate all race/ethnicities that applied to a child. The race 

analyses reported in the NIS–4 Report to Congress (Sedlak et al., 2010) simplified this information and related it to the corresponding simplified 

Census categories: White non-Hispanic, Black non-Hispanic and Hispanic. Each of the other race categories had too few sample children to support 

estimates for those groups (i.e., American Indian or Alaskan Native, Asian, Native Hawaiian or other Pacific Islander, and mixed race). 

3 The Harm Standard is more stringent, typically requiring that a child be harmed by maltreatment in order to be included in the study estimates. The 

Endangerment Standard is more lenient, also permitting children to enter the estimates who were endangered by maltreatment. The Endangerment 

Standard estimates include children who meet the Harm Standard. Chapter 2 in the NIS–4 Report to Congress (Sedlak et al., 2010) summarizes these 

standards. The NIS–4 Analysis Report (Sedlak, Mettenburg, Winglee, Ciarico, and Basena, 2010) gives further details. 

4 Statistically significant differences have a probability of less than 5 percent of having occurred by chance (i.e., reflecting purely random factors), 

whereas statistically marginal differences have a probability of less than 10 percent of having occurred by chance. Differences that arise from chance 

or random factors are not statistically reliable and would not likely emerge in an exact replication of the study. 

5 Extensive race analyses were conducted using NIS–3 data (Sedlak and Schultz, 2005). See Chapter 2 for discussion of the results. 

4
 

 

Another possibility is that the risk factors relate to maltreatment rates differently now, 

perhaps due to unmeasured changes in the surrounding social context of other risk-related 

circumstances or associated protective factors. For instance, if being in a family with more children 

is more strongly associated with maltreatment than it was in the past (say, for example, because 

available community and extended-family support systems are weaker or less effective than they 

were), then even if there were no changes in the racial distribution by family size, the fact that more 

Black children are in larger families would lead to higher maltreatment rates for that group. It is not 

possible to examine this hypothesis empirically. Comparisons of the relative strength of different 

risk factors during the two time periods yield ambiguous results because the NIS–4 data offer 

greater statistical power. That is, any risk factor may appear to be more strongly related to 

maltreatment rates in the NIS–4 because of its greater statistical power to detect the association, 

rather than because of any underlying change in the true strength of the association. Also, the NIS 

has no independent measures of potentially important mitigating factors in the surrounding social 

context during the two time periods. 

More precise estimates in NIS–4. The NIS–4 sampled more counties and more CPS and 

sentinel agencies than the NIS–3 and collected considerably more data forms. As a consequence, 

the NIS–4 estimates were more precise (i.e., had smaller standard errors) than the NIS–3 estimates. 

Comparison of the NIS–3 findings with the NIS–4 findings (Appendix A) shows that the BlackWhite differences in NIS–3, while not statistically significant, tended in the same direction as those 

subsequently found in the NIS–4. The NIS–4 design may have afforded increased statistical power 

to detect differences due to its lower standard errors, resulting in tighter confidence intervals around 

the estimates. 

Two estimates do not differ significantly if either estimate falls within the confidence interval 

of the other estimate. At the other extreme, if the confidence intervals do not overlap, then the 

estimates are statistically different. More precise estimates have smaller (i.e., narrower) confidence 

intervals. Even if two studies are done simultaneously (which means the true maltreatment rates in 

the population are actually identical), the confidence intervals will be less likely to overlap in the 

study that offers more precise estimates. The NIS–3 estimates have rather large confidence intervals, 

with the Black and White intervals overlapping a great deal and often including the other estimate, 

whereas the NIS–4 intervals are considerably smaller and, in those maltreatment categories where 

the races differ, they do not include the other estimate. 

5
 
 

 


 

Figures 1–1 and 1–2 demonstrate this, displaying the 95-percent confidence intervals on the 

NIS–3 and NIS–4 estimates for all Harm Standard maltreatment and Harm Standard physical abuse, 

respectively. Appendix A presents tables showing the NIS–3 and NIS–4 confidence intervals for all 

maltreatment categories where the NIS–4 found statistically reliable Black/White rate differences. 

Figure 1–1. Estimated Rates of all Harm Standard Maltreatment for White and Black Children in 

the NIS–3 and NIS–4, With Their 95-percent Confidence Intervals. 

Thus, the greater precision of the NIS–4 estimates (i.e., their smaller confidence 

intervals) enhanced that study’s ability to detect differences and this may have contributed to the 

NIS–4 findings of race-related differences in maltreatment rates. 

Changes in the circumstances of Black and White children. The NIS–4 not only 

revealed unprecedented race differences in rates of maltreatment, as described above, but the study 

also demonstrated statistically meaningful changes since the NIS–3 in maltreatment rates for Black 

and White children. Under both definitional standards, rates of all abuse and of physical abuse 

decreased for both races, but the decrease was greater for White children. The rate of Harm 

Standard emotional neglect decreased for White children but increased for Black children, while the 

rate of Endangerment Standard emotional neglect increased for both race groups, but the increase 

was greater for Black children.6 Thus, overall, rates of maltreatment for White children decreased 

6 The race analyses reported in the NIS–4 Report to Congress (Sedlak et al., 2010) included Hispanic children and compared changes across the three 

race/ethnicity groups. With two exceptions, changes in maltreatment rates for Hispanic children were between the changes for White children and 

6
 
 

more or increased less than maltreatment rates for Black children—consistent with the fact that the 

NIS–4 found higher maltreatment rates for Black children whereas the NIS–3 did not. It is 

important to note that the NIS–4 detected no statistically reliable race-related changes since the 

NIS–3 in rates of all maltreatment, all neglect, physical neglect or educational neglect, under both 

definitional standards. 

Figure 1–2. Estimated Rates of Harm Standard Physical Abuse for White and Black Children in the 

NIS–3 and NIS–4, With Their 95-percent Confidence Intervals. 

Throughout its history, the NIS has consistently found a powerful relationship between 

family structural or socioeconomic characteristics and maltreatment rates. Both the NIS–3 and the 

NIS–4 found that children’s risk of maltreatment related significantly to the family’s socioeconomic 

status, parents’ employment, family structure, and the number of children in the household (Sedlak 

& Broadhurst, 1996; Sedlak & Schultz, 2005; Sedlak et al., 2010). At the same time, Black and White 

children differed significantly on four risk factors at the time of both studies, as illustrated in Table 

1–1. 

Black children. The exceptions were in the categories of Harm Standard physical abuse and emotional neglect under both standards, where the 

changes in maltreatment rates for Hispanic children resembled the changes in rates for Black children. 

7 
Table 1–1. Differences in Percentages of White and Black Children With Specific Family Risk 

Conditions, 1993 and 2006. 

   

   

   

   

      


 

Family Characteristic 

1993 2006 

% of 

White 

Children 

% of 

Black 

Children 

% of 

White 

Children 

% of 

Black 

Children 

Family Structure

Two parents 79.1 35.3 75.9 34.5 

Single parent 19.3 57.3 20.8 56.1 

No parent 1.5 7.3 3.2 9.4 

Single parent with partnera 1.5 2.3 3.5 4.4 

Single parent, no partner 17.8 55.1 17.3 51.6 

Parents’ Employment

Unemployed 16.4 18.8 8.5 12.4 

Employed 76.8 51.0 84.2 65 

Not in Labor Force 5.2 22.8 4.0 13.2 

Family Size

1 child 23.1 21.1 24.5 24.2 

2 children 43.4 31 41.8 33.8 

3 children 22.6 24.2 22.6 21.2 

4 or more children 10.9 23.8 11 20.7 

Parents’ Education

Less than high school 7.0 20.4 4.3 12.7 

High school 29.5 36.7 20.4 30.0 

Some college 29.9 24.7 29.0 28.3 

College graduate 19.6 7.8 25.7 12.5 

Advanced degree 12.5 3.1 17.5 6.5 

Household Income

<$15,000 15.7 52.5 8.9 29.8 

$15,000-$24,999 12.6 16.1 6.7 17.1 

$25,000-$39,999 21.4 13.6 11.9 17.0 

$40,000-$54,999 20.0 9.0 13.2 10.8 

$55,000-$74,999 16.1 4.8 16.5 10.3 

$75,000-$99,999 8.0 2.8 15.6 7.5 

>=$100,000 6.2 1.1 27.3 7.5 

Other Economic Measures

Low Socioeconomic Statusb 21.8 61.6 15.0 45.9 

Household participates in 

poverty program 

12.7 46.9 8.2 32.6 

Notes: Gray shading indicates that the percentages of Black children and White children differ 

significantly; differences in Black and White percentages in green shaded cells are statistically marginal. a

The definition of this category does not exactly conform to that used in the NIS–4 Report to Congress, 

because 1993 Census data combined parents’ partners with roommates. The comparison here includes 

opposite-sex parents/partners in both time frames. 

b

The child is classified as in a family of low socioeconomic status if the household income was less than 

$15,000, the parent(s) were not high school graduates, or the household participated in a poverty program. 

8
 

 

Within each year, adjacent cells that are shaded differ statistically. During both study 

years, significantly lower percentages of Black children were in the lower risk condition of twoparent families, while significantly higher percentages were in the higher risk conditions of singleparent families or not living with any parent. Significantly lower percentages had employed parents, 

while significantly higher percentages had parents who were not in the labor force—the higher risk 

condition. During both time periods, higher percentages of Black children lived in the largest 

families, with 4 or more children, where children had the highest risk of maltreatment. This race 

difference was statistically significant in 1993 but statistically marginal in 2006. A lower percentage 

of Black children lived in 2-child households in 1993, another statistically marginal difference. 

Throughout its history, the NIS has consistently demonstrated that socioeconomic 

factors are strongly predictive of child maltreatment. Table 1–1 shows that substantially and 

significantly higher percentages of Black children lived in families of low socioeconomic status and 

in households that participated in a poverty program, which are the circumstances associated with 

higher maltreatment rates. A similar pattern occurs in the distributions of Black and White children 

by specific categories of household income: During both time periods, the race differences in the 

extreme ranges are consistent. Significantly higher percentages of Black children were in the lowest 

income households, while significantly lower percentages were in the highest income households. 

For children in households with incomes in the intermediate ranges, $40,000 to $74,999, race 

differences in 1993 favored White children, but no differences were statistically reliable in 2006. 

The NIS–4 research team considered the possibility that, since the time of the NIS–3, 

circumstances may have changed disproportionately for the different races, lowering the 

maltreatment risk for White children disproportionately relative to that of Black children. In 

examining Table 1–1, it is apparent that, for most of the characteristics listed, this is not what 

occurred. Rather, in certain disadvantaging circumstances, where Black children have been 

historically overrepresented, the racial differences in percentages of children actually diminished 

between 1993 and 2006. The racial gap most notably decreased in the percentages of children living 

in households that participate in a poverty program (down by 9.8%) and for children whose parents 

are not in the labor force (down by 8.4%). The gap also decreased, although to a lesser extent, for 

children whose parents have less than a high school education (down by 5.0%), who live in the 

largest families (with 4 or more children) (down by 3.2%), and who live with single parents (down by 

2.8%). Similarly, the racial gaps in the percentages of children who live in several lower risk 

circumstances, where Black children have been historically underrepresented, also decreased during 

the time interval. The percentages of children living with two parents decreased for both races, but 

9
 

 

the percentage of Black children in this category decreased less than the percentage of White 

children in this category, which reduced the racial gap by 2.4%. The percentage of children living 

with employed parents increased for both races, but the increase was greater for Black children thus 

reducing the race gap in this category (by 6.6%). The percentage of White children in 2-child 

families decreased while the percentage of Black children in these families increased, reducing the 

racial gap by 4.4% in this, the lowest risk category on this measure. The racial gap also decreased by 

4.6% among children whose parents had some college, primarily because the percentage of Black 

children in this circumstance increased more than the percentage of White children. With the 

exception of other shifts in the racial distributions by income, other changes in Table 1–1 have 

relatively little effect on the racial gaps. 

The race-related shifts in household income are qualitatively different than the changes 

described above, all of which reduced the racial gap that disadvantaged Black children. Figure 1–3 

graphs the Table 1–1 income data to illustrate. All incomes rose during the 1993-2006 time interval, 

but while the improved household incomes of Black children primarily lifted them out of the lowest 

income categories, the improvements in household incomes for White children raised them 

disproportionately into the higher income categories. This is evident in the change in direction for 

the 2006 distribution of White children, which is the only line in the graph that slopes upward. 

Figure 1–3. Percentages of White Children and of Black Children Who Were Living in Households 

With Different Incomes in 1993 and in 2006 

10
 

 

Census findings on median income as well as other sources also document that, during 

the time interval between NIS–3 and NIS–4, the socioeconomic status of both Blacks and Whites 

improved, but the status of Whites improved more than the status of Blacks. Crane and Heaton 

(2007) reported that while the rising economic tide of the 1990’s reduced the nation’s poverty rate, 

the gap between poor children and their middle-class and affluent counterparts actually increased. 

Nichols (2006) reported that between 2000 and 2004, Black children lost ground relative to White 

children at a faster rate than in recovery years following past recessions. Census data show that, 

between 1993 and 2006, median income for all families with children rose by $20,588. However, 

while incomes of White families with children increased by $26,330, incomes of Black families with 

children rose by notably less: $16,078. As a result, the gap between the median incomes of these 

race groups increased substantially, from a difference of $23,556 in 1993 to a difference of $33,808 

in 2006 (U.S. Census Bureau, 2009). Figure 1–4 shows that the rise in median family income for 

Black children over this time period essentially matched the increase in the racial gap in median 

income. 

Figure 1–4. Changes in Median Income for Families With Children (derived from data in Table F-9, 

U.S. Census Bureau, 2009). 

Thus, among all the demographic shifts in family characteristics that are related to 

maltreatment risk, differential changes in family incomes stand out as the one change that could 

potentially account for the higher relative risk of Black children at the time of the NIS–4. 

11
 
 

 


 

2. RATIONALE, BACKGROUND, AND PURPOSE OF 

MULTI-FACTOR ANALYSES OF NIS–4 DATA 

The previous chapter informally explored two potential explanations for the NIS–4 

findings on race differences in maltreatment rates—the greater precision of the NIS–4 estimates and 

changes in the distribution of the race groups on important risk factors, such as the economic status 

of the child’s family. While plausible, without more rigorous analytic support, those explanations 

remain speculative. 

The key hypothesis in the remainder of this report is that the observed race differences 

in the NIS–4 stem from the other risk factors that are associated with race. This implies that the 

race differences will disappear when the effects of the other important risk factors are taken into 

account. 

2.1 Rationale 

Multi-factor analyses are necessary to test the proposed hypothesis because the 

individual risk factors are not distributed independently in the population; neither can one assume 

that their effects on maltreatment risk are independent of one another. Table 1–1 shows that the 

family characteristics are differentially distributed by race. These characteristics are also 

intercorrelated; that is, parents’ employment, family structure, low socioeconomic status, and family 

are all significantly correlated with each other.7

 This means that children who are in a given category 

on one measure are more likely to be in a specific category on another measure. To illustrate this, 

Figure 2–1 shows that children who live with two married parents are much less likely to be in a 

family of low socioeconomic status.8

 Figure 2–2 indicates that a substantially higher percentage of 

White children live in households with their married biological parents, whereas a considerably 

higher percentage of Black children live in households with their single parent who has no partner. 

Multi-factor analyses take the interlinkages among the risk factors into account. They can also reveal 

whether one risk factor modifies the way another factor affects maltreatment risk. 

7 NIS–4 analysts assessed this using the Rao-Scott RS3 statistic (Rao and Scott, 1981, 1984). 

8 The classification of family structure in this graph follows that used in the NIS–4 Report to Congress (Sedlak et al., 2010). 

12
 

 

Figure 2–1. Percentage of Children in Low SES Households by Their Family Structure 

Figure 2–2. Percentage of Black Children and White Children Living in Different Family Structures 

2.2 Background

After the NIS–3, Sedlak and Schultz (2005) undertook a similar multi-factor analysis 

effort to understand the NIS findings on race. However, the foremost question was quite different 

then, and they used a directional analytic strategy to address it. At that time, the consistent lack of 

statistically significant race differences in the first three cycles of the NIS was puzzling because a 

13
 

 

number of factors correlated with race did reliably predict child maltreatment. Moreover, the fact 

that the foster care population included a disproportionate number of minority children implied that 

these children were more often maltreated or that some other dynamics were bringing more 

minority children into the foster care system. To understand why the NIS–3 found no race effects 

in these circumstances, Sedlak and Schultz (2005) conducted a series of multi-factor analyses, 

examining race in the context of the other factors that related to children’s risk of maltreatment. 

The NIS–3 had found that child’s age, sex, number of children in the household, family 

structure, parental employment status, and household income were risk factors for at least one 

category of child maltreatment. At the same time, Black and White children had significantly 

different distributions on a number of risk factors. Black children were more likely than White 

children to be in low income households, have parents who were unemployed or not in the labor 

force, live with single parents, and live in households where there were 4 or more children. These 

four factors were all also significantly correlated with one another. Sedlak and Schultz (2005) sought 

to learn what race effects could be detected in the NIS–3 data when the influences of these other 

risk factors were taken into account. They combined the NIS–3 data, which includes only maltreated 

children, with Census data on the general population of children in the United States in order to 

construct a nationally representative synthetic database that included records for both maltreated 

and nonmaltreated children. 

As noted above, at the time of this earlier work, no NIS had found any race differences, 

so Sedlak and Schultz (2005) sought to learn whether race differences would emerge when the 

influences of other confounding factors were partialed out. Because of this goal, they followed a 

topically directed approach in their forward stepwise model-building. They began with race as the 

sole predictor of maltreatment and then examined each additional risk factor independently as 

expansions of this basic model, both alone and in interaction with race. At each stage of model 

building, they selected the expansion that maximally revealed race-related patterns in risk. 

This strategy yielded a consistent pattern. Where race effects emerged, White children 

who were living in higher risk situations (e.g., low income families) were maltreated at a greater rate 

than Black children. However, in all maltreatment categories analyzed, race interacted with other risk 

factors in determining risk. For instance, race interacted with income in accounting for the risk of 

all Harm Standard maltreatment. The difference between White and Black children appeared in the 

lowest income group, with White children in that group more at risk than Black children. At higher 

income levels, this race difference disappeared. Race interacted with parental employment in 

14
 

 

accounting for the risk of physical abuse. White children whose parents were not in the labor force 

were at greater risk of maltreatment than Black children in similar circumstances. Also, race 

interacted with family size in accounting for risk of all Harm Standard maltreatment and physical 

neglect. Among children living in households with four or more children, White children were more 

likely to be maltreated. 

The authors concluded that when these disadvantaging characteristics were taken into 

account, Black children had a lower risk of being maltreated than White children. At the same time, 

the various risk conditions still generally raised the maltreatment risk of any children in those 

circumstances. Thus, the overall NIS–3 finding of no race differences appeared to reflect the fact 

that more Black children lived under the higher risk conditions (such as in larger households) 

compared to White children, obviating their relatively lower risk compared to White children in that 

condition. Because the summative effects of all the disadvantaging factors occurred 

disproportionately for Black children, the maltreatment rate for Black children rose to a level that 

was statistically equivalent to the White rate. 

2.3 Purpose 

As described earlier, for the first time in the history of the NIS, the NIS–4 found race 

differences in rates of maltreatment. The goal of the work described in the subsequent chapters is 

to assess the hypothesis that the observed race differences in the NIS–4 actually arise from other 

risk factors that are associated with race by seeing whether the race differences drop out when the 

effects of the other important risk factors are taken into account. This is conceptually the reverse of 

what Sedlak and Schultz (2005) did in their previous multi-factor study on the NIS–3 data. Where 

they began in the context of no race differences and undertook multi-factor model-building to 

uncover any latent race differences in the NIS–3 data, the effort here begins in the context of the 

NIS–4 race difference findings and undertakes multi-factor model-building to discover whether the 

race differences dissipate in the context of other risk factors. Because the present effort, like the 

earlier one, builds multi-factor models of maltreatment risk, it used similar methods in constructing 

the multi-factor database for the analyses. However, because the present effort begins in a different 

context and has a very different goal, it used a quite different model-building strategy. These points 

of similarity and difference are noted in the next chapter, which describes the construction of the 

NIS–4 multi-factor database and procedures used to build the NIS–4 multi-factor risk models. 

15
 

 

3. METHODOLOGY 

The NIS provides data only on maltreated children. In order to compare the relative 

maltreatment risk of different groups of children, one needs information about the number of 

children with the same characteristics in the total population of children, or about nonmaltreated 

children with the same characteristics. The analyses for the NIS–4 Report to Congress used the Census 

data on the size of a group (e.g., children in a given age range) in the general population. The NIS–4 

analysis team divided the estimated number of maltreated children in the group by the Census total 

and then by 1,000 in order to compute the rate of maltreatment per 1,000 children with that 

characteristic (e.g., in that age range) in the general population (Sedlak et al., 2010). That approach is 

feasible with single-factor analyses, where groups are defined by a single characteristic. However, 

the hypothesis this report addresses requires multi-factor analyses. In order to support these more 

complex analyses, the NIS–4 research team had to integrate the NIS data with Census data in a 

multi-factorial framework, linking these two information sources on every combination of 

characteristics. This paralleled the approach that Sedlak and Schultz used in conducting multi-factor 

analyses of the NIS–3 data. Having constructed the synthetic multi-factor database, the analysts 

designed an objective, empirically based approach for building multi-factor models that differed 

substantially from the directional strategy that Sedlak and Schultz used. 

This chapter first summarizes the database construction and then describes the modelbuilding strategy. Finally, the last section explains the follow-up calculations used to further examine 

any race differences that emerged in the final multi-factor models. 

3.1 Construction of the Synthetic Database 

The NIS–4 multi-factor analyses required a synthetic database that combined 

information from two sources: (1) the NIS–4 nationally representative data on children who 

experienced countable maltreatment during the NIS–4 study year, 2005-2006, and (2) data on 

children in the general population from the March 2006 supplement to the Current Population 

Survey (U.S. Bureau of the Census, 2006). The NIS–4 data included records on all children who 

were classified as maltreated under the standardized study definitions of maltreatment. Only the 

March supplement of the Current Population Survey provides information on parental employment, 

so that source was preferred for the general population information. 

16
 
 


 

To develop the synthetic database, the NIS–4 analysts defined common measures in 

both the NIS–4 and Census data, imputed values for NIS–4 children with missing data on these 

measures, and then integrated the two sources to generate records for nonmaltreated children. 

Equivalent measures. Before combining the NIS–4 data with the Census data, the 

NIS–4 team had to define common variables with substantively equivalent meanings and 

classification schemes in the two data sources. This entailed deriving new measures in both the NIS– 

4 and Census databases. In addition, although the NIS–4 data already provided measures at the child 

level of analysis, developing comparable measures in the Census data often meant combining 

information across both person-level and household-level data items with complex derivation rules. 

For example, in order to extract child-level information from the Census about parents’ 

employment, analysts had to (a) determine from the person-level data which records corresponded 

to dependent children living in households, then (b) for each of these children, locate the associated 

record for their household to identify the person codes for their parents, if any were present, and 

finally (c) locate the person records for the identified parents to determine their employment status. 

The variables included in the unified synthetic database were the same as those used in 

the NIS–4: child’s sex, child’s age, child’s race and ethnicity, family structure and living arrangement, 

parents’ employment, number of children in the household, and socioeconomic status. Table 3–1 

lists these measures and gives the classification categories for each. 

All classification categories followed the definitions used for the analyses reported in the 

NIS–4 Report to Congress. As noted in that report, the categorization of children by their parents’ 

employment was hierarchical. First, all children who had any parent unemployed, either currently or 

during the past year, was classified as “Parent(s) Unemployed.” Second, among the remaining 

children, those with any parent employed comprised the “Parent(s) Employed” category. Then, of 

the children still unclassified, those with parent(s) not in the labor force (e.g., retired homemaker, 

not working and not looking for work, disabled, in the hospital, or in jail) were assigned to that 

category. Finally, children with no parent living in their household were assigned to a separate “No 

Parent Present” category on the parental employment measure. 

Previous NIS cycles had demonstrated a strong association between family income and 

children’s maltreatment risk. Unfortunately, the NIS–4 had considerable missing data on income, so 

the analysis team had to devise a strategy to index socioeconomic status with the data available: 

household income, parents’ education, and household participation in a poverty program (such as 

17
 
 


 

food stamps or Temporary Assistance to Needy Families, TANF). In order to maximize the number 

of children who could be classified directly using the available data, the NIS–4 team created an 

inclusive socioeconomic status (SES) measure that defined a child as living in a low-SES family on 

the basis of any of these three measures. That is, children were classified as living in low-SES 

households if their parent(s)’ highest education level was less than high school, their household had 

an annual income below $15,000, or any household member participated in a poverty program. 

Table 3–1. Measures in the NIS–4 Synthetic Database 

Measure Classification Categories 

Child’s age (6 levels) Birth-2, 3-5, 6-8, 9-11, 12-14, 15-17 

Child’s sex (2 levels) Male, Female 

Child’s race/ethnicity (4 levels) Non-Hispanic White, Non-Hispanic Black, 

Hispanic, Other9 

Number of children in household (4 levels) 1 child, 2 children, 3 children, 4 or more 

children 

Family structure (6 levels) 

Married biological parents, Other married 

parents, Unmarried parents, Single parent with 

partner, Single parent without partner, No 

parent present 

Parents’ employment status (4 levels) 

Any parent unemployed, Parent(s) employed, 

Parent(s) not in the labor force, No parent 

present 

Socioeconomic status (2 levels) Low, not low 

Imputation. Construction of the synthetic database required that all children be 

classified on all variables, so it was necessary to impute values for children with missing data on any 

of the seven common measures. The NIS–4 had a considerable amount of missing data on two 

measures. Parents’ employment was missing for 42.4% of the children, and SES was missing for 

44.9% of the children. In imputing values for missing demographic data on countable children in the 

9 The “Other” race and ethnicity category included American Indian or Alaska Native, Asian, Native Hawaiian or other 

Pacific Islander, and mixed race children. 

18
 
 

 


 

NIS, the NIS–4 team made special efforts to preserve the covariance structure of the measures, 

using a method known as Chi-Square Automatic Interaction Detector (CHAID) analysis. In order 

to impute each measure, the team applied CHAID to form homogenous subgroups of records for 

imputation according to their category of countable maltreatment, its severity, and the Census region 

and metropolitan status of the child’s county of residence. Then, within each imputation class, the 

team applied a hot-deck procedure to select a random sample of records to serve as donors for 

records with missing values. The known values of the measure on the donor records were randomly 

assigned to those records in the imputation class with missing data on the measure. This approach 

maintained both the covariance structure within the demographic variables and the relationship 

between the demographic predictors and the maltreatment measures. 

Imputation started with the variable with the smallest proportion of missing values, in 

this case, child’s sex (3.4% missing). Once a measure was imputed, it had no missing values and was 

used to identify imputation classes for the next measure with missing data. Appendix B describes the 

imputation methodology in greater detail. The Census data did not require imputation.10 

Database integration. Using the seven equivalent variables listed in Table 3–1, the 

NIS–4 analysts entered both the Census and the NIS data into the full seven-way cross-classification 

matrix defined by the variables. They developed two estimates within each cell: (1) from the Census 

data, an estimate of the number of children in the general population with the combination of 

characteristics defined by the cell, and (2) from the NIS, an estimate of the total number of children 

with those characteristics who experienced countable maltreatment. 

The team derived an estimate of the number of nonmaltreated children in each cell by 

subtracting the estimated number of maltreated children (2) from the estimated general population 

total (1). For any cell in which the NIS estimate was higher than the Census estimate, analysts set the 

non-maltreated total to 0. The next step was to construct synthetic records for non-maltreated 

children in the matrix, weighted to represent the number of non-maltreated children with each 

combination of characteristics. Finally, in order to support accurate computations of variance and 

model significance tests, the NIS–4 team developed replicate weights for the synthetic nonmaltreated child records by replicating the subtraction procedure for each of the replicate weights on 

the NIS–4 records in the cells. 

10 Appendix B includes a description of how the small number of Census records with missing data were resolved. 

19
 
 


 

The resulting database includes 16,366 records—12,408 NIS–4 records on maltreated 

children and 3,958 synthetic records on non-maltreated children. It is nationally representative of 

children in households in the United States in 2006, reflecting an estimated total of 74,040,548 

children. Appendix C describes the creation of the synthetic database in more detail. 

3.2 Model-building Procedures 

Before beginning the model-building, the authors made several adjustments to the synthetic 

data, subsetting it to Black and White children and then into separate databases for children with 

parents and for all children. They also simplified the codes for some of the measures, as detailed 

below. 

Model-building then proceeded in two phases. During the first phase, the authors took 

advantage of automated model-building procedures to build starting models for input to the second 

phase. These first-phase models do not consider the clustering in the data due to the NIS–4 multistage sample design, so they are too liberal in the set of predictors they identify and their model fit 

statistics are not accurate. The second phase trimmed these first-phase models, using appropriate 

variance measures and objective exclusion criteria. 

Synthetic database adjustments. To simplify the race analyses and focus them on the 

main NIS–4 finding of interest—the significant difference in the maltreatment rates of Black and 

White children, the authors subset the database for model building to an extract that included only 

the Black and White children. This extract comprised 10,794 records—8,728 NIS–4 records on 

maltreated children and 2,066 synthetic records on non-maltreated children. The final synthetic 

database represented all the Black and White children in the United States in 2006—a weighted total 

of 53,775,594 children (10,929,648 Black children and 42,845,946 White children). 

In order for all children to have values on all the predictor variables, both the parents’ 

employment and family structure measures included a level for children with “No Parent Present” 

(Table 3–1). Because the “No Parent” levels of both measures include the same children and do not 

occur in combination with any of the other levels of the alternate measure, they could not be used 

together in the same model with all their levels. To address this, the NIS–4 analysis team created 

two versions of the synthetic database. One version excluded children with no parent in their 

household, thereby excluding the “no parent” level of both parents’ employment and family 

20
 
 

 


 

structure. This version, which excluded 4.5% of all children, supported model building using the 

remaining levels of both parents’ employment and family structure. The other version, which 

included all children, supported model building with all 6 levels of the family structure measure, but 

did not support models with parents’ employment. 

Model predictors and outcomes. Model development used seven predictor variables, 

each of which was associated with risk of at least one maltreatment outcome in the NIS–4. The 

predictor variables are those listed above, in Table 3–1, with two modifications. The following 

variables were recoded to reduce the number of levels from those given above, making the modeling 

more efficient: 

• Child age (0-5, 6-11, 12-17) 

• Number of children in the household (1, 2, 3 or more) 

The multi-factor modeling was directed at identifying the unique contribution of race to 

child maltreatment outcomes when analyzed in the context of other risk factors correlated with race. 

Analysts fit models for each maltreatment category, under both the Harm and Endangerment 

Standards. They fit models for both databases, comprising all Black and White children: (1) the 

database that included children with no parents present, but excluded the employment variable, and 

(2) the database that included the subset of children with parents present, where the employment 

variable could be included in the models. 

The outcomes modeled here represent the major maltreatment categories used in the 

NIS. For both Harm and Endangerment Standard maltreatment, the authors modeled:11 

• All Maltreatment 

• Physical Abuse 

• Sexual Abuse 

• Emotional Maltreatment (either emotional abuse or emotional neglect.) 

• Physical Neglect 

11 The choice of these maltreatment categories followed the approach used in the NIS–3 multi-factor analyses. They economize on the number of 

models to be built, and in view of the fact that the Emotional Maltreatment measure combines both abuse and neglect, they omit the summary 

measures of Overall Abuse and Overall Neglect. Note, however, that unlike the earlier NIS–3 analyses which focused only on children countable 

under the Harm Standard, these NIS–4 multi-factor analyses examined race effects in risk of maltreatment under both definitional standards. 

21
 
 


 

Model-building Phase I: Starting models. NIS–4 demonstrated main effects on 

child maltreatment for the 7 predictor variables in Table 3–1, so it was important to include all those 

factors as predictors of maltreatment in the multi-factor modeling. It is important to recall that the 

NIS–4 race findings were main effects, not adjusted by any other factors. The modeling discussed 

here examined race in the context of correlated risk factors. 

It would have been unwieldy to test fully articulated models that included all 7 factors, 

all two-way interactions among the factors, and all three-way and higher order interactions. In 

addition, even the large size of the synthetic database did not afford sufficient degrees of freedom to 

test higher-order effects, given the complex NIS–4 sampling design reflected in the data. Thus, the 

authors limited modeling to main effects and two-way interactions and began the process using an 

automated model selection procedure 

Automated model selection procedures are unavailable for complex survey data, which 

cannot be assumed to comprise independent observations due to the clustered nature of the data. 

Automated procedures are available, however, for data obtained by simple random sampling, which 

consist of independent observations. To facilitate the modeling process, analysts began with an 

automated procedure, ignoring clustering in the data, to produce a set of starting “best fit” models 

for input to a subsequent modeling procedure that took the complex NIS sample design into 

account. It is known that the effect of clustering is to decrease significance; that is, for the same 

sample size, when the data are assumed to be independent, observed p-values for effects are smaller 

than if the data came from a clustered sample. Thus, modeling clustered data with such a procedure 

would likely produce models including terms that would drop out when clustering was taken into 

consideration. Because these “best” models were too liberal, there was no concern that race would 

be erroneously excluded from the starting models, if indeed it was still an important predictor when 

other risk factors were considered. 

Model-building Phase II: Final models. For each maltreatment category, analysts 

started with the “best” model that resulted from the Phase I automated modeling procedures and 

then implemented a backward stepwise logistic regression approach to fit the most parsimonious 

model, this time accounting for the clustered nature of the data.12,13 Since the Phase I forward 

12 WesVar, statistical analysis software for use with complex survey data, uses replication methods to produce correct variance estimates in these 

contexts, taking clustering into account (Westat, 2007). 

13 Sedlak and Schultz (2005) were limited to using selective forward modeling in their analyses due to the smaller sample design of the NIS–3. The 

NIS–4 afforded sufficient degrees of freedom to enable the preferred backwards stepwise approach. 

22
 

 

selection procedure was allowed to choose effects from the entire pool of all main effects and twoway interactions among the 7 study variables (including the main effect of race and all its two-way 

interactions), one can be confident that race had little predictive or explanatory value for 

maltreatment in categories where the final models did not include race. 

3.3 Follow-up Analyses 

The final regression models provide information about the relative contribution of each 

factor in the model to the outcome measure. Each regression coefficient in a final model (Appendix 

E) gives detail about the influence of a given factor holding all the other predictor terms in the 

model constant. Obtaining the final models and regression coefficients is often the stopping point 

for regression analyses; analysts look at the value of the coefficients and interpret the effects. 

However, a regression coefficient for the main effect of a predictor does not tell the complete story 

because the population is not evenly distributed across the other model parameters and these 

unequal distributions can influence the overall observed result. Moreover, when there are 

interaction terms in the model, it can be difficult to understand what is going on in the data by 

simply graphing the interaction with the input data, since this ignores the effects of the other 

important risk factors. That is, graphing the isolated interaction using the input data does not show 

what the model is describing, because the model takes the effects of the other factors into account, 

whereas the simple input data graph does not. In the present case, one might construct a graph of 

what appears to be a “race” difference that actually simply reflects the different distributions of 

White and Black children on other important predictors in the model. 

For any final multi-factor models that included race as a significant predictor, whether 

alone or in interaction with another predictor, the authors further examined the race effects by 

computing the model-based marginal probabilities of maltreatment while equalizing the race 

distribution across the unrelated predictor variables. 

Each final model is a mathematical formula that indicates the measures that are 

important predictors of the maltreatment in question and specifies how each measure contributes to 

a child’s risk of maltreatment. In categories where race entered the final model in the current 

analyses, either alone or in an interaction with another predictor, the authors computed model-based 

maltreatment rates in order to understand the effect that race had, when all the other predictors in 

the model are taken into account. 

23
 

 

In presenting the relationships reflected in multi-factor logistic models, the effects of 

any one factor or relationship can only be specified by making explicit assumptions about the child 

in terms of all the other predictive factors in the model. In order to compute the race-related 

differences in marginal probabilities from a logistic model, the authors first applied the model 

parameters to compute the value of the logit for every combination of predictor characteristics in 

the model. Then, they transformed the logit value into a probability value by exponentiating the 

logit, and then transforming the result to make p the subject of the formula. This yielded the modelbased cell-level probability of maltreatment in the cell. 

The next step assumed a hypothetical population in which there were an equal number 

of Black and White children in every cell in the fully crossed matrix in the synthetic database that 

was specified by the predictors in the final model. This hypothetical population equalized the 

distribution of race across all factors in the model. Then, the authors applied the model-based 

probability of maltreatment in each cell, as described above, to the hypothetical equal-distribution 

population in order to compute marginal probabilities. These marginal probabilities are completely 

independent of any race-related differences in distributions on the other factors in the model. 

The marginal probabilities give an undistorted view of what the model parameters 

indicate about race differences in risk of maltreatment. The graphs of the marginal probabilities in 

the next chapter show the race differences that remain after all the other predictors are taken into 

account and in an equitable world where all the risk factors associated with race are evenly 

distributed between the races. This entirely removes the effects of other disadvantaging factors 

from the assessment, to illuminate clearly the race differences identified by the model, after 

accounting for the effects of all other covariates. 

However, because the marginal probabilities are based on a hypothetical distribution, 

they artificially inflate the overall level of probability in the population by giving equal weight to 

sparsely populated high risk and to densely populated low risk cells. To remove this artificial 

inflation, the authors adjusted the marginal probabilities by multiplying them by a constant. The 

constant, developed separately for each maltreatment category, was set to the value that ensured that 

the overall marginal probability for the population of Black and White children matched the 

estimated imputed probability of maltreatment as computed from the synthetic database of Black 

and White children. 

24
 
 


 

4. MULTI-FACTOR MODELS 

The multi-factor modeling presented here addresses the question of whether, given the 

NIS–4 race effects, the other important predictors of maltreatment risk can account for, or aid in 

understanding, the overall NIS–4 race differences in maltreatment rates. 

The first section below presents the model-fit statistics for the final multi-factor models 

for Harm Standard maltreatment for both all Black and White children and for Black and White 

children with parents present. The next section presents the model-fit statistics for the 

Endangerment Standard final multi-factor models. Appendix E contains the full regression model 

results, including the model parameter estimates, for all maltreatment categories on both databases. 

In understanding what the models indicate about race differences in NIS–4, the primary 

issue is whether race (here, Black versus White) emerged as a significant predictor in a given model, 

either alone or in interaction with another predictor. In cases where race did enter the final multifactor model for a specific maltreatment category, the next issue to consider is what effect race has, 

according to the model, when all other important predictors of maltreatment are taken into account. 

To address this question, the authors generated model-based marginal probabilities and graphed the 

significant race effects. These graphs display what the model parameters indicate about the race 

effects, controlling for the other significant risk factors in the model and assuming that there are no 

inequities in how the races are distributed on any of the risk factors. 

Note that, because the authors imputed missing data, as described in Chapter 3 and 

detailed in Appendix B, and because the marginal probabilities are calibrated to the overall imputed 

maltreatment rates, the probabilities in these graphs are slightly higher than the rates given in the 

NIS–4 Report to Congress. This is because that report computed subgroup rates that excluded 

maltreated children with missing data on a specific demographic characteristic (e.g., children with 

missing data on race were omitted from the analyses on race differences). Imputation assigned these 

maltreated children to demographic groups corresponding to their imputed values.14 Bear in mind 

that the imputation process respected the correlations between race and other important risk factors. 

14 For example, race was missing for 8.8 percent of the children who experienced Endangerment Standard neglect in the NIS–4. After imputation, the 

synthetic database included more Black and White maltreated children than the original NIS–4 analysis database. This shifted the estimated 

(imputed) rates of maltreatment upward relative to the original rates of maltreatment. For example, the estimated rate of Endangerment Standard 

maltreatment for Black children rose from an estimated 49.6 children per 1,000 to an imputed estimate of 61.0 children per 1,000, while the White 

maltreatment rate in this category rose from an estimated 28.6 children per 1,000 to an imputed estimate of 33.2 children per 1,000. 

25
 

 

Since disproportionately more Black children have other disadvantaging characteristics, it is not 

surprising that imputation typically made a greater difference in their maltreatment rate across the 

maltreatment categories. 

For each category of maltreatment, the following sections revisit the findings on Black 

versus White differences in maltreatment rates in the NIS–4 Report to Congress and then indicate the 

findings for any overall difference in Black versus White in their estimated imputed rates in the 

synthetic database. In maltreatment categories where the final risk model included significant race 

effects, readers should not compare the model-based effects displayed in the graphs against the 

findings in the NIS–4 Report to Congress. Rather, the marginal probabilities in the graphs must be 

understood in the context of the estimated imputed rates in the synthetic database and should be 

interpreted as what the final model conveys about the race differences that remain after all other 

predictors under consideration have been taken into account and in a world where the races were 

distributed equitably on all the risk factors. 

4.1 Harm Standard Maltreatment 

Although race was allowed to enter the models for every maltreatment category, 

physical abuse was the only category of Harm Standard maltreatment where the final model included 

a significant effect of race on maltreatment risk. As documented below, for every other category of 

maltreatment, race did not enter or remain in the final model; that is, Black and White children did 

not differ in their risk of other categories of Harm Standard maltreatment. 

All Harm Standard maltreatment. The NIS–4 Report to Congress reported a significant 

race effect for all Harm Standard maltreatment. The rate for Black children (24.0 children per 1,000) 

was nearly twice the rate for White children (12.6 per 1,000). In the synthetic database, where the 

imputed rates are all slightly higher, the estimated imputed rate for Black children was 27.3 per 

1,000, which is significantly higher than the estimated imputed rate for White children (13.7 per 

1,000). However, the final multi-factor logistic model indicated that, when the other important 

predictors of risk are taken into account, race did not affect the overall Harm Standard maltreatment 

rate for either all Black and White children or the subpopulation of Black and White children with 

parents present. 

26
 

 

Table 4–1 presents the final multi-factor model for all Black and White children. 

Socioeconomic status (SES) was the strongest risk factor, followed by its interaction with family 

structure. Appendix E (Table E–1) provides the model parameters. 

When children without parents were excluded, thus allowing parents’ employment to 

enter the model as a predictor, the final model included the same factors shown in Table 4–1, with 

the addition of parents’ employment and its interaction with SES. Appendix E (Table E–2) provides 

that full model (model-fit statistics and model parameters). Here, and throughout the remainder of 

this report, the alternate models for the subgroup of children with parents are not given in the text 

because they do not alter the principal results regarding race differences in maltreatment risk. 

Table 4–1. Multi-Factor Model Predicting All Harm Standard Maltreatment for All Black and White 

Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 80.57 15 48 .001 

Socioeconomic status 331.71 1 62 .001 

Family structure 19.82 5 58 .001 

Child age 11.35 2 61 .001 

Number of children 6.83 2 61 .002 

Family structure x socioeconomic status 26.66 5 58 .001 

Both the full-population model and the model for children with parents indicate that 

the best predictors of children’s risk of all Harm Standard maltreatment are characteristics that are 

correlated with race, rather than race per se. In both models, SES was a very strong predictor of 

maltreatment risk. This result resembles Sedlak and Schultz’s (2005) findings. 

Harm Standard physical abuse. The NIS–4 found a significant race difference in risk 

of Harm Standard physical abuse (Sedlak et al., 2010). The rate for Black children (6.6 per 1,000) was 

notably higher than the rate for White children (3.2 per 1,000). The races also differed significantly 

in their estimated imputed rates of this maltreatment in the synthetic database; the estimated 

imputed rate for Black children was 7.7 per 1,000, whereas the rate for White children was 3.5 per 

1,000. 

The final multi-factor logistic model also indicated that race played a significant role in 

risk for physical abuse, even in the context of the other risk factors. Table 4–2 gives the overall 

27
 
 

 


 

model for Harm Standard physical abuse for all Black and White children. Appendix E (Table E-3) 

provides the parameter estimates. 

Table 4–2. Multi-factor Model Predicting Harm Standard Physical Abuse for All Black and White 

Children. 

Test F value Numerator df 

Denominator df p≤

Overall Fit 45.22 15 48 .001 

Family Structure 23.37 5 58 .001 

Socioeconomic Status 50.80 1 62 .001 

Child’s Race 10.11 1 62 .002 

Child’s Age 5.27 2 61 .008 

Child’s Race x Socioeconomic Status 4.01 1 62 .049 

Family Structure x Socioeconomic Status 14.95 5 58 .001 

Both race and the interaction of race with SES were significant in this final model. 

Moreover, considering the model F’s, it appears that the influence of SES is much larger than that of 

child’s race. As described in the previous chapter, the authors examined these effects further by 

computing the marginal probabilities of Harm Standard physical abuse by race and SES. The 

marginal probabilities take the effects of all other model predictors into account while also 

equalizing the race distribution across the predictor variables, as described in the previous chapter. 

Equalizing the race distributions here is important because, as presented in Chapter 1, Black and 

White children have substantially different distributions on a number of predictors, and these other 

predictors also interact with each other in determining risk of maltreatment (i.e., Table 4–2 indicates 

that family structure interacts with SES in determining risk of Harm Standard physical abuse). 

Figure 4–1 displays the race by SES interaction using the model-based marginal probabilities 

for the race by SES interaction for Harm Standard physical abuse, also showing the approximate 

95% confidence intervals for these computed probabilities.15 

15 Analysts computed standard errors for the marginal probabilities and used these to create confidence intervals under the assumption of a normal 

distribution. Note that the normality assumption is not strictly correct; therefore the confidence intervals are approximate. 

28
 

 

Figure 4–1. Model-based Marginal Probabilities of Harm Standard Physical Abuse (and Approximate 

Confidence Intervals) by Child’s Race and SES 

The figure reveals that even when it is assumed that Black children and White children 

are spread in equal numbers across all the levels of all the other model variables, the race by SES 

interaction in Harm Standard physical abuse still has significant explanatory power. Also note that 

low SES elevated the risk of Harm Standard physical abuse for both Black and White children. The 

graph shows that when Black and White children were both living in low SES circumstances, the 

higher-risk situation, the difference between their marginal probabilities of maltreatment was 

comparatively smaller, at less than one tenth of one percent (.0062 versus .0053), and the confidence 

intervals of the estimated probabilities are large and overlapping, indicating that the races do not 

differ in their risk in the low SES condition, the condition where children have a higher risk of 

maltreatment. Appendix F provides the race-related marginal probabilities and their confidence 

intervals. 

In contrast, when SES was not low, the difference between Black children and White 

children was twice as large, at 1.8 percent (i.e., .0039 versus .0021), and the approximate confidence 

intervals on the estimates in this SES condition do not overlap, indicating that, among children who 

do not live in low SES families, Black children have significantly higher risk of experiencing Harm 

Standard physical abuse than White children. 

These results signify that, when the two races’ distributions on correlated risk factors are 

equalized, the race effect occurs only in the not-low SES condition. This effect, reflected in the final 

29
 
 


 

multi-factor model (Table 4–2) as the race interaction with SES, was weaker than the other effects in 

the model and just barely within the 95% probability level for statistical significance (F = 4.01; p ≤

.049). Chapter 5 considers the implications of this residual race effect. 

When the authors excluded children without parents to allow parents’ employment to 

enter the model, the result was a final model similar to that above (Table 4–2), but the relatively 

weak race by SES interaction dropped out. In this population, there was simply an overall race 

difference: all Black children with parents present were at greater risk for Harm Standard physical 

abuse than corresponding White children. Table 4–3 presents the final overall model. Appendix E 

(Table E–4) provides the model parameters. 

Table 4–3. Multi-factor Model Predicting Harm Standard Physical Abuse for Black and White 

Children Living With Parents 

Test F value Numerator df 

Denominator df p≤

Overall fit 52.26 12 51 .001 

Family Structure 21.73 4 59 .001 

Socioeconomic Status 55.07 1 62 .001 

Child’s Race 6.75 1 62 .012 

Child’s Age 4.07 2 61 .022 

Family Structure x Socioeconomic Status 21.92 4 59 .001 

It is noteworthy that parents’ employment did not emerge as a risk factor in this model, 

despite the fact that it had the opportunity to do so. Also, it is unclear why the interaction of race 

with SES dropped out of the model when children without parents were excluded. It is possible that 

the decreased statistical power resulting from the slightly smaller (-4.5%) database accounted for it. 

Generally, results based on the full sample are more reliable than those based on partial samples. 

Harm Standard sexual abuse. The NIS–4 Report to Congress (Sedlak et al., 2010) 

indicated that there was a statistically marginal race effect for Harm Standard sexual abuse (2.6 per 

1,000 Black children versus 1.4 per 1,000 White children). In the synthetic database, the races 

differed significantly in their estimated imputed rates of this maltreatment; the estimated imputed 

rate for Black children was 3.2 per 1,000, whereas the rate for White children was 1.5 per 1,000. 

However, race was not significant in the final multi-factor models predicting the risk of sexual abuse, 

whether the data included or excluded children without parents. As Table 4–4 shows, the significant 

factors related to sexual abuse were the child’s sex, SES, family structure, the interactions of SES 

30
 

 

with number of children, child’s age, and family structure, the interaction between child’s sex and 

the number of children, and the interaction between family structure and the child’s age. Appendix 

E (Tables E–5 and E–6) provides the final models and model parameters for all Black and White 

children and for Black and White children living with parents, respectively. 

Table 4–4. Multi-factor Model Predicting Harm Standard Sexual Abuse for All Black and White 

Children. 

Test F value Numerator df 

Denominator df p≤

Overall fit 28.55 32 31 .001 

Family structure 17.08 5 58 .001 

Child’s sex 61.50 1 62 .001 

Socioeconomic status 15.81 1 62 .001 

Child age 1.05 2 61 .357 

Number of children 0.51 2 61 .601 

Child’s sex x number of children 3.37 2 61 .041 

Socioeconomic status x number of children 6.45 2 61 .003 

Family structure x child age 3.07 10 53 .004 

Socioeconomic status x child age 3.52 2 61 .036 

Family structure x socioeconomic status 6.52 5 58 .001 

Harm Standard emotional maltreatment. The NIS–4 did not find race effects on 

risk of Harm Standard emotional maltreatment (Sedlak et al., 2010), although in the synthetic 

database, the estimated imputed rates for Black children (6.2 per 1,000) and White children (4.2 per 

1,000) did differ significantly. Nevertheless, no race effects emerged in the multi-factor logistic 

regression models when the other important predictors of this maltreatment were taken into 

account. Table 4–5 below presents the final overall model of Harm Standard emotional 

maltreatment for all Black and White children. The significant risk factors were the child’s age, 

family structure, and socioeconomic status. For all Black and White children, the interactions 

between SES and both child’s age and family structure were significant. When children with no 

parents present were excluded, the SES by age interaction dropped out. Appendix E (Tables E–7 

and E–8) provides the model parameters. 

31
 

 

Table 4–5. Multi-factor Model Predicting Harm Standard Emotional Maltreatment for All Black and 

White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 26.57 15 48 .001 

Family structure 10.70 5 58 .001 

Child age 26.68 2 61 .001 

Socioeconomic status 60.48 1 62 .001 

Socioeconomic status x child age 3.19 2 61 .048 

Family structure x socioeconomic status 5.41 5 58 .001 

Harm Standard physical neglect. The NIS–4 did not find any statistically reliable 

race difference in risk of Harm Standard physical neglect (Sedlak et al., 2010). Although the 

estimated imputed rates in the synthetic database did differ significantly (6.2 per 1,000 Black children 

versus 3.1 per 1,000 White children), the multi-factor models did not find any effects of race on risk 

of this maltreatment. In the final logistic regression model predicting risk of Harm Standard physical 

neglect based on all Black and White children (Table 4–6), only SES, family structure, and their 

interaction were significant. Excluding children with no parents present, thereby allowing the parent 

employment variable into the models, only SES, parent employment, and their interaction were 

required to explain physical neglect. Appendix E (Tables E–9 and E–10) gives the model parameters 

for both groups of children. 

Table 4–6. Multi-factor Model Predicting Harm Standard Physical Neglect for All Black and White 

Children. 

Test F value Numerator df 

Denominator df p≤

Overall fit 17.20 11 52 .001 

Socioeconomic status 111.69 1 62 .001 

Family structure 3.13 5 58 .014 

Family structure x socioeconomic status 15.58 5 58 .001 

Summary of Harm Standard findings. A clear pattern that emerged from the Harm 

Standard multi-factor model building analyses was that SES and family structure were much more 

powerful predictors of the risk of child maltreatment than was race. Race emerged as a significant 

factor in only one Harm Standard maltreatment category, physical abuse. After eliminating the 

contaminating influence of risk factors correlated with race through deriving the marginal 

probabilities of maltreatment for race and SES, the predictive value of SES appeared strong, while 

that of race was relatively small, but still evident. Black children were at somewhat greater risk of 

32
 

 

physical abuse overall, and the race difference in risk was greater among children classified as not 

living in a low socioeconomic status household. 

4.2 Endangerment Standard Maltreatment 

The Endangerment Standard is more lenient than the Harm Standard, in that it allows 

the study to count children who are not yet directly harmed by maltreatment, but who are deemed to 

be in danger of harm from maltreatment. Four of the five multi-factor models for Endangerment 

Standard maltreatment included a significant race factor. The final models accounting for the risk of 

Endangerment Standard maltreatment are more complex than the final models for Harm Standard 

maltreatment. Because the present study is concerned with race effects, and the race effects did not 

differ for any category of Endangerment Standard maltreatment when children without parents were 

excluded, this section presents only the models based on all Black and White children, with no 

further discussion of the subset excluding children without parents. Appendix E provides the full 

models and model parameters for both groups of children. 

All Endangerment Standard maltreatment. The NIS–4 found a race effect for all 

Endangerment Standard maltreatment. Black children experienced Endangerment Standard 

maltreatment of some type at the rate of 49.6 per 1,000, whereas the rate for White children was 

28.6 per 1,000 (Sedlak et al., 2010). Similarly, the synthetic data produced significantly different 

estimated imputed rates of Endangerment Standard maltreatment for Black children (61.0 per 1,000) 

and White children (33.2 per 1,000). The final multi-factor logistic model for this maltreatment 

category also found that race related to risk of maltreatment, but while the overall effect of race was 

marginal when the other important predictors were taken into account, there were race differences 

that varied significantly depending on both family structure and SES. Table 4–7 presents the modelfit statistics for all Black and White children, and Appendix E (Tables E–11 and E–12) provides the 

model parameters for this model and the model statistics and parameters for Black and White 

children living with parents. 

33
 
 

 

 


 

Table 4–7. Multi-factor Model Predicting All Endangerment Standard Maltreatment for All Black 

and White Children. 

Test F value Numerator df 

Denominator df p≤

Overall Fit 118.76 30 33 .001 

Socioeconomic Status 269.94 1 62 .001 

Family Structure 48.42 5 58 .001 

Child’s Race 3.58 1 62 .063 

Number of Children 4.53 2 61 .015 

Child’s Race x Socioeconomic Status 41.57 1 62 .001 

Child’s Race x Family Structure 5.29 5 58 .001 

Family Structure x Socioeconomic Status 55.51 5 58 .001 

Family Structure x Number of Children 2.64 10 53 .011 

The authors explored both the race by SES and the race by family structure interactions 

by computing and graphing the model-based marginal probabilities.16 Figure 4–2 displays the 

marginal probabilities for all Endangerment Standard maltreatment by race and SES. Under low 

SES, White and Black children experienced essentially the same level of risk of Endangerment 

Standard maltreatment. However, in families where SES was not low, the risk of Endangerment 

Standard maltreatment appears to be twice as high for Black children as for White children. The 

confidence intervals in this case suggest wider variation in these patterns than observed above in 

Figure 4–1, but readers should bear in mind that these confidence intervals are approximate. 

16 The earlier discussion of confidence intervals in Chapter 1 offered guidelines for understanding their implications in making simple comparisons 

between two estimates. However, in interpreting the interactions in the graphs in this chapter, the patterns can signify meaningful differences even 

when confidence intervals overlap substantially, as they do in Figure 4-2. This is because (1) the model shows that this interaction is significant, 

which means that the graph displays significantly different risk patterns for Black children and White children; and (2) these confidence intervals are 

approximate at best, because the data undoubtedly violate their assumption of normal distributions. In understanding the graphs in this chapter, one 

should not attempt to interpret the overall interaction by focusing on a single family structure. Rather, the recommended approach is to observe 

where the largest differences occur and where patterns reverse direction. Nevertheless, interpretations of the race by family structure interactions 

must be cautious because they involve twelve different conditions, and the sparse distribution of cases in some of these conditions can reduce the 

reliability of individual cell estimates. 

34
 

 

Figure 4–2. Model-based Marginal Probabilities of All Endangerment Standard Maltreatment 

(and Approximate Confidence Intervals) by Child’s Race and Socioeconomic Status 

The interaction between race and family structure with respect to all Endangerment 

Standard maltreatment is more complex. Figure 4–3 includes two graphs that show the modelbased marginal probabilities for this interaction. The top section displays conditions where children 

live with two parents, while the bottom section displays the single-parent and no-parent conditions. 

The graph indicates that Black and White children experienced elevated risk under different living 

arrangements, and that the race difference was negligible under some conditions. White children had 

a notably higher probability of maltreatment when they lived with married parents who were not 

both biologically related to them and a slightly higher maltreatment rate when they lived with a 

single parent who had no cohabiting partner, whereas Black children had a considerably higher 

maltreatment probabilities when they lived with their unmarried parents and when they lived with a 

single parent living with a partner. The races do not appear to have different probabilities of 

Endangerment Standard maltreatment among children living with their married biological parents or 

among children who do not live with any parent. 

35
 

 

Figure 4–3. Model-based Marginal Probabilities of All Endangerment Standard Maltreatment 

(and Approximate Confidence Intervals) by Child’s Race and Family Structure 

Endangerment Standard physical abuse. The NIS–4 found a race difference in 

rates of Endangerment Standard physical abuse (Sedlak et al., 2010). The rate for Black children (9.7 

per 1,000) was significantly higher than the rate for White children (4.6 per 1,000). The estimated 

imputed rates in the synthetic database also differ significantly and, as expected, they are slightly 

higher (11.4 per 1,000 for Black children and 5.2 per 1,000 for White children). The multi-factor 

logistic regression models also revealed that a significant race difference remained even when other 

36
 
Table 4–8. Multi-factor Model Predicting Endangerment Standard Physical Abuse for All Black and 

White Children. 


 

important risk factors were taken into account, but that the effect of race depended significantly on 

both household SES and family structure. 

Table 4–8 gives the multi-factor model-fit statistics predicting Endangerment Standard 

physical abuse for all Black and White children. Appendix E (Tables E–13 and E–14) provides the 

model parameters for all Black and White children and the model statistics and parameters for Black 

and White children with parents present. The model shows significant effects for race and its 

interaction with SES and family structure, the same race effects seen above for all Endangerment 

Standard maltreatment. 

Test F value Numerator df 

Denominator df p≤

Overall fit 55.69 37 26 .001 

Family Structure 28.77 5 58 .001 

Socioeconomic Status 50.40 1 62 .001 

Child’s Race 20.10 1 62 .001 

Number of Children 1.09 2 61 .344 

Child’s Sex 5.32 1 62 .024 

Child’s Age 4.94 2 61 .010 

Family Structure x Socioeconomic Status 17.06 5 58 .001 

Child’s Race x Family Structure 2.81 5 58 .024 

Child’s Sex x Child’s Age 5.54 2 61 .006 

Socioeconomic Status x Number of Children 5.30 2 61 .008 

Family Structure x Number of Children 2.43 10 53 .018 

Child’s Race x Socioeconomic Status 13.53 1 62 .001 

Figure 4–4 displays the marginal probabilities for the race by SES interaction, also indicating 

their 95% confidence intervals. This graph shows that, when race distributions on other factors are 

equivalent, Black children have higher risk than White children in both SES conditions, but that the 

risk difference is notably larger for children categorized as not in low SES households. 

37
 

 

Figure 4–4. Model-based Marginal Probabilities of Endangerment Standard Physical Abuse (and 

Approximate Confidence Intervals) by Race and SES 

The model statistics in Table 4–8 show a significant interaction between race and family 

structure, indicating that the relationship between child’s race and risk of Endangerment Standard 

physical abuse also significantly depends on family structure. Figure 4–5 displays this relationship in 

two graphs, using the model-based marginal probabilities of the maltreatment rate in each condition. 

Inspection of these marginal probabilities suggests that Black children’s risk for physical abuse is 

considerably elevated in comparison to that of White children among children who live with 

unmarried parents or with a single parent with a cohabiting partner in the household. One must be 

careful not to overinterpret this pattern, but it does indicate that the risk to Black children under 

these living circumstances was considerably elevated over not only White children’s risk but also that 

of Black children living with either single parents without partners or married biological parents. 

There also appears to be tendency for Black children to have higher risk of Endangerment Standard 

physical abuse when living with married parents who are not both related to them biologically, but 

risk levels in the other conditions show negligible race differences. 

38
 

 

Figure 4–5. Model-based Marginal Probabilities of Endangerment Standard Physical Abuse (and 

Approximate Confidence Intervals) by Child’s Race and Family Structure 

Endangerment Standard sexual abuse. Analyses of the NIS–4 data for the Report to 

Congress did not find any race differences for Endangerment Standard sexual abuse (Sedlak et al., 

2010), although analysis of the synthetic database did show that Black children had a slightly but 

significantly higher imputed maltreatment rate (3.8 per 1,000) compared to White children (2.0 per 

1,000). Nevertheless, race was not a predictor of Endangerment Standard sexual abuse in the final 

multi-factor logistic regression model. Table 4–9 presents the model-fit statistics for the model that 

predicts this maltreatment for all Black and White children. Appendix E (Tables E–15 and E–16) 

gives the parameter estimates as well as the model-fit statistics and parameters for those Black and 

White children who lived with parents. In addition to the child’s sex, the risk factors for sexual abuse 

39
 

 

were family structure, SES, number of children in the household, and the interactions of SES with 

number of children and with family structure. 

Table 4–9. Multi-factor Model Predicting Endangerment Standard Sexual Abuse for All Black and 

White Children. 

Test F value Numerator df 

Denominator df p≤

Overall fit 30.75 16 47 .001 

Family Structure 17.89 5 58 .001 

Child’s Sex 40.10 1 62 .001 

Socioeconomic Status 22.76 1 62 .001 

Number of Children 2.58 2 61 .084 

Socioeconomic Status x Number of Children 4.01 2 61 .023 

Socioeconomic Status x Family Structure 9.75 5 58 .001 

Endangerment Standard emotional maltreatment. The NIS–4 found that Black 

children experienced Endangerment Standard emotional neglect at a higher rate (18.2 per 1,000) 

than White children (12.1 per 1,000), but did not find any race difference in rates of emotional abuse 

(Sedlak et al., 2010). As described earlier, the analyses presented here used a measure that combined 

emotional abuse and neglect. Preliminary examination of the synthetic database showed that Black 

children had a significantly higher imputed rate of emotional maltreatment on this combined 

measure (26.2 Black children per 1,000 versus 16.1 White children per 1,000). Table 4–10 presents 

the model-fit statistics for the multi-factor logistic model predicting the risk of emotional 

maltreatment for all Black and White children. Appendix E (Tables E–17 and E–18) provides the 

model parameters for this model as well as the model-fit statistics and model-parameters for the 

final model for Black and White children with parents present in their household. 

40
 

 

Table 4–10. Multi-factor Model Predicting Endangerment Standard Emotional Maltreatment for 

All Black and White Children. 

Test F value Numerator df 

Denominator df p≤

Overall fit 106.73 25 38 .001 

Socioeconomic Status 142.03 1 62 .001 

Family Structure 48.86 5 58 .001 

Child’s Race 2.23 1 62 .141 

Number of Children 4.17 2 61 .020 

Family Structure x Number of Children 2.59 10 53 .012 

Child’s Race x Family Structure 7.36 5 58 .001 

Child’s Race x Socioeconomic Status 48.97 1 62 .001 

Table 4–10 shows that, similar to the final models for all Endangerment Standard 

maltreatment and for Endangerment Standard physical abuse, this final model for Endangerment 

Standard emotional maltreatment included significant interactions between race and SES and 

between race and family structure. However, similar to the final model for all Endangerment 

Standard maltreatment, but unlike that for Endangerment Standard physical abuse, the overall race 

effect is not significant. 

Figure 4–6 displays the model-based marginal probabilities for the race by SES 

interaction in predicting risk of Endangerment Standard emotional maltreatment. Examination of 

this plot reveals that the interaction of race and SES for emotional maltreatment is similar to the 

pattern in overall Endangerment Standard maltreatment. Black children and White children were 

maltreated at similar rates in low SES households, but Black children were at higher risk in the more 

favorable SES category. 

41
 

 

Figure 4–6. Model-based Marginal Probabilities of Endangerment Standard Emotional 

Maltreatment (and Approximate Confidence Intervals) by Child’s Race and SES 

The race by family structure interaction appears in Figure 4–7, given as the model-based 

marginal probabilities. This pattern also resembles that observed above for overall Endangerment 

Standard maltreatment. It shows that Black children were at comparatively elevated risk for 

emotional maltreatment when living with unmarried parents or a single parent with a partner in the 

household, whereas the risk for White children in those circumstances was considerably lower. At 

the same time, White children appeared to have somewhat higher risk than Black children when 

living with married parents who were not both biologically related to them and when living with a 

single parent who had no cohabiting partner. Negligible race differences appear among children 

living with their married biological parents or with no parent. 

42
 
 


 

Figure 4–7. Model-based Marginal Probabilities of Endangerment Standard Emotional 

Maltreatment (and Approximate Confidence Intervals) by Child’s Race and Family 

Structure 

Endangerment Standard physical neglect. The NIS–4 found a statistically marginal 

race effect on Endangerment Standard physical neglect (Sedlak et al., 2010), with Black children 

experiencing this maltreatment at a higher rate (17.9 per 1,000) than White children (12.2 per 1,000). 

Analysis of the synthetic database found significantly different imputed rates of 22.3 per 1,000 for 

Black children and 14.6 per 1,000 for White children. Table 4–11 provides the model-fit statistics for 

the final multi-factor logistic regression model on all Black and White children, and Appendix E 

gives the parameter estimates (Table E–19) as well as the model statistics and parameter for the 

model based on the subset of children living with parents (Table E–20). 

43
 

 

Table 4–11. Multi-factor Logistic Model Predicting Endangerment Standard Physical Neglect for All 

Black and White Children. 

Test F value Numerator df 

Denominator df p≤

Overall fit 95.56 27 36 .001 

Socioeconomic Status 101.46 1 62 .001 

Family Structure 28.54 5 58 .001 

Number of Children 13.38 2 61 .001 

Child’s Race 4.47 1 62 .039 

Child’s Age 1.17 2 61 .317 

Child’s Race x Socioeconomic Status 13.52 1 62 .001 

Family Structure x Child’s Age 3.12 10 53 .003 

Family Structure x Socioeconomic Status 29.29 5 58 .001 

The model-fit statistics indicate a significant effect of race and indicate that the race 

interacts with SES. In this case, the model parameters reveal that the overall race effect is actually 

opposite to the effects reported above in other maltreatment categories. That is, taking the effects 

of the other important predictors into account, White children were physically neglected at a higher 

rate than Black children. However, this difference depends on SES. Figure 4–8 gives the marginal 

probabilities for the race by SES interaction, which reflect the model parameters clearly, unclouded 

by differences in race distributions in the real world and unaffected by the other important risk 

predictors in the model. 

Figure 4–8. Model-based Marginal Probabilities of Endangerment Standard Physical Neglect 

(and Approximate Confidence Intervals) by Child’s Race and SES 

The pattern in this figure departs from the race by SES interactions found for other 

maltreatment categories, given above. Here, the races differ in risk in the low SES condition, with 

44
 

 

White children at much greater risk than Black children in this circumstances, but no race difference 

appears under somewhat better socioeconomic circumstances. 

Summary of Endangerment Standard findings. Endangerment Standard 

maltreatment presents a more complex picture than Harm Standard maltreatment. Apart from 

sexual abuse, where there were no race effects, the final multi-factor models for the remaining 

maltreatment categories all included interactions between race and SES, and all but one also included 

an interaction between race and family structure. 

Three maltreatment categories involved race by SES interactions, and two of these 

yielded a similar pattern: in overall Endangerment Standard maltreatment and in emotional 

maltreatment, Black and White children had similar levels of risk in low socioeconomic 

circumstances, but Black children were at greater risk than White children when they were not in 

low socioeconomic circumstances. In physical abuse, race appeared to contribute more to risk, with 

Black children at higher risk than White children in both SES conditions. The race by SES 

interaction in this category indicates that the race difference was greater among children not in low 

SES households. Finally, a quite different pattern emerged in the model predicting risk of 

Endangerment Standard physical neglect: White children were at higher risk for this maltreatment 

than Black children, a difference that occurred only in the low SES households. 

The race by family structure interactions were also complex. They suggest that, with 

overall Endangerment Standard maltreatment, physical abuse, and emotional maltreatment, Black 

children were at notably greater risk of maltreatment when there were two unmarried adults in the 

household—either unmarried biological parents or a single parent with a cohabiting partner. These 

circumstances elevated Black children’s risk relative to White children living in similar arrangements 

and relative to Black children living in other family arrangements. In Endangerment Standard 

maltreatment overall and in emotional maltreatment, White children were at greater risk than Black 

children when living with married parents who were not both biologically related to the child and 

when living with a single parent alone, with no cohabiting partner. The races did not differ in their 

risk of any maltreatment when children lived with their married biological parents or with no parent. 

45
 

 

5. DISCUSSION 

For the first time in the history of the National Incidence Study of Child Abuse and 

Neglect, the most recent cycle, the NIS–4, found race differences in maltreatment rates, with Black 

children experiencing maltreatment at higher rates than White children in several categories. The 

efforts described in this report attempted to understand this finding by considering possible reasons 

why the NIS–4 results diverged from the findings in earlier cycles and by using multi-factor logistic 

modeling to reanalyze the NIS–4 data in order to isolate whether and how race contributed to 

maltreatment risk independent of the other important risk factors that correlated with race. These 

efforts focused on understanding the NIS–4 race effects and on why the race effect often varied 

depending on two other risk factors—socioeconomic status and family structure. 

5.1 Differences Between NIS–3 and NIS–4 

The authors examined two possible explanations for why the NIS–4 found statistically 

reliable race differences in rates of some categories of child maltreatment, in contrast to the findings 

of previous NIS cycles: the greater statistical power of the NIS–4 and the fact that the changes in 

other risk factors since the time of the NIS–3 were not equivalent for Black and White children. 

Greater precision of the NIS–4 estimates. The NIS–3 maltreatment rates for Black 

and White children show nonsignificant differences that are in the same direction as the statistically 

reliable NIS–4 race differences. At the same time, the NIS–4 samples were considerably larger than 

the samples used in earlier NIS cycles and, as a result, the NIS–4 estimates were more precise. The 

greater precision of the NIS–4 estimates could have allowed this latest study to detect race 

differences in maltreatment rates, even if the same underlying patterns of risk and resulting 

maltreatment may have held previously. This explanation remains plausible for the different race 

findings across the NIS cycles. 

Differential changes in other, correlated risk factors. The NIS–4 Report to Congress 

indicated that, generally, observed changes in maltreatment rates physical abuse and emotional 

neglect decreased more or increased less for White children compared to changes in the 

corresponding maltreatment rates for Black children (Sedlak et al., 2010). Concurrently, there were 

statistically reliable changes in the distributions of Black children and White children on a number of 

46
 
 


 

family characteristics, including family structure, parents’ employment, family size, parents’ 

education, and household income. The authors examined the demographic changes and concluded 

that—with the exception of income—the observed shifts could not explain why race differences in 

maltreatment appear greater in the NIS–4. Except for income, the changes on all characteristics 

considered actually decreased the racial gap across the risk conditions. In the case of income, however, 

the racial gap increased. The graphs in Figures 1-3 and 1-4 displayed this pattern. Incomes of all 

race groups rose during the 1993-2006 time period, but the improvements in household incomes for 

White children far outpaced those of the Black children. As a result, although the income 

improvements for Black children raised them from the lowest income categories, the improvements 

for White children moved them disproportionately into the higher income categories. Census data 

on changes in median family income over the entire course of the 1993-2006 time period show that 

Black families’ median incomes increased at the same pace as the racial gap, while White families’ 

median incomes moved progressively upward. 

At the same time, income (or socioeconomic status in the NIS–4) has consistently been 

the factor most strongly associated with risk in all categories of maltreatment but sexual abuse, 

where it ranks below child’s sex as a predictor of maltreatment. Thus, examination of demographic 

shifts since the time of the NIS–3 suggest that differential changes in the economic circumstances of 

Black and White children could account both for the NIS–4 findings on race differences in 

maltreatment rates and for the observed race-related differences in changes in maltreatment rates 

since the time of the NIS–3.17 

5.2 Race Differences in the NIS–4 Isolated from Other, Correlated Risk Factors 

The authors built multi-factor logistic regression models to assess whether any race 

differences in maltreatment risk remained after the effects of the other, correlated risk factors were 

taken into account. The results, detailed and summarized in the previous chapter, indicated that race 

continued to contribute as a predictor of risk in 5 maltreatment categories—physical abuse under 

both the Harm and Endangerment Standards, overall Endangerment Standard maltreatment, and 

Endangerment Standard emotional maltreatment and physical neglect. However, in nearly all cases, 

17 There may, of course, have been other race-related changes in risk factors that the present analyses could not examine. This is especially true for race 

differences in family structure and living arrangement. At the time of the NIS–3, census data could not distinguish the 6 levels of family structure and 

living arrangement that the NIS–4 identified. 

47
 

 

the effect of the child’s race on maltreatment risk depended on the SES of the child’s household, 

and in 3 of these maltreatment categories, the effect of race depended on family structure as well. 

Socioeconomic status. Across maltreatment categories, socioeconomic status was a 

key risk factor for maltreatment. Apart from sexual abuse, where the child’s sex was always the 

strongest predictor, SES was the strongest predictor in all maltreatment categories. In almost all 

maltreatment categories where race entered the final model, it interacted with SES. In most cases, 

the races showed no or smaller differences in risk in the low SES condition, but Black children had 

higher risk in households that were not low SES. The one exception to this typical pattern, was in 

the category of Endangerment Standard physical neglect, where the race and SES interaction 

indicated that White children were at higher risk than Black children in the low SES households, but 

the races did not differ in households not low in SES. 

Of necessity, these analyses used the NIS–4 definition of low SES. As mentioned 

earlier, in order to minimize missing data, this measure classified children as low SES based any one 

of three characteristics: household income below $15,000, parents’ highest education level less than 

high school, or household participation in any poverty program. This poses a problem for 

interpreting the results of the present analyses, because Black children and White children have very 

different distributions within the “not low SES” category. Black and White children in non-low SES 

households live in very different circumstances. In Chapter 1, Figure 1-3 showed the percentages of 

each race at different income levels, demonstrating a marked racial inequality in families with 

incomes greater than $15,000. In 2006, more than one-third of Black children (34%) lived in 

households with incomes greater than $15,000 but below $40,000, compared to less than one-fifth 

of White children (19%). Almost three-fourths of White children (73%) lived in homes where the 

income was above $40,000, compared to just over one-third of Black children (36%). About 43% of 

White children lived in homes where the income was $75,000 or more, compared to just 15% of 

Black children. Thus, the Black children in households that were “not low SES” were predominantly 

at the lower end of the income range in this category; they lived in households with incomes well 

below those of White children in the “not low SES” category. 

The NIS–4 also used parents’ education as a proxy indicator of SES in lieu of household 

income. A report issued by the National Center for Children in Poverty (Koball, Chau, and 

Douglas-Hill, 2006), using 2005 Census data, indicated that the relationship between income and 

parents’ education differs for Black and White children. Among children whose parents had some 

college education, 44% of Black children lived in low-income families as compared to only 18% of 

48
 
 

 


 

White children. 18

 Thus, parents’ education is not an equivalent proxy for SES for Black children and 

White children. Considering that more Black children with more highly educated parents are actually 

in low income households, the NIS–4 low SES measure may have over-assigned Black children with 

missing income data to the not-low SES category. 

The consequence of both of these disparities is the same: the NIS–4 not-low SES category 

does not adequately equalize the races on this dimension.19 However, recognizing that Black and 

White children very probably have different underlying SES distributions within the NIS–4 non-low 

SES category can aid interpretation of the present findings. As summarized above, in all 

maltreatment categories where race entered the final risk model, it interacted with SES, and in 

almost cases (except for Endangerment Standard physical neglect), the interaction showed that Black 

children had higher maltreatment rates than White children in the not-low SES condition, whereas 

in the low SES condition the race difference was attenuated or nonexistent. It is possible that, had 

the NIS–4 defined SES differently, such as by using a higher income cut-off point, or if the NIS–4 

had less missing data on children’s household income, these analyses may not have yielded any race 

by SES interaction at all. That is, had the non-low SES Black children been as well-off as the nonlow SES White children, the observed pattern of higher risk for Black children under non-low SES 

conditions may not have emerged. Although this interpretation is speculative, it is informed by the 

documented powerful influence that SES (or income) has on rates of child maltreatment20

 and the 

very likely difference between the Black and White children whom the NIS–4 definition assigned to 

the same SES level. This reasoning implies that nearly all the multi-factor findings on the interaction 

of race and SES arise not because Black children in not-low SES households are at greater risk for 

maltreatment because they are Black; they are at greater risk because they are poorer than the White 

children in these households. 

This interpretation does not explain the race by SES interaction in Endangerment 

Standard physical neglect, where White children experienced higher risk than Black children in the 

low SES condition, while the races did not differ in the not-low SES condition. Although this result 

departs from all other race by SES interactions in the multi-factor models presented here, it does 

resemble a finding reported by Sedlak and Schultz (2005) in their analyses of the NIS–3 data. 

18 The National Center for Children in Poverty (Koball, Chau, and Douglas-Hall, 2006) defined the low income threshold for a family of four in 2006 

as $40,000 (twice the federal poverty line). 

19 Future research might explore whether a similar series of analyses using a different definition of SES would produce different results. 

20 The NIS–4 found that low-SES children were 7 times more likely to be maltreated than their counterparts (Sedlak et al, 2010). 

49
 
 


 

Despite several differences,21

 their analyses produced a similar interaction for risk of all Harm 

physical neglect, emotional maltreatment, and overall maltreatment, in which White children were 

maltreated at significantly higher rates than Black children in the poorest families (with household 

incomes below $15,000). 

In discussing these surprising NIS–3 findings, Hill (2006) noted that stronger extended 

family networks in Black families and communities may serve as a protective factor for Black 

children, and other researchers have reported similar patterns for child maltreatment rates at the 

community level (Korbin, Coulton, Chard, et al., 1998) and for spousal violence (Cazenave and 

Straus, 1979). However, research has yet to determine whether, when, and how such protective 

factors can tip the balance of risk in the low income or low SES households toward higher risks for 

White children compared to Black children in that condition. Until these dynamics are better 

understood, it is difficult to explain why the present analyses found this pattern only in 

Endangerment Standard physical neglect and not in the other maltreatment categories where Sedlak 

and Schultz reported it. 

Family structure. The present analyses also found a complex race by family structure 

interaction for three categories of Endangerment Standard maltreatment: overall maltreatment, 

physical abuse, and emotional maltreatment. The authors computed marginal probabilities of 

maltreatment in the different conditions, which took into account the effects of all other risk factors 

in the model and assumed that Black and White children were distributed equivalently across all risk 

conditions. Because of the many cells involved in the race by family structure interaction, it is 

important to avoid overinterpreting the patterns. Nevertheless, it is clear that family structure 

affects maltreatment risk differently for Black and White children. 

The resulting patterns indicate that risk of maltreatment is elevated for Black children 

living with two unmarried adults—whether both are the child’s biological parents or a single parent 

has an unmarried partner. Black children in these conditions appear to have elevated risk of 

maltreatment relative to the risk for White children in the same circumstances and relative to the risk 

for Black children in other living arrangements. In two Endangerment Standard maltreatment 

categories, overall maltreatment and emotional maltreatment, it also appeared that the risk for White 

children was higher than the risk for Black children when living with either a single parent who had 

no partner or with married parents who were not their biological parents. Risk levels for White 

21 They analyzed Harm Standard maltreatment categories only, their final models did not include family structure or child’s age, as the model here did, 

and they used income rather than a composite SES measure as in the present case. 

50
 

 

children and Black children did not appear to differ for children who were living with their married 

biological parents or with no parent. 

The finding that family structure relates to risk of child maltreatment is not new. Nearly 

two decades ago, Wilson, Daly, and Weghorst (1980) reported increased risk for children living in 

households with a parent and a surrogate parent (whether stepparent or cohabiting partner) 

compared to children in mother-only households. The NIS–3 documented a higher risk for children 

in single-parent households in 1993, but did not distinguish between those whose parent had a 

cohabiting partner and those whose single parent had no partner in the household. 

Until very recently, the United States Census data did not obtain the information 

needed to distinguish between children in households with unmarried biological parents and those 

living with a parent and that parent’s unrelated cohabiting partner. The NIS–4 (Sedlak et al., 2010) 

provides the first national data on child maltreatment rates in 6 types of family structure, 

distinguishing single parents with partners from those without partners, parents who are biologically 

related to a household child from nonbiological parents, and married biological parents from 

unmarried biological parents. 

The Report to Congress indicated that children living with a single parent with a partner in 

the household experienced Harm Standard abuse at a rate 11 times greater than children living with 

two biological parents. What is new about the multi-factor findings here is that, holding all other risk 

factors constant, it appears that Black children in this living arrangement are at much greater risk of 

maltreatment than White children living in this circumstance or than Black children who live in 

other family structures. Nevertheless, this pattern probably does not account for the overall higher 

risk of Black children in the single-factor analyses, because similar percentages of Black and White 

children live in these family structures (Figure 2-2 in Chapter 2). It should be noted that race-related 

differences in risk across the family structures probably reflect differences in the context associated 

with these structures in Black and White communities. Future research is needed to uncover how 

the associated context shapes the differential risk across family structures. 

51
 
 

 


 

5.3 Limitations 

The multi-factor risk models convey the race effects that remain after the effects on risk 

of all the other model predictors are taken into account, but their results are constrained by the 

measures available to the model-building procedures in the first place. 

The key limitation of the present efforts and the results they yield is the number and 

range of the risk factors that were available to enter the models. Only 7 demographic characteristics 

were available in both the NIS and Census data to enter the synthetic database that was needed for 

the logistic models. This set of predictors may mark circumstances that are associated with children’s 

risk of maltreatment, but it certainly excludes a number of other important risk factors that have no 

available measures in these sources, such as neighborhood characteristics, social isolation, alcohol or 

drug use, or mental illness. 

Despite the fact that socioeconomic status is the most powerful predictor of 

maltreatment in the entire set available in NIS, it was less than ideal for the present study for two 

reasons: it had extensive missing data, and it appears that the not-low SES condition, as defined in 

the NIS–4, had different meanings for Black children than it did for White children. 

First, due to extensive missing data, the NIS–4 analysts had to impute SES for almost 

half of the maltreated child records. Although the NIS–4 analysts used state-of-the-art imputation 

methods, they essentially relied on the patterns and correlations in the records with complete 

information and extrapolated these to assign values to records with missing data. If there are biases 

in the patterns of missing data, with certain values more likely to be missing than other values, then 

the assumption that the missing data should look like the complete data would not be valid. The 

NIS data do not offer independent means to assess the extent of any such bias, but its potential does 

qualify the present findings. 

Second, the SES measure was very rudimentary and probably obscured important race 

differences across the ranges of household incomes grouped together in the not-low SES condition. 

In fact, the NIS–4 definition of SES classified almost one-third of Black children whom the 

National Center for Children in Poverty (Koball, Chau, and Douglas-Hall, 2006) called “low 

income” into the not-low SES households.22 This means that the NIS–4 SES measure is not truly 

22 This results from its very low income cut-off, considering that children in households with incomes of $15,000 or more are not low in SES. Based 

on 2005 Census data, Koball, Chau, and Douglas-Hall (2006) defined “low income” as households below $40,000, which is twice the poverty level 

52
 
 

independent of race, as it should be for the model findings to have unambiguous interpretations. 

What appear to be race differences in the model results may arise from the differences in SES that 

remain associated with race in the measure used, which, as the earlier discussion suggested, could be 

the reason why race differences generally appeared only, or more strongly, in the not-low SES 

condition.23 If this was the case, then with a better measure of SES, the final multi-factor models 

may have included fewer race effects. 

5.4 Conclusions 

The fact that the NIS–4 found race differences while early NIS cycles did not is likely, at 

least partly, a consequence of the greater precision of the NIS–4 estimates and partly due to the 

enlarged gap between Black and White children in economic well-being. Income, or socioeconomic 

status, is the strongest predictor of maltreatment rates, but since the time of the NIS–3, incomes of 

Black families have not kept pace with the incomes of White families. 

Race correlates with a number of other predictors of maltreatment, so it was important 

to take the effects of these other correlated predictors into account when evaluating the effects of 

race. The authors attempted to do this by building multi-factor models that incorporated all the 

statistically reliable predictors of maltreatment in the category. The final multi-factor models 

revealed that race did have effects on risk in certain maltreatment categories, even after the effects of 

other important predictors were considered. 

Black children were at significantly greater risk than White children of experiencing 

physical abuse under both the Harm and Endangerment Standards, but in both cases, this race 

difference depended on SES. The race difference was small or nonexistent among children living in 

low SES households, but it was notably larger for children in not-low SES households. 

In two maltreatment categories, Endangerment Standard emotional maltreatment and 

overall Endangerment Standard maltreatment, race differences depended on SES and family 

structure. There were no race differences among children in low SES households, but the 

for a family of four. Using this income cut-off would reclassify nearly 995 of the 12,408 maltreated child records in the NIS–4 data into the low SES 

condition (734 of whom were included in the present analyses). 

23 Parents’ employment was another measure that was less than ideal. It strictly reflected the employment status of the child’s parents, so children who 

had no parent in the household received no value on this measure. Thus, the present analyses had to omit those children in order to include the 

measure. 

53 

 

maltreatment risk for Black children in not-low SES households was two or more times greater than 

the risk for White children in this condition. Black children were also at comparatively elevated risk 

when living with unmarried parents or a single parent with a partner in the household, whereas the 

risk for White children in those circumstances was considerably lower. At the same time, White 

children appeared to have somewhat higher risk than Black children when living with married 

parents who were not both biologically related to them and when living with a single parent who had 

no cohabiting partner. 

White children had significantly higher risk for Endangerment Standard physical 

neglect, but this race difference appeared only among children in low SES households. This pattern 

resembled the earlier findings of multi-factor analyses of the NIS–3 data, which applied in more 

maltreatment categories in that study (Sedlak and Schultz, 2005). 

The present findings are qualified by the limitations of the predictors that were available 

for the NIS–4 multi-factor analyses, which comprised only general demographic characteristics of 

the children and their families. The key measure of SES was less than ideal in two respects—the 

large amount of missing data that required imputation and the fact race differences that emerged in 

the not-low SES condition could, in part, actually reflect the underlying income differences. For 

these reasons, the race differences observed in the not-low SES condition in this report must be 

interpreted with caution. 

54
 
 


 

REFERENCES 

Cazenave, N. & Straus, M. (1979). Race, class and network embeddedness and family violence. 

Journal of Comparative Families Studies, 10(3): 281-300. 

Hill, R.B. (2006). Synthesis of Research on Disproportionality in Child Welfare: An Update. Casey CSSP 

Alliance for Racial Equity in the Child Welfare System. 

Koball, H., Chau, M., and Douglas-Hall, A. (2006). The Racial Gap in Parental Education. New York, 

NY: National Center for Children in Poverty, Mailman School of Public Health, Columbia 

University. Accessed 10/09 at www.nccp.org. 

Nichols, A. (2006). Understanding Recent Changes in Child Poverty. Issue paper No.A-71, August, 2006. 

Washington, DC: The Urban Institute. 

Rao, J.N.K., and Scott, A.J. (1981). The Analysis of Categorical Data from Complex Sample 

Surveys: Chi-Squared Tests for Goodness of Fit and Independence in Two-Way Tables. 

Journal of the American Statistical Association, 76, 221-230. 

Rao, J.N.K., and Scott, A.J. (1984). On Chi-Squared Tests for Multiway Contingency Tables with 

Cell Proportions Estimated from Survey Data. Annals of Statistics, 12, 46-60. 

Sedlak, A.J. & Broadhurst, D.D. (1996). Third National Incidence Study of Child Abuse and Neglect: 

Final Report. Washington, DC: U.S. Department of Health and Human Services. 

Sedlak, A.J., Mettenburg, J., Basena, M., Petta, I., McPherson, K., Greene, A., & Li, S. (2010). Fourth 

National Incidence Study of Child Abuse and Neglect (NIS–4): Report to Congress. Washington, DC: 

U.S. Department of Health and Human Services, Administration for Children and Families. 

55
 

 

Sedlak, A.J., Mettenburg, J., Winglee, M., Ciarico, J., and Basena, M. (2010). Fourth National Incidence 

Study of Child Abuse and Neglect (NIS–4): Analysis Report. Washington, DC: U.S. Department of 

Health and Human Services, Administration for Children and Families. 

Sedlak, A.J. & Schultz, D. (2005). Race differences in risk of maltreatment in the general child 

population. In D.M. Derezotes, J. Poertner, & M. Testa (Eds.), Race matters in child welfare. 

Washington, DC. CWLA Press. 

Westat. (2007). WesVar 4.3 User’s Guide. Rockville, MD: Westat, Inc. 

Wilson, M.I., Daly, M., & Weghorst, S. (1980). Household composition and the risk of child abuse 

and neglect. Journal of Biosocial Science, 12, 333-340. 

U.S. Census Bureau. (2009). CPS March Supplement, 2006 Data File. Available online: 

http://www.bls.census.gov/cps_ftp.html#cpsbasic_extract 

U.S. Census Bureau. (2009). Historical Income Tables. Table F-9. Presence and Number of Related Children 

Under 18 Years Old—Families by Median and Mean Income. U.S. Census Bureau, Housing and 

Household Economic Statistics Division. Accessed 11/09 at 

http://www.census.gov/hhes/www/income/histinc/incfamdet.html 

56
 

 

Appendix A 

Confidence Intervals for NIS–3 and NIS–4 Maltreatment Estimates 

for Black and White Children 

Table A–1. Estimated Rates of Harm Standard Maltreatment and Their 95-percent Confidence 

Intervals for White and Black Children in the NIS–3 and NIS–4 

Maltreatment Category 

NIS–3 NIS–4 

White 

Rate per 1,000 

(CI) 

Black 

Rate per 1,000 

(CI) 

White 

Rate per 1,000 

(CI) 

Black 

Rate per 1,000 

(CI) 

Any maltreatment 20.39 

(11.14–29.63) 

31.61 

(19.06–44.17) 

12.60 

(10.37–14.83) 

23.97 

(17.26–30.67) 

Any abuse 10.48 

(6.15–14.82) 

12.51 

(6.73–18.29) 

5.99 

(5.09–6.9) 

10.41 

(8.35–12.40) 

Physical abuse 5.19 

(3.00–7.38) 

7.77 

(4.59–10.95) 

3.24 

(2.66–3.8) 

6.63 

(5.42–7.83) 

Sexual Abuse 3.17 

(1.63–4.71) 

3.44 

(-.09–6.97) 

1.36 

(1.08–1.63) 

2.61 

(1.54–3.68) 

Any neglect 10.91 

(5.31–16.51) 

19.62 

(11.09–28.14) 

7.4 

(5.62–9.29) 

14.65 

(8.49–20.82) 

Notes: Gray shaded cells contain estimates that differ significantly; the differences between estimates in the green 

shaded cells are statistically marginal. CI = confidence interval. The 95-percent confidence interval indicates the 

precision of the estimate, specifying the range in which the estimate would fall in 95 out of 100 comparable replications 

of the study. White rates presented here differ somewhat from those in the NIS–3 report. The NIS–3 final report did 

not separate Hispanic and non-Hispanic White children. The rates here are based on non-Hispanic Whites and nonHispanic Blacks only. 

A-1
 

 

Table A–2. Estimated Rates of Endangerment Standard Maltreatment and Their 95-percent 

Confidence Intervals for White and Black Children in the NIS–3 and NIS–4 

Maltreatment Category 

NIS–3 NIS–4 

White 

Rate per 1,000 

(CI) 

Black 

Rate per 1,000 

(CI) 

White 

Rate per 1,000 

(CI) 

Black 

Rate per 1,000 

(CI) 

Any maltreatment 36.50 

(21.93–51.06) 

54.96 

(33.61–76.30) 

28.58 

(24.43–32.73) 

49.55 

(39.25–59.85) 

Any abuse 17.32 

(9.64–25.00) 

19.05 

(11.34–26.77) 

8.73 

(7.57–9.89) 

14.91 

(12.30–17.51) 

Physical abuse 8.60 

(4.95–12.25) 

11.34 

(6.70–15.98) 

4.63 

(3.88–5.39) 

9.66 

(8.04–11.29) 

Any neglect 24.45 

(14.44–34.46) 

41.09 

(24.59–57.60) 

22.42 

(18.65–26.19) 

36.83 

(28.10–45.55) 

Physical neglect 16.62 

(10.28–22.97) 

27.58 

(16.17–38.99) 

12.20 

(9.75–14.66) 

17.87 

(13.69–22.05) 

Emotional neglect 8.64 

(4.73–12.55) 

9.10 

(4.82–13.38) 

12.13 

(10.10–14.17) 

18.16 

(14.77–21.55) 

Notes: Gray shaded cells contain estimates that differ significantly; the differences between estimates in the green 

shaded cells are statistically marginal. CI = confidence interval. The 95-percent confidence interval indicates the 

precision of the estimate, specifying the range in which the estimate would fall in 95 out of 100 comparable replications 

of the study. White rates presented here differ somewhat from those in the NIS–3 report. The NIS–3 final report did 

not separate Hispanic and non-Hispanic White children. The rates here are based on non-Hispanic Whites and nonHispanic Blacks only. 

A-2
 
 

Appendix B 

Imputation of Missing Demographic Data Items 

This appendix describes the imputation of the risk analysis demographic variables for 

the maltreated children in the NIS-4 database. The imputation procedure attempted to preserve the 

covariance structure of the data as much as possible. NIS–4 analysts carried out the imputation of 

each demographic variable in two stages. The first stage was a modeling effort. Using the known 

values of the variable to be imputed and a set of covariates, analysts developed a model to identify 

subgroups of data records that differed most distinctly on the values of the variable to be imputed. 

The second stage of the process used these subgroups as classes in a hot-deck procedure to impute 

the missing values of the variable. 

All demographic variables had some missing values, but the percentage of records with 

missing values varied greatly across the variables. Table B-1 shows the demographic variables that 

had to be imputed and the percentage of NIS–4 maltreated child records where their values were 

missing. The proportion of missing values ranged from 3.4 percent for child’s sex to 44.9 percent 

for socioeconomic status. 

Table B–1. Demographic Variables for the Multi-factor Modelbuilding Effort and Percentage of Their Values Missing 

Variable Percent Missing 

Child's sex 3.4 

Number of children in the household 3.8 

Any parent present 4.4 

Family structure 5.7 

Child's age 6.8 

Child's race 8.8 

Parental employment 42.4 

Socioeconomic status 44.9 

The imputation process started with imputation of the variable with the lowest 

percentage of missing data, child’s sex. To impute child’s sex, analysts first developed a predictive 

model for child’s sex using an Automatic Interaction Detector (AID) type of algorithm. This 

modeling algorithm is described in more detail below. Modeling included only those child records 

B-1 
Table B–2. Study Outcome Variables and Geographic Variables Included as Potential Predictors 

in Imputation 


 

with known sex. Study outcome variables as well as geographic variables served as potential 

predictors in this modeling effort. Table B-2 lists these variables. 

Variable Categories 

Study Outcome Variables 

Sexual abuse Harm Standard countable; only Endangerment Standard countable; 

not countable 

Physical abuse Harm Standard countable; only Endangerment Standard countable; 

not countable 

Emotional abuse Harm Standard countable; only Endangerment Standard countable; 

not countable 

Physical neglect Harm Standard countable; only Endangerment Standard countable; 

not countable 

Educational neglect Harm Standard countable; only Endangerment Standard countable; 

not countable 

Emotional neglect Harm Standard countable; only Endangerment Standard countable; 

not countable 

Severity Serious harm; moderate harm; inferred harm; endangered; 

serious harm only from Endangerment Standard maltreatment; moderate 

harm only from Endangerment Standard maltreatment; inferred harm only 

from Endangerment Standard maltreatment; endangered by Endangerment 

Standard maltreatment; other 

Geographic Variables 

Census region Northeast; Midwest; South; West 

Metropolitan status MSA with a population of 1 million or more; MSA with a population of 

less than 1 million; Non-MSA 

For child’s sex, the first imputed variable, none of the demographic variables were 

included as predictors in the modeling effort because of their missing values. The model identified 

homogeneous subsets of data records with respect to child’s sex. In the second stage, analysts 

imputed child’s sex by randomly assigning values to the cases where it was missing within each 

subset of records. 

Imputation of the variables in Table B-1 followed a series of cycles, with each variable 

imputed in an independent cycle. After imputing child’s sex, we imputed the number of children in 

the household, which had the next smallest missing proportion. Since all records that previously had 

B-2
 
 


 

missing values for child’s sex had imputed values at this stage, we included it in the potential 

predictor set along with the outcome and geographic variables. The imputation process continued in 

this manner, sequentially imputing each demographic variable listed in Table B-1 and then adding it 

to the list of predictors for imputing the next variable. The last variable imputed was socioeconomic 

status, which had the largest percentage of records with missing values. Note that this meant that all 

the other demographic variables served as potential predictors in the imputation modeling for 

socioeconomic status, since all were imputed prior to this variable. Doing this not only preserved the 

covariance structure between the demographic and outcome variables but also preserved the 

covariance structure among the demographic variables. 

The modeling process identified the imputation classes using a procedure known as 

Chi-Square Automatic Interaction Detector, or CHAID (Magidson, 1988; Ripley, 1996). This 

approach performs segmentation modeling—a statistical stepwise procedure that divides a set of 

records into segments (subgroups) that differ with respect to a designated criterion. The CHAID 

procedure creates a hierarchical tree-like structure that partitions the data records with known values 

on the target variable (i.e., the variable needing imputation) into homogenous subsets with respect to 

the selected target variable. To accomplish this, it progressively builds the segmentation model. It 

first merges values of the predictors that are statistically homogeneous with respect to the target 

variable and maintains all other heterogeneous values. It then selects the predictor in the model with 

the smallest p-value as the best predictor and thus forms the first branch in the decision tree. It 

continues applying the same process within the subgroups (nodes) defined by the "best" predictor 

chosen in the preceding step. This process continues until no additional significant predictors are 

found or until a specified minimum node size is reached; in this case, the specified the minimum 

node size was 30. The subgroups of data records (nodes of the tree) that CHAID identified then 

serve as imputation classes in the second stage of an imputation cycle. 

The second imputation stage assigns values for the target variable on the records where 

it is missing. For imputing missing values on the NIS-4 records, analysts used Westat’s imputation 

software, WESDECK (Krenzke & Judkins, 2008). WESDECK performs a hot-deck imputation. 

Hot-deck imputation fills in missing values on incomplete records using values from similar, but 

complete records of the same dataset.24

 WESDECK draws a random sample of records with known 

values within each imputation class to serve as donors. Then, the known values of the variable on 

the donor records are assigned randomly to the records in the imputation class with missing values. 

24 There are a variety of hot-deck methods (Ford, 1983; Sande, 1983). WESDECK is a proprietary software package developed by Westat that has 

several advantages (Winglee, Ryaboy, and Judkins, 1993). 

B-3
 

 

This approach assumes that, within each imputation class, the values of the variable are missing at 

random; that is, it assumes that the probability of having a known value on the variable is 

independent of the level of the value itself within an imputation class. This is a reasonable 

assumption, because the process developed the imputation classes by identifying homogeneous 

subsets of data with respect to the variable being imputed. One important feature of WESDECK is 

that it allows analysts to restrict the number of times the same donor contributes to different 

recipients. The multiple use of the donors can result in an increase in the variance of the survey 

estimates (Kalton and Kish, 1984). The present imputation restricted the number of donations from 

a donor to 2. 

References 

Ford, B.L. (1983). An overview of hot-deck procedures. In Incomplete Data in Sample Surveys. Vol. 3: 

Proceedings of a Symposium. Madow, W.G., and Olkin, I. (Eds.), New York: Academic Press. 

Kalton, G., and Kish, L. (1984). Some efficient random imputation methods. Communications in 

Statistics—Theory and Methods, 19(16), 1919-1939. 

Krenzke, T., and Judkins, D. (2008). Filling in the blanks: Some guesses are better than others. 

Chance, 21(3), 7-13. 

Magidson, J. (1988). Improved Statistical Techniques for Response Modeling. Journal of Direct 

Marketing, 2 (4), 6–18. 

Ripley, B. (1996). Pattern Recognition and Neural Networks. Cambridge: Cambridge University Press. 

Sande, I.G. (1983). Hot-deck imputation procedures. In Incomplete Data in Sample Surveys. Vol. 3: 

Proceedings of a Symposium. Madow, W.G., and Olkin, I. (Eds.), New York: Academic Press. 

B-4
 
 

 


 

Appendix C 

Construction of the Synthetic Database for Use in Building Multi-factor Logistic Models 

In order to support the development of multivariate logistic models on factors related 

to risk of child abuse and neglect, it was necessary to construct a special analysis database. This 

database is a combination of the countable maltreated child population from the Fourth National 

Incidence Study of Child Abuse and Neglect (NIS-4) and the records representing the 

nonmaltreated child population. The NIS–4 analysts developed records for nonmaltreated children 

by subtracting the maltreated children from the full child population in the United States, using data 

from the U.S. Bureau of the Census. 

Selection of the Census database source. Researchers chose to use the March 2006 

supplement of the Current Population Survey (CPS) from the U.S. Bureau of the Census to develop 

the population count of nonmaltreated children. Careful consideration was taken in selecting the 

Census supplement that would most accurately reflect the NIS-4 reference periods, which covered 

both the fall of 2005 and spring of 2006. The two options considered were (1) to combining the 

March 2005 and March 2006 supplements and use an average of their weighted counts, or (2) to use 

only the March 2006 supplement. The ultimate decision was to use only the 2006 data as the most 

appropriate. Although differences between the 2005 and 2006 data on the key measures were very 

small, the measure of parental employment was pivotal.25 The NIS–4 asked about the parents’ 

employment both “in past year” and “at time of maltreatment,” with the time of maltreatment being 

close to the time of completing the data form as well as included in the past year (i.e., last 12 

months). Thus, NIS respondents indicated the employment of children’s parents at the time of 

maltreatment and in the past year, which effectively covered the interval from the beginning of 

September 2004 (i.e., 12 months prior to the beginning of the first NIS reference period) to the 

beginning of May 2006 (i.e., at the end of the last NIS reference period). The Current Population 

Survey asks respondents about their employment status during the preceding calendar year and 

during the week prior to the interview. Therefore, if both 2005 and 2006 Current Population 

Surveys had been used, the general population data would have used an employment measure that 

covered the full 2004 calendar year, which would have extended well beyond the period of time 

referenced by the answers on employment status in the NIS-4 data. 

25 Differences for all marginal distributions were less than 1% except for children in households with the highest level of the income ($55,000 or 

more), a group that increased in size in the March 2006 CPS by 2.13% compared to the previous year. 

C-1
 

 

Development of the 2006 Census extract database. Before constructing the 

synthetic database, the NIS–4 analysts had to create a March 2006 child extract with the key 

variables needed. Children from the March 2006 CPS were identified as being under the age of 18, 

not living in group quarters and not coded as the 'reference person of family' or 'spouse of reference 

person'. If family relationship was ‘both parents present’, ‘mother only present’ or ‘father only 

present’, education and employment variables were merged onto the child record from the 

corresponding parent record(s). The Census collects information on income and poverty program 

participation at the household level and includes it on each family member’s record. Analysts 

derived the predictor variables of child’s sex, child’s age, child’s race, number of children in the 

household, socioeconomic status, and family structure. The derivation of socioeconomic status at 

the child level combined information on parent’s education, household income, and household 

poverty program participation. Initial review of the frequencies on these measures suggested that the 

Census data might require imputation. Information was missing on parents’ education and parents’ 

employment status for 1,036,545 children. Review of these records showed that the children were 

either living in a home without parents (982,662 children) or were part of a subfamily in which the 

Census classified their family relationship as ‘not in the universe of parents’ (53,883 children). For 

the former, analysts resolved the missing data by setting the derived parents’ education and parents’ 

employment status to the “no parent present” category, which correctly reflected the child’s family 

structure. For the latter, where children were part of a subfamily in a household, the parent record 

indicator on the child record helped to resolve the family structure. That is, if the family relationship 

was ‘not in the universe of parents,’ but a corresponding parent’s record was found, the education 

and employment variables from that corresponding record were used. This resolved missing data 

for both education and employment status and no imputation of the CPS data was necessary. The 

interim CPS file representing the general population of children comprised 73,735,720 child level 

records, but the family structure measure was not yet final. 

Although the March 2006 CPS supplement offered the most equivalent measures 

needed for the NIS analyses, it had a key weakness: it did not distinguish between children living 

with their unmarried parents and children living with a single parent with a cohabiting partner. As a 

result, analysts could not construct all 6 levels of the family structure variable from the 2006 Census 

data, as the NIS–4 defined this measure. The 2007 Census data did have the information needed for 

this definition. The solution was to base the assignment of family structure in the 2006 data on the 

distribution of this measure in the March 2007 CPS. To complete the CPS data file, analysts 

developed the final family structure variable in two steps. By first constructing it in the March 2007 

CPS data and then matching the 2007 and 2006 data on all the other variables and assigning the 

C-2
 
 

 


 

2007 family structure distributions to the corresponding (matched) cells in the March 2006 CPS. 

However, this process did not apply to children who had been assigned to the “no parent present” 

category. Those children were appropriately coded in the 2006 and they retained that code in the 

final family structure. The matching process and extrapolation process did not apply to them. 

The matching process occurred in two rounds. The first round matched the bulk of the 

cells on the key analysis variables of child’s sex, child’s age, child’s race, parents’ employment status, 

socioeconomic status and number of children in the household. Round 2 matched only on child’s 

sex, child’s age and child’s race and picked up any 2006 non-matches from the first round. In each 

database, analysts summed the weights for every unique combination of the first round matching 

variables. Excluding cases coded as ‘no parents present,’ the March 2006 CPS produced 1,092 

summarized cells to match with the March 2007 CPS.26 Child records coded as ‘no parents present’ 

summarized separately to 371 cells. The same process was applied to the March 2007 CPS data 

except that cells were determined based on the unique combinations of the first round matching 

variables plus family structure. This produced 3,582 cells to match with the March 2006 CPS.27 

Analysts calculated the weighted percent distribution for family structure (excluding level 6, ‘neither 

parent present’) within each cell. The final step of the first round match was to merge the like cells 

from 2006 and 2007, adding the codes for family structure to the March 2006 CPS and apportion 

the 2006 weight based on the calculated distribution from 2007. Round 1 resulted in matches for 

1,061 cells from the 2006 side. Because there were multiple values of family structure from 2007 for 

each 2006 cell, this produced a match file of 3,536 cells. From the 2006 side, 31 cells did not match. 

Subsequent steps dropped the 46 cells from the 2007 side that did not match. 

The second round assigned values of family structure to the records in unmatched cells 

in a similar manner, except that it applied a simplified classification, matching cells solely on child’s 

sex, child’s age and child’s race. The weights on the 31 unmatched 2006 cells from the first round 

then produced 23 cells for matching to the March 2007 CPS. The summarized 2007 data including 

family structure produced 240 cells for matching. The like cells from 2006 and 2007 were merged 

together and codes for family structure were added. This match produced 115 cells and the 2006 

weight was apportioned based on the 2007 distribution of family structure. The 115 cells were 

merged back with the 31 unmatched from the 2006 side and their weights were further apportioned 

26 The 2006 CPS has 62,628 cases that meet the study criteria for children less than 18 years of age. Of these cases, 2,736 are coded as ‘no parents 

present’. 59,892 cases remained to be matched with the March 2007 CPS. 

27 The 2007 CPS has 61,536 cases that meet the study criteria for children less than 18 years of age. Of these cases, 2,130 are coded as ‘no parents 

present’ or ‘not in universe of parents’. 59,406 cases remained to be matched with the March 2006 CPS. 

C-3
 
 

 


 

based on the distribution of parental employment status, lower socioeconomic status, and number 

of children in the household within child’s sex, child’s age, child’s race and family structure. This 

completed the process of adding a family structure measure to the March 2006 CPS and produced 

the final March 2006 CPS extract database. 

Construction of the synthetic database. In order to construct the synthetic database 

for use in the multi-factor model-building work, it was necessary to first create a synthetic database 

of nonmaltreated children and then combine this with the countable maltreated children from the 

NIS-4. The 7 child and family characteristics that were required for the analyses define a 7-way 

matrix. The child-level records in both the final Census extract and the NIS–4 data have unique cell 

assignments in this matrix based on their coded characteristics. The number of nonmaltreated 

children in the population was calculated by subtracting the known number of maltreated children 

with a given set of characteristics (i.e., the weighted NIS records in a given cell), from the total 

general population of children with same set of characteristics (i.e., the weighted records in the final 

March 2006 CPS extract in the corresponding cell). 

The weighted cells in the 7-way matrix of the final Census data extract each represented 

the children in the U.S. population who all possess that unique combination of the seven 

characteristics. A similar matrix defined the fully imputed NIS-4 data, subset to include only the 

children with countable maltreatment (a weighted total of 2,905,838 maltreated children). The two 

databases were merged together by all seven predictor variables and the NIS-4 weighted total was 

subtracted from the CPS weighted total in each cell.6 If the resultant weighted remainder, or 

nonmaltreated child population, in a given cell was negative, the nonmaltreated child population in 

that cell was set to zero. That is, analysts considered that all children with that particular set of 

characteristics in the child population were maltreated because the estimated number of maltreated 

children in the NIS-4 (an estimate that is qualified by sampling error) was greater than the number 

of children in the general population for that cell. Cells with negative remainders summed to a total 

of (negative) 94,631 nonmaltreated children in the nation. This process resulted in a database with 

weighted records that summed to 71,148,090 non-maltreated children. Finally, the non-maltreated 

database was concatenated with the NIS-4 database of countable maltreated children to create the 

synthetic database that included both maltreated and nonmaltreated children with known 

characteristics in 7 domains (listed in Table 3-1 and Appendix Table B-1). Analysts carried selected 

maltreatment variables from the NIS-4 data over to the new synthetic database and created dummy 

6 Both the NIS–4 annualized full-sample child weights and NIS–4 annualized replicated child weights were subtracted from the Census estimate in 

each cell.. 

C-4
 
 

 

C-5
 
 

variables for each level of the predictor variables for use in regression modeling. The final synthetic 

database represented a total of 74,040,548 maltreated and non-maltreated children.7 

7 Children with unique sets of characteristics on the seven predictor variables were found in the NIS-4 but not found in the general population of 

children. This resulted in a population of maltreated and non-maltreated children that exceeded the March 2006 CPS total by 318,208 children. 
 

 

 

 

 


 

Appendix D 

Procedures for Generating Marginal Probabilities from Final Logistic Models 

D.1 Derivation of Unadjusted Marginal Probabilities for Specific Subgroups from a 

Given Logistic Model 

Given a logistic model, the method of using the model parameters to derive 

probabilities for specific subgroups of children defined according to their unique combination of 

characteristics is as follows: 

Assume that the model in question involves m parameters or characteristics, that Bi is 

the model coefficient for characteristic i, and that Xi functions as the selector for the characteristic in 

question. That is, 

1 if the characteristic is selected 

Xi = 0 otherwise 

Then 

m m 

y = ∑ Bi

Xi = B0 + ∑ (Bi

Xi) 

i=0 i=1 

Thus, each parameter coefficient is multiplied by its selector and the products are 

summed across all parameters in the model. The rightmost expression above indicates that the 

parameter for the intercept is always selected. When a parameter Bi

 is associated with an interaction 

term, then the value of Xi

 is automatically given as the product of the Xi values for the individual 

factors that are involved in the interaction. 

The value y is the logit, and it can be transformed into a probability value as follows: 

z = exp(y) 

and 

__z__ p = 1 + z 

D-1
 
 

 

 


 

An example will illustrate the approach. Consider the procedure used to derive the 

unadjusted probability of Harm Standard physical abuse for children who are Black, between 6 and 

11 years old, and living in low SES households with their unmarried parents. The final logistic 

model (Table E-3b) had 16 parameters, including the intercept and 5 interaction terms. These are 

listed in the first column of Table D-1, and their model coefficients (i.e., parameter estimates) are 

given in the second column. 

Table D–1. Example Calculation of the Predicted Probability of a Specific Type of Child 

Experiencing Harm Standard Physical Abuse 

Parameter 

Parameter 

Estimate 

(Bi) 

Selector 

Value 

(Xi) 

Product 

(BiXi) 

Intercept -6.81083 1 -6.81083 

Other married parents 1.83465 0 0 

Unmarried parents 1.65535 1 1.65535 

Single parent with partner 2.18824 0 0 

Single parent no partner 1.37032 0 0 

No parent present 1.00161 0 0 

Low SES 2.23084 1 2.23084 

Black 0.63403 1 0.63403 

Birth-5 years -0.17208 0 0 

6-11 years 0.21723 1 0.21723 

Black x low SES -0.46944 1 -0.46944 

Other married parents x low SES -0.86435 0 0 

Unmarried parents x low SES -1.73282 1 -1.73282 

Single parent with partner x low SES -1.56647 0 0 

Single parent no partner x low SES -1.8294 0 0 

No parent present x low SES -1.31977 0 0 

Logit -4.27564 

Unadjusted 

Probability .0137 

The third column in Table D-1 specifies the value that must be assigned to the selector 

factor in order to describe the type of child of interest. Note that the intercept is automatically 

selected (i.e., assigned a value of 1). The characteristic “unmarried parents” is also selected via a 

value of 1 in this column. In order to specify that the child is living in a low SES household, that 

parameter is assigned a selector value of 1 as well. Because the child is Black and between the ages 

of 6 and 11, those parameters are also selected. The non-applicable single-factor selectors are set to 

D-2
 

 

zero. Then, the selector factors for the remaining parameters, which are all interaction terms, are 

automatically calculated by multiplying the selector terms for their component factors. For example, 

the selector for “Other married parents x low SES” is computed by multiplying the selector for 

“Other married parents,” which is zero, by the selector for “low SES,” which is 1. The product, 

zero, is entered for this interaction term. Similarly, the selector term for “Unmarried parents x low 

SES” is computed by multiplying the selector factor for “Unmarried parents,” which is 1, by the 

selector factor for “low SES,” which is also 1. The product, 1, is entered as the selector for this 

interaction term. The selectors for the remaining interaction terms are computed in a like manner, 

which in this example sets them all to zero. 

The last column in Table D-1 shows the product derived by multiplying the coefficient 

for the parameter by the value of the selector factor within each row. By summing the products in 

the last column, one calculates the value of the logit. The unadjusted probability itself is then 

derived from the logit according to the last two formulae given above. 

D.2 Computing Adjusted Marginal Probabilities for the Interactions Graphed in 

Chapter 4 

In order to construct a graph from the parameters of a final logistic model, one must 

compute the unadjusted probabilities for all cells specified in the model. Thus, in order to graph the 

race by SES interaction for the final multi-factor model predicting children’s risk of Harm Standard 

physical abuse (given in Figure 4-1), the authors first computed the unadjusted probabilities for each 

of the 72 cells in the matrix defined by the predictors in the model: family structure (6) x SES (2) x 

Race (2) x Age (3). Next, they computed the simple average across the cells in the 4 categories 

defined by the interaction term: Black-low SES, White-low SES, Black-not low SES, and White-not 

low SES. Finally, the resulting unadjusted average probabilities were multiplied by a constant term 

in order to ensure that the overall probability of Harm Standard physical abuse generated by the 

model exactly matched the probability of this maltreatment category computed directly from the 

synthetic database. 

D-3
 

 


 

Appendix E
 

Final Logistic Regression Models for All Maltreatment Categories 

Table E–1a. Model-fit Statistics for the Multi-factor Logistic Model Predicting All Harm Standard 

Maltreatment for All Black and White Children 

Test F value Numerator 

df 

Denominator df p≤

Overall fit 80.573 15 48 .001 

SES 331.713 1 62 .001 

Family structure 19.818 5 58 .001 

Number of children 6.834 2 61 .002 

Child’s age 11.349 2 61 .001 

Family structure x SES 26.658 5 58 .001 

Table E–1b. Model Parameters for the Multi-factor Logistic Model Predicting All Harm Standard 

Maltreatment for All Black and White Children 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -5.57902 0.10800 -51.75 .001 

Low SES 2.74331 0.14500 18.98 .001 

Other married parents 1.43087 0.15900 8.99 .001 

Unmarried parents 1.89881 0.28900 6.58 .001 

Single parent with partner 2.17212 0.22300 9.74 .001 

Single parent no partner 1.83573 0.17300 10.61 .001 

No parent present 1.66000 0.22400 7.42 .001 

1 child 0.24217 0.08200 2.96 .004 

3 or more children 0.25803 0.10600 2.44 .018 

Birth-5 years -0.63542 0.13300 -4.79 .001 

6-11 years -0.2056 0.10500 -1.95 .056 

Other married parents x low SES -0.91537 0.20500 -4.46 .001 

Unmarried parents x low SES -2.17162 0.33800 -6.43 .001 

Single parent with partner x low SES -1.61578 0.25100 -6.43 .001 

Single parent no partner x low SES -2.08958 0.20200 -10.35 .001 

No parent present x low SES -2.22733 0.25000 -8.89 .001 

E-1
 
Table E–2a. Model-fit Statistics for the Multi-factor Logistic Model Predicting All Harm Standard 

Maltreatment for Black and White Children Living With Parents 

 


 

Test F value Numerator df 

Denominator df p≤

Overall fit 74.256 17 46 .001 

SES 35.851 1 62 .001 

Family structure 23.331 4 59 .001 

Parent’s employment 14.761 2 61 .001 

Child’s age 9.699 2 61 .001 

Number of children 6.528 2 61 .003 

Family structure x SES 30.653 4 59 .001 

SES x parent’s employment 8.251 2 61 .001 

Table E–2b. Model Parameters for the Multi-factor Logistic Model Predicting All Harm Standard 

Maltreatment for Black and White Children Living With Parents 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -5.64448 0.11300 -49.99 .001 

Low SES 2.75436 0.15300 18.05 .001 

Other married parents 1.4099 0.15900 8.88 .001 

Unmarried parents 1.78766 0.27900 6.42 .001 

Single parent with partner 2.12272 0.22500 9.43 .001 

Single parent no partner 1.73037 0.15900 10.91 .001 

Any parent unemployed 0.31913 0.23900 1.34 .186 

Parent(s) not in labor force 1.53964 0.29000 5.32 .001 

Birth-5 years -0.61086 0.13800 -4.43 .001 

6-11 years -0.19486 0.11000 -1.77 .081 

1 child 0.25089 0.09300 2.70 .009 

3 or more children 0.27778 0.10900 2.54 .014 

Other married parents x low SES -0.89461 0.20700 -4.32 .001 

Unmarried parents x low SES -2.06116 0.34300 -6.00 .001 

Single parent with partner x low SES -1.55785 0.24700 -6.30 .001 

Single parent no partner x low SES -1.98131 0.20100 -9.84 .001 

Low SES x any parent unemployed -0.20126 0.25700 -0.78 .437 

Low SES x parent(s) not in labor force -1.54529 0.381 -4.054 .001 

E-2
 
Table E–3b. Model Parameters for the Multi-factor Logistic Model Predicting All Harm Standard 

Physical Abuse for All Black and White Children 

 


 

Table E–3a. Model-fit Statistics for the Multi-factor Logistic Model Predicting All Harm Standard 

Physical Abuse for All Black and White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 45.218 15 48 .001 

Family structure 23.368 5 58 .001 

SES 50.799 1 62 .001 

Race 10.113 1 62 .002 

Child’s age 5.272 2 61 .008 

Race x SES 4.014 1 62 .049 

Family structure x SES 14.951 5 58 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.81083 0.19700 -34.60 .001 

Other married parents 1.83465 0.25900 7.09 .001 

Unmarried parents 1.65535 0.34700 4.77 .001 

Single parent with partner 2.18824 0.24000 9.13 .001 

Single parent no partner 1.37032 0.16200 8.46 .001 

No parent present 1.00161 0.26400 3.79 .001 

Low SES 2.23084 0.22900 9.74 .001 

Black 0.63403 0.14900 4.25 .001 

Birth-5 years -0.17208 0.12000 -1.43 .158 

6-11 years 0.21723 0.10300 2.10 .040 

Black x low SES -0.46944 0.23400 -2.00 .049 

Other married parents x low SES -0.86435 0.29200 -2.96 .004 

Unmarried parents x low SES -1.73282 0.35400 -4.89 .001 

Single parent with partner x low SES -1.56647 0.26000 -6.04 .001 

Single parent no partner x low SES -1.8294 0.27000 -6.77 .001 

No parent present x low SES -1.31977 0.37900 -3.48 .001 

E-3
 
Table E–4a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Harm Standard 

Physical Abuse for Black and White Children Living With Parents 

Table E–4b. Model Parameters for the Multi-factor Logistic Model Predicting Harm Standard 

Physical Abuse for Black and White Children Living With Parents 

 


 

Test F value Numerator df 

Denominator df p≤

Overall fit 52.262 12 51 .001 

Family structure 21.734 4 59 .001 

SES 55.073 1 62 .001 

Race 6.747 1 62 .012 

Child’s age 4.066 2 61 .022 

Family structure x SES 21.917 4 59 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.73425 0.19200 -34.99 .001 

Other married parents 1.84313 0.25800 7.14 .001 

Unmarried parents 1.72189 0.34200 5.03 .001 

Single parent with partner 2.20056 0.24100 9.13 .001 

Single parent no partner 1.4434 0.15500 9.29 .001 

Low SES 2.14676 0.22700 9.46 .001 

Black 0.36791 0.14200 2.60 .012 

Birth-5 years -0.21404 0.12800 -1.67 .100 

6-11 years 0.14716 0.11600 1.27 .209 

Other married parents x low SES -0.89048 0.29000 -3.07 .003 

Unmarried parents x low SES -1.79752 0.35200 -5.11 .001 

Single parent with partner x low SES -1.60068 0.26400 -6.07 .001 

Single parent no partner x low SES -1.98518 0.24100 -8.25 .001 

E-4
 
Table E–5b. Model Parameters for the Multi-factor Logistic Model Predicting Harm Standard 

Sexual Abuse for All Black and White Children 


 

Table E–5a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Harm Standard 

Sexual Abuse for All Black and White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 28.549 32 31 .001 

Family structure 17.084 5 58 .001 

Child’s sex 61.498 1 62 .001 

SES 15.81 1 62 .001 

Child’s age 1.047 2 61 .357 

Number of children 0.513 2 61 .601 

Child’s sex x number of children 3.369 2 61 .041 

SES x number of children 6.447 2 61 .003 

Family structure x child’s age 3.073 10 53 .004 

SES x child’s age 3.522 2 61 .036 

Family structure x SES 6.518 5 58 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Birth-5 years -0.7816 0.36800 -2.12 .038 

6-11 years -0.73586 0.35000 -2.10 .040 

1 child -0.7142 0.28600 -2.50 .015 

3 or more children -0.10225 0.25500 -0.40 .690 

Male x 1 child 0.88132 0.53800 1.64 .107 

Male x 3 or more children 1.4427 0.55100 2.62 .011 

Low SES x 1 child 0.19875 0.50300 0.40 .694 

Low SES x 3 or more children -1.02276 0.45800 -2.24 .029 

Other married parents x birth-5 years 1.32132 0.60500 2.18 .033 

Other married parents x 6-11 years 0.27075 0.38500 0.70 .484 

Unmarried parents x birth-5 years 1.49955 1.32300 1.13 .261 

Unmarried parents x 6-11 years 0.92696 0.94400 0.98 .330 

Single parent with partner x birth-5 years 1.25038 0.76100 1.64 .105 

Single parent with partner x 6-11 years -1.01171 0.83800 -1.21 .232 

Single parent no partner x birth-5 years 1.37328 0.53200 2.58 .012 

Single parent no partner x 6-11 years 0.45001 0.45200 1.00 .323 

No parent present x birth-5 years 0.40954 0.58000 0.71 .483 

No parent present x 6-11 years 1.32977 0.62000 2.15 .036 

Low SES x birth-5 years -0.7013 0.27500 -2.55 .013 

Low SES x 6-11 years 0.21049 0.36700 0.57 .568 

E-5
 

 

Table E–5b. Continued. 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Other married parents x low SES -0.33336 0.41100 -0.81 .421 

Unmarried parents x low SES -3.56688 1.07700 -3.31 .002 

Single parent with partner x low SES -1.71742 0.89700 -1.92 .060 

Single parent no partner x low SES -2.05576 0.55800 -3.69 .001 

No parent present x low SES -2.39073 0.60800 -3.93 .001 

E-6
 
Table E–6a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Harm Standard 

Sexual Abuse for Black and White Children Living With Parents 

 


 

Test F value Numerator df 

Denominator df p≤

Overall fit 34.06 26 37 .001 

Family structure 20.608 4 59 .001 

Child’s sex 51.167 1 62 .001 

SES 12.544 1 62 .001 

Number of children 1.279 2 61 .286 

Child’s age 0.661 2 61 .520 

Child’s sex x child’s age 3.461 2 61 .038 

Family structure x child’s age 2.651 8 55 .016 

SES x number of children 4.762 2 61 .012 

Family structure x SES 6.464 4 59 .001 

Table E–6b. Model Parameters for the Multi-factor Logistic Model Predicting Harm Standard 

Sexual Abuse for Black and White Children Living With Parents 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -7.20688 0.36600 -19.71 .001 

Other married parents 1.7236 0.37700 4.58 .001 

Unmarried parents 2.29519 0.86000 2.67 .010 

Single parent with partner 3.44599 0.91400 3.77 .001 

Single parent no partner 1.80899 0.36700 4.93 .001 

Male -2.39412 0.34000 -7.05 .001 

Low SES 2.91302 0.44300 6.57 .001 

1 child -0.53248 0.30800 -1.73 .089 

3 or more children 0.18413 0.30400 0.61 .547 

Birth-5 years -1.25883 0.33900 -3.72 .001 

6-11 years -0.9026 0.34700 -2.60 .012 

Male x birth-5 years 1.05165 0.50300 2.09 .041 

Male x 6-11 years 1.49304 0.60500 2.47 .016 

Other married parents x birth-5 years 1.24085 0.61600 2.02 .048 

Other married parents x 6-11 years 0.28875 0.39000 0.74 .462 

Unmarried parents x birth-5 years 1.68529 1.45900 1.16 .252 

Unmarried parents x 6-11 years 0.88904 0.95600 0.93 .356 

Single parent with partner x birth-5 years 1.13258 0.81900 1.38 .172 

Single parent with partner x 6-11 years -0.94455 0.87100 -1.09 .282 

Single parent no partner x birth-5 years 1.21283 0.52900 2.29 .025 

E-7
 

 

Table E–6b. Continued. 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Single parent no partner x 6-11 years 0.49291 0.43000 1.15 .256 

Low SES x 1 child 0.25444 0.55900 0.46 .651 

Low SES x 3 or more children -1.00343 0.52300 -1.92 .060 

Other married parents x low SES -0.29359 0.44200 -0.67 .509 

Unmarried parents x low SES -3.94261 1.33500 -2.95 .004 

Single parent with partner x low SES -1.90561 0.97700 -1.95 .056 

Single parent no partner x low SES -2.1231 0.55700 -3.81 .001 

E-8
 
Table E–7b. Model Parameters for the Multi-factor Logistic Model Predicting Harm Standard 

Emotional Maltreatment for All Black and White Children 

 


 

Table E–7a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Harm Standard 

Emotional Maltreatment for All Black and White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 26.568 15 48 .001 

Family structure 10.704 5 58 .001 

Child’s age 26.675 2 61 .001 

SES 60.478 1 62 .001 

SES x child’s age 3.194 2 61 .048 

Family structure x SES 5.409 5 58 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.36219 0.20500 -31.03 .001 

Other married parents 1.47141 0.30300 4.86 .001 

Unmarried parents 1.88842 0.70600 2.68 .010 

Single parent with partner 1.94822 0.39900 4.88 .001 

Single parent no partner 1.49821 0.22900 6.56 .001 

No parent present 1.87264 0.46600 4.02 .001 

Birth-5 years -2.09953 0.30600 -6.85 .001 

6-11 years -0.36169 0.30800 -1.17 .245 

Low SES 2.22186 0.31700 7.01 .001 

Low SES x birth-5 years 0.89362 0.35400 2.52 .014 

Low SES x 6-11 years 0.08722 0.35000 0.25 .804 

Other married parents x low SES -0.49263 0.46200 -1.07 .291 

Unmarried parents x low SES -1.39107 0.81100 -1.72 .091 

Single parent with partner x low SES -0.84504 0.42900 -1.97 .053 

Single parent no partner x low SES -1.48488 0.36800 -4.04 .001 

No parent present x low SES -2.78509 0.56100 -4.96 .001 

E-9
 
Table E–8a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Harm Standard 

Emotional Maltreatment for Black and White Children Living With Parents 

 


 

Test F value Numerator df 

Denominator df p≤

Overall fit 31.334 11 52 .001 

Child’s age 16.33 2 61 .001 

Family structure 12.844 4 59 .001 

SES 75.343 1 62 .001 

Family structure x SES 4.556 4 59 .003 

Table E–8b. Model Parameters for the Multi-factor Logistic Model Predicting Harm Standard 

Emotional Maltreatment for Black and White Children Living With Parents 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.4715 0.20400 -31.70 .001 

Birth-5 years -1.3954 0.24400 -5.72 .001 

6-11 years -0.25381 0.15000 -1.69 .096 

Other married parents 1.53536 0.30000 5.11 .001 

Unmarried parents 1.81119 0.69900 2.59 .012 

Single parent with partner 1.97221 0.40000 4.93 .001 

Single parent no partner 1.54068 0.23400 6.58 .001 

Low SES 2.36077 0.31200 7.56 .001 

Other married parents x low SES -0.58185 0.47100 -1.24 .221 

Unmarried parents x low SES -1.26338 0.78400 -1.61 .112 

Single parent with partner x low SES -0.88257 0.42900 -2.06 .044 

Single parent no partner x low SES -1.53497 0.37500 -4.10 .001 

E-10
 
Table E–9b. Model Parameters for the Multi-factor Logistic Model Predicting Harm Standard 

Physical Neglect for All Black and White Children 

 


 

Table E–9a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Harm Standard 

Physical Neglect for All Black and White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 17.204 11 52 .001 

SES 111.686 1 62 .001 

Family structure 3.132 5 58 .014 

Family structure x SES 15.575 5 58 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -7.54708 0.26300 -28.67 .001 

Low SES 3.60797 0.30800 11.70 .001 

Other married parents 1.47176 0.40300 3.65 .001 

Unmarried parents 1.88298 0.43900 4.29 .001 

Single parent with partner 1.87946 0.40200 4.68 .001 

Single parent no partner 2.0598 0.25500 8.07 .001 

No parent present 2.43285 0.51600 4.72 .001 

Other married parents x low SES -1.88128 0.51300 -3.66 .001 

Unmarried parents x low SES -2.42518 0.52800 -4.59 .001 

Single parent with partner x low SES -2.2618 0.53300 -4.25 .001 

Single parent no partner x low SES -2.60408 0.35400 -7.35 .001 

No parent present x low SES -3.60918 0.48600 -7.43 .001 

E-11
 

 

Table E–10a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Harm Standard 

Physical Neglect for Black and White Children Living With Parents 

Test F value Numerator df 

Denominator df p≤

Overall fit 58.96 5 58 .001 

SES 51.345 1 62 .001 

Parent’s employment 15.659 2 61 .001 

SES x parent’s employment 11.305 2 61 .001 

Table E–10b. Model Parameters for the Multi-factor Logistic Model Predicting Harm Standard 

Physical Neglect for Black and White Children Living With Parents 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.869 0.21700 -31.64 .001 

Low SES 2.34273 0.24000 9.78 .001 

Any parent unemployed 1.11391 0.37200 2.99 .004 

Parent(s) not in labor force 2.22893 0.33200 6.72 .001 

Low SES x any parent unemployed -0.53162 0.44500 -1.19 .237 

Low SES x parent(s) not in labor force -2.16782 0.47100 -4.60 .001 

E-12
 
 

 

 


 

Table E–11a. Model-fit Statistics for the Multi-factor Logistic Model Predicting All Endangerment 

Standard Maltreatment for All Black and White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 118.76 30 33 .001 

SES 269.94 1 62 .001 

Family structure 48.42 5 58 .001 

Race 3.58 1 62 .063 

Number of children 4.53 2 61 .015 

Race x SES 41.57 1 62 .001 

Race x family structure 5.29 5 58 .001 

Family structure x SES 55.51 5 58 .001 

Family structure x number of children 2.64 10 53 .011 

Table E–11b. Model Parameters for the Multi-factor Logistic Model Predicting All Endangerment 

Standard Maltreatment for All Black and White Children 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -5.04 0.10000 -50.40 .001 

Low SES 2.89 0.11200 25.75 .001 

Other married parents 1.53 0.16000 9.58 .001 

Unmarried parents 2.14 0.33300 6.43 .001 

Single parent with partner 2.52 0.19000 13.28 .001 

Single parent no partner 1.68 0.09800 17.18 .001 

No parent present 1.55 0.28600 5.43 .001 

Black 0.49 0.17300 2.86 .006 

1 child 0.13 0.16900 0.76 .453 

3 or more children 0.32 0.16400 1.97 .053 

Black x low SES -0.76 0.11700 -6.45 .001 

Other married parents x Black -0.25 0.22800 -1.12 .269 

Unmarried parents x Black 0.55 0.24100 2.27 .027 

Single parent with partner x Black 0.79 0.40400 1.95 .056 

Single parent no partner x Black -0.43 0.23600 -1.82 .074 

No parent present x Black 0.04 0.23200 0.16 .873 

Other married parents x low SES -0.66 0.22000 -3.00 .004 

Unmarried parents x low SES -1.91 0.29300 -6.53 .001 

Single parent with partner x low SES -1.81 0.22300 -8.11 .001 

Single parent no partner x low SES -1.74 0.12600 -13.85 .001 

No parent present x low SES -2.13 0.19000 -11.24 .001 

Other married parents x 1 child -0.35 0.30700 -1.13 .264 

E-13
 

 

Table E–11b. Continued 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Other married parents x 3 or more children -0.14 0.23000 -0.60 .550 

Unmarried parents x 1 child -0.38 0.26400 -1.45 .153 

Unmarried parents x 3 or more children -0.25 0.28300 -0.90 .371 

Single parent with partner x 1 child -0.75 0.28000 -2.68 .009 

Single parent with partner x 3 or more 

children -0.27 0.36300 -0.75 .458 

Single parent no partner x 1 child 0.17 0.15700 1.07 .287 

Single parent no partner x 3 or more 

children 0.36 0.18500 1.95 .056 

No parent present x 1 child -0.12 0.31700 -0.37 .709 

No parent present x 3 or more children -0.16 0.26900 -0.61 .546 

E-14
 
Table E–12b. Model Parameters for the Multi-factor Logistic Model Predicting All Endangerment 

Standard Maltreatment for Black and White Children Living With Parents 

 


 

Table E–12a. Model-fit Statistics for the Multi-factor Logistic Model Predicting All Endangerment 

Standard Maltreatment for Black and White Children Living With Parents 

Test F value Numerator df 

Denominator df p≤

Overall fit 244.47 43 23 .001 

SES 42.70 1 65 .001 

Family structure 22.11 4 62 .001 

Child’s age 2.18 2 64 .121 

Number of children 5.17 2 64 .008 

Parent’s employment 32.48 2 64 .001 

Race 3.46 1 65 .067 

Family structure x number of children 3.39 8 58 .003 

Family structure x SES 45.70 4 62 .001 

Race x SES 45.38 1 65 .001 

Race x family structure 6.66 4 62 .001 

Family structure x parent’s employment 2.94 8 58 .008 

Child’s age x parent’s employment 3.44 4 62 .013 

SES x parent’s employment 24.73 2 64 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -5.15 0.10000 -51.39 .001 

Low SES 2.84 0.14300 19.84 .001 

Other married parents 1.55 0.18500 8.37 .001 

Unmarried parents 2.11 0.33600 6.27 .001 

Single parent with partner 2.52 0.18000 14.05 .001 

Single parent no partner 1.60 0.10700 14.89 .001 

Birth-5 years -0.03 0.10800 -0.28 .784 

6-11 years 0.07 0.08700 0.77 .442 

1 child 0.12 0.17300 0.72 .475 

3 or more children 0.34 0.16200 2.09 .040 

Any parent unemployed 0.29 0.17900 1.64 .107 

Parent(s) not in labor force 2.35 0.33700 6.98 .001 

Black 0.49 0.17800 2.73 .008 

Other married parents x 1 child -0.34 0.30700 -1.10 .277 

Other married parents x 3 or more children -0.17 0.23300 -0.75 .458 

Unmarried parents x 1 child -0.37 0.26500 -1.39 .168 

Unmarried parents x 3 or more children -0.25 0.28200 -0.88 .383 

E-15
 
 

 


 

Table E–12b. Continued 

Single parent with partner x 1 child -0.79 0.28500 -2.76 .007 

Single parent with partner x 3 or more 

children -0.30 0.35300 -0.86 .395 

Single parent no partner x 1 child 0.18 0.16200 1.09 .280 

Single parent no partner x 3 or more 

children 0.33 0.18500 1.80 .077 

Other married parents x low SES -0.54 0.23300 -2.31 .024 

Unmarried parents x low SES -1.72 0.30700 -5.61 .001 

Single parent with partner x low SES -1.63 0.21700 -7.53 .001 

Single parent no partner x low SES -1.53 0.12900 -11.84 .001 

Black x low SES -0.87 0.12900 -6.74 .001 

Other married parents x Black -0.19 0.22100 -0.86 .391 

Unmarried parents x Black 0.63 0.23800 2.62 .011 

Single parent with partner x Black 0.85 0.41200 2.06 .044 

Single parent no partner x Black -0.34 0.23300 -1.45 .152 

Other married parents x any parent 

unemployed -0.13 0.29100 -0.44 .659 

Other married parents x parent(s) not in 

labor force -0.84 0.24100 -3.47 .001 

Unmarried parents x any parent 

unemployed 0.06 0.26100 0.22 .830 

Unmarried parents x parent(s) not in labor 

force -1.28 0.38100 -3.37 .001 

Single parent with partner x any parent 

unemployed 0.09 0.27100 0.34 .736 

Single parent with partner x parent(s) not 

in labor force -1.20 0.38100 -3.15 .003 

Single parent no partner x any parent 

unemployed -0.08 0.19400 -0.41 .684 

Single parent no partner x parent(s) not in 

labor force -0.94 0.25300 -3.73 .001 

Birth-5 years x any parent unemployed 0.06 0.14700 0.44 .663 

Birth-5 years x parent(s) not in labor force 0.45 0.17600 2.57 .012 

6-11 years x any parent unemployed 0.28 0.15200 1.83 .073 

6-11 years x parent(s) not in labor force 0.07 0.16600 0.43 .666 

Low SES x any parent unemployed -0.22 0.20200 -1.07 .290 

Low SES x parent(s) not in labor force -1.58 0.23400 -6.75 .001 

E-16
 
 


 

Table E–13a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Endangerment 

Standard Physical Abuse for All Black and White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 55.69 37 26 .001 

Family structure 28.77 5 58 .001 

SES 50.40 1 62 .001 

Race 20.10 1 62 .001 

Number of children 1.09 2 61 .344 

Child’s sex 5.32 1 62 .024 

Child’s age 4.94 2 61 .010 

Family structure x SES 17.06 5 58 .001 

Race x family structure 2.81 5 58 .024 

Child’s sex x child’s age 5.54 2 61 .006 

SES x number of children 5.30 2 61 .008 

Family structure x number of children 2.43 10 53 .018 

Race x SES 13.53 1 62 .001 

Table E–13b. Model Parameters for the Multi-factor Logistic Model Predicting Endangerment 

Standard Physical Abuse for All Black and White Children 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.50 0.22800 -28.47 .001 

Other married parents 2.24 0.33400 6.70 .001 

Unmarried parents 1.74 0.52500 3.32 .002 

Single parent with partner 2.14 0.25500 8.40 .001 

Single parent no partner 1.72 0.23200 7.40 .001 

No parent present 1.30 0.30000 4.35 .001 

Low SES 1.95 0.26700 7.32 .001 

Black 0.73 0.28400 2.57 .013 

1 child 0.31 0.32200 0.95 .347 

3 or more children -0.09 0.26000 -0.34 .734 

Child’s sex -0.28 0.14100 -1.97 .053 

Birth-5 years -0.51 0.13600 -3.75 .001 

6-11 years -0.12 0.11700 -1.02 .312 

Other married parents x low SES -0.74 0.22800 -3.25 .002 

Unmarried parents x low SES -1.49 0.40400 -3.70 .001 

Single parent with partner x low SES -1.56 0.22900 -6.81 .001 

Single parent no partner x low SES -1.80 0.23000 -7.86 .001 

No parent present x low SES -1.36 0.36600 -3.72 .001 

E-17
 
Table E–13b. Continued 

 

 


 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Other married parents x Black -0.09 0.28400 -0.31 .755 

Unmarried parents x Black 0.93 0.43900 2.12 .038 

Single parent with partner x Black 0.29 0.31100 0.94 .352 

Single parent no partner x Black -0.39 0.31100 -1.25 .216 

No parent present x Black 0.04 0.46100 0.10 .925 

Male x birth-5 years 0.82 0.27300 2.99 .004 

Male x 6-11 years 0.63 0.20200 3.13 .003 

Low SES x 1 child 0.74 0.22500 3.27 .002 

Low SES x 3 or more children 0.15 0.27200 0.56 .576 

Other married parents x 1 child -0.65 0.52200 -1.25 .215 

Other married parents x 3 or more children 0.01 0.38900 0.02 .985 

Unmarried parents x 1 child -0.66 0.59900 -1.11 .273 

Unmarried parents x 3 or more children -0.18 0.54100 -0.34 .734 

Single parent with partner x 1 child -0.40 0.41600 -0.97 .334 

Single parent with partner x 3 or more 

children 0.38 0.34900 1.10 .275 

Single parent no partner x 1 child -0.52 0.38200 -1.36 .179 

Single parent no partner x 3 or more 

children 0.51 0.31900 1.60 .115 

No parent present x 1 child -0.70 0.43500 -1.62 .111 

No parent present x 3 or more children -0.02 0.41100 -0.04 .968 

Black x low SES -0.60 0.16200 -3.68 .001 

E-18
 
 


 

Table E–14a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Endangerment 

Standard Physical Abuse for Black and White Children Living With Parents 

Test F value Numerator df 

Denominator df p≤

Overall fit 38.47 32 42 .001 

Family structure 34.92 4 70 .001 

SES 9.61 1 73 .003 

Number of children 2.82 2 72 .066 

Race 18.15 1 73 .001 

Parent’s employment 6.04 2 72 .004 

Child’s age 2.96 2 72 .058 

Child’s sex 5.61 1 73 .021 

Race x SES 13.60 1 73 .001 

SES x parent’s employment 3.56 2 72 .034 

Child’s sex x child’s age 4.29 2 72 .017 

Race x family structure 3.32 4 70 .015 

SES x number of children 4.32 2 72 .017 

Number of children x parent’s 

employment 3.44 4 70 .013 

Family structure x SES 16.80 4 70 .001 

Table E–14b. Model Parameters for the Multi-factor Logistic Model Predicting Endangerment 

Standard Physical Abuse for Black and White Children Living With Parents 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.41 0.2500 -25.62 .001 

Other married parents 2.07 0.1970 10.50 .001 

Unmarried parents 1.48 0.4490 3.31 .001 

Single parent with partner 2.15 0.2030 10.61 .001 

Single parent no partner 1.66 0.2050 8.12 .001 

Low SES 2.06 0.2680 7.68 .001 

1 child -0.11 0.1560 -0.68 .500 

3 or more children 0.02 0.2210 0.11 .916 

Black 0.71 0.2820 2.53 .013 

Any parent unemployed -0.38 0.3080 -1.24 .219 

Parent(s) not in labor force 0.93 0.4060 2.29 .025 

Birth-5 years -0.54 0.1400 -3.87 .001 

6-11 years -0.15 0.1210 -1.23 .224 

Male -0.24 0.1470 -1.66 .101 

Black x low SES -0.58 0.1560 -3.69 .001 

E-19
 
Table E–14b. Continued 

 

 


 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Low SES x any parent unemployed -0.26 0.2660 -0.96 .340 

Low SES x parent(s) not in labor force -1.18 0.4400 -2.69 .009 

Malexbirth-5 years 0.81 0.2840 2.85 .006 

Malex6-11 years 0.55 0.2240 2.44 .017 

Other married parents x Black -0.07 0.2840 -0.25 .801 

Unmarried parents x Black 0.95 0.4390 2.16 .034 

Single parent with partner x Black 0.30 0.3110 0.96 .339 

Single parent no partner x Black -0.31 0.3100 -1.01 .315 

Low SES x 1 child 0.76 0.2590 2.94 .004 

Low SES x 3 or more children 0.10 0.2700 0.35 .726 

1 child x any parent unemployed -0.23 0.3720 -0.63 .531 

1 child x parent(s) not in labor force -0.18 0.3290 -0.54 .592 

3 or more children x any parent 

unemployed 0.63 0.2140 2.96 .004 

3 or more children x parent(s) not in labor 

force 0.33 0.4090 0.80 .425 

Other married parents x low SES -0.74 0.2250 -3.30 .001 

Unmarried parents x low SES -1.46 0.4180 -3.50 .001 

Single parent with partner x low SES -1.49 0.2320 -6.45 .001 

Single parent no partner x low SES -1.67 0.2340 -7.15 .001 

E-20
 
Table E–15b. Model Parameters for the Multi-factor Logistic Model Predicting Endangerment 

Standard Sexual Abuse for All Black and White Children 

 

 


 

Table E–15a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Endangerment 

Standard Sexual Abuse for All Black and White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 30.75 16 47 .001 

Family structure 17.89 5 58 .001 

Child’s sex 40.10 1 62 .001 

SES 22.76 1 62 .001 

Number of children 2.58 2 61 .084 

SES x number of children 4.01 2 61 .023 

Family structure x SES 9.75 5 58 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -7.55 0.25900 -29.20 .001 

Other married parents 2.13 0.27400 7.77 .001 

Unmarried parents 2.98 0.85600 3.49 .001 

Single parent with partner 3.55 0.66000 5.38 .001 

Single parent no partner 2.32 0.30700 7.58 .001 

No parent present 2.64 0.44300 5.95 .001 

Male -1.23 0.19500 -6.33 .001 

Low SES 2.95 0.34500 8.56 .001 

1 child -0.45 0.22000 -2.03 .047 

3 or more children 0.02 0.24100 0.07 .943 

Low SESx1 child 0.07 0.39400 0.18 .859 

Low SESx3 or more children -0.77 0.36300 -2.13 .037 

Other married parents x low SES -0.46 0.39600 -1.15 .254 

Unmarried parents x low SES -3.34 0.92000 -3.63 .001 

Single parent with partner x low SES -2.09 0.78500 -2.66 .010 

Single parent no partner x low SES -2.20 0.43000 -5.13 .001 

No parent present x low SES -2.22 0.53500 -4.14 .001 

E-21
 
Table E–16a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Endangerment 

Standard Sexual Abuse for Black and White Children Living With Parents 

Table E–16b. Model Parameters for the Multi-factor Logistic Model Predicting Endangerment 

Standard Sexual Abuse for Black and White Children Living With Parents 

 


 

Test F value Numerator df 

Denominator df p≤

Overall fit 38.51 16 47 .001 

Family structure 22.68 4 59 .001 

Child’s sex 40.72 1 62 .001 

SES 25.94 1 62 .001 

Parent’s employment 4.45 2 61 .016 

Number of children 1.88 2 61 .162 

SES x number of children 3.95 2 61 .024 

Family structure x SES 11.26 4 59 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -7.49 0.25900 28.95 .001 

Other married parents 2.14 0.27500 -7.80 .001 

Unmarried parents 2.98 0.85700 -3.48 .001 

Single parent with partner 3.53 0.65900 -5.35 .001 

Single parent no partner 2.30 0.30700 -7.48 .001 

Male -1.30 0.20400 6.38 .001 

Low SES 3.01 0.35900 -8.38 .001 

Any parent unemployed -0.59 0.21300 2.77 .007 

Parent(s) not in labor force 0.18 0.27300 -0.65 .519 

1 child -0.43 0.24000 1.80 .077 

3 or more children 0.01 0.25300 -0.04 .969 

Low SES x 1 child 0.18 0.43300 -0.41 .681 

Low SES x 3 or more children -0.79 0.40500 1.96 .055 

Other married parents x low SES -0.44 0.39800 1.11 .271 

Unmarried parents x low SES -3.41 0.91700 3.72 .001 

Single parent with partner x low SES -2.15 0.76800 2.80 .007 

Single parent no partner x low SES -2.23 0.43300 5.14 .001 

E-22
 
Table E–17a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Endangerment 

Standard Emotional Maltreatment for All Black and White Children 

 


 

Test F value Numerator df 

Denominator df p≤

Overall fit 106.73 25 38 .001 

SES 142.03 1 62 .001 

Family structure 48.86 5 58 .001 

Race 2.23 1 62 .141 

Number of children 4.17 2 61 .020 

Family structure x number of children 2.59 10 53 .012 

Race x family structure 7.36 5 58 .001 

Race x SES 48.97 1 62 .001 

Table E–17b. Model Parameters for the Multi-factor Logistic Model Predicting Endangerment 

Standard Emotional Maltreatment for All Black and White Children 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -5.34 0.11500 -46.28 .001 

Low SES 1.73 0.13900 12.45 .001 

Other married parents 1.40 0.24300 5.75 .001 

Unmarried parents 1.18 0.21400 5.51 .001 

Single parent with partner 1.58 0.22800 6.95 .001 

Single parent no partner 0.65 0.11600 5.59 .001 

No parent present 0.36 0.39900 0.91 .366 

Black 0.50 0.15700 3.20 .002 

1 child -0.39 0.17200 -2.29 .025 

3 or more children 0.41 0.14200 2.87 .006 

Other married parentsx1 child -0.01 0.38300 -0.03 .973 

Other married parentsx3 or more children -0.21 0.24400 -0.87 .388 

Unmarried parents x 1 child 0.26 0.41100 0.63 .532 

Unmarried parents x 3 or more children -0.28 0.28700 -0.99 .325 

Single parent with partner x 3 or more 

children 0.04 0.39700 0.09 .926 

Single parent with partner x 3 or more 

children -0.28 0.29700 -0.95 .346 

Single parent no partner x 3 or more 

children 0.75 0.32100 2.35 .022 

Single parent no partner x 3 or more 

children 0.30 0.25000 1.20 .235 

No parent present x 1 child 0.14 0.50100 0.29 .775 

No parent present x 3 or more children -0.43 0.36000 -1.20 .237 

E-23
 
Table E–17b. Continued 


 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Other married parents x Black -0.54 0.23500 -2.32 .024 

Unmarried parents x Black 0.92 0.32700 2.82 .006 

Single parent with partner x Black 0.76 0.29600 2.58 .012 

Single parent no partner x Black -0.46 0.23000 -2.00 .050 

No parent present x Black 0.09 0.37100 0.23 .818 

Black x low SES -0.91 0.13000 -7.00 .001 

E-24
 
 


 

Table E–18a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Endangerment 

Standard Emotional Maltreatment for Black and White Children Living With Parents 

Test F value Numerator df 

Denominator df p≤

Overall fit 448.37 55 9 .001 

SES 73.36 1 63 .001 

Family structure 38.62 4 60 .001 

Race 0.90 1 63 .347 

Number of children 6.51 2 62 .003 

Parent’s employment 11.21 2 62 .001 

Child’s age 1.49 2 62 .232 

SES x parent’s employment 13.78 2 62 .001 

Family structure x number of children 2.44 8 56 .024 

Family structure x parent’s employment 6.09 8 56 .001 

Race x family structure 6.61 4 60 .001 

Race x SES 23.17 1 63 .001 

Number of children x parent’s 

employment 4.27 4 60 .004 

Family structure x child’s age 2.15 8 56 .045 

Child’s age x parent’s employment 2.72 4 60 .038 

Family structure x SES 16.66 4 60 .001 

Table E–18b. Model Parameters for the Multi-factor Logistic Model Predicting Endangerment 

Standard Emotional Maltreatment for Black and White Children Living With Parents 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -5.84 0.14200 -41.27 .001 

Low SES 2.48 0.14100 17.56 .001 

Other married parents 1.70 0.24300 7.01 .001 

Unmarried parents 2.58 0.38100 6.78 .001 

Single parent with partner 2.71 0.22100 12.28 .001 

Single parent no partner 1.56 0.18800 8.27 .001 

Black 0.32 0.19000 1.67 .100 

1 child -0.29 0.18900 -1.55 .126 

3 or more children 0.19 0.15100 1.26 .212 

Any parent unemployed 0.57 0.24800 2.29 .026 

Parent(s) not in labor force 1.85 0.36600 5.05 .001 

Birth-5 years 0.02 0.17300 0.14 .886 

6-11 years 0.37 0.14600 2.52 .014 

Low SES x any parent unemployed -0.20 0.21100 -0.94 .350 

E-25
 
 

 


 

Table E–18b. Continued 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Low SES x parent(s) not in labor force -1.12 0.21700 -5.18 .001 

Other married parents x 1 child -0.04 0.40000 -0.11 .914 

Other married parents x 3 or more children -0.16 0.24500 -0.64 .524 

Unmarried parents x 1 child 0.27 0.40600 0.67 .509 

Unmarried parents x 3 or more children -0.16 0.27700 -0.57 .573 

Single parent with partner x 1 child -0.06 0.41100 -0.14 .891 

Single parent with partner x 3 or more 

children -0.08 0.28900 -0.29 .777 

Single parent no partner x 1 child 0.64 0.33600 1.92 .059 

Single parent no partner x 3 or more 

children 0.50 0.24300 2.07 .042 

Other married parents x any parent 

unemployed -0.68 0.42000 -1.63 .108 

Other married parents x parent(s) not in 

labor force -0.76 0.30200 -2.52 .014 

Unmarried parents x any parent 

unemployed -0.09 0.32700 -0.27 .788 

Unmarried parents x parent(s) not in labor 

force -1.36 0.37900 -3.59 .001 

Single parent with partner x any parent 

unemployed -0.17 0.34600 -0.50 .620 

Single parent with partner x parent(s) not 

in labor force -1.46 0.28600 -5.12 .001 

Single parent no partner x any parent 

unemployed -0.53 0.30900 -1.70 .094 

Single parent no partner x parent(s) not in 

labor force -1.02 0.23700 -4.31 .001 

Other married parents x Black -0.47 0.24400 -1.92 .060 

Unmarried parents x Black 0.81 0.35500 2.29 .026 

Single parent with partner x Black 0.76 0.29500 2.57 .013 

Single parent no partner x Black -0.43 0.22300 -1.91 .060 

Black x low SES -0.66 0.13800 -4.81 .001 

1 child x any parent unemployed -0.33 0.27700 -1.19 .238 

3 or more children x parent(s) not in labor 

force 0.03 0.28800 0.12 .907 

3 or more children x any parent 

unemployed 0.43 0.16400 2.62 .011 

3 or more children x parent(s) not in labor 

force -0.29 0.24600 -1.17 .245 

Other married parents x birth-5 years 0.02 0.50700 0.03 .973 

E-26
 

 

Table E–18b. Continued 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Other married parents x 6-11 years -0.22 0.22600 -0.98 .332 

Unmarried parents x birth-5 years -0.93 0.38900 -2.38 .020 

Unmarried parents x 6-11 years -0.83 0.42900 -1.93 .058 

Single parent with partner x birth-5 years -0.53 0.36000 -1.47 .147 

Single parent with partner x 6-11 years -0.41 0.28800 -1.43 .156 

Single parent no partner x birth-5 years -0.32 0.25700 -1.23 .224 

Single parent no partner x 6-11 years -0.57 0.16600 -3.42 .001 

Birth-5 years x any parent unemployed 0.02 0.19500 0.11 .917 

Birth-5 years x parent(s) not in labor force 0.81 0.31500 2.56 .013 

6-11 years x any parent unemployed 0.06 0.21000 0.30 .765 

6-11 years x parent(s) not in labor force 0.56 0.21700 2.60 .012 

Other married parents x low SES -0.29 0.27600 -1.05 .299 

Unmarried parents x low SES -1.12 0.37100 -3.03 .004 

Single parent with partner x low SES -1.40 0.23500 -5.96 .001 

Single parent no partner x low SES -1.16 0.17900 -6.48 .001 

E-27
 
Table E–19b. Model Parameters for the Multi-factor Logistic Model Predicting Endangerment 

Standard Physical Neglect for All Black and White Children 

 


 

Table E–19a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Endangerment 

Standard Physical Neglect for All Black and White Children 

Test F value Numerator df 

Denominator df p≤

Overall fit 95.56 27 36 .001 

SES 101.46 1 62 .001 

Family structure 28.54 5 58 .001 

Number of children 13.38 2 61 .001 

Race 4.47 1 62 .039 

Child’s age 1.17 2 61 .317 

Race x SES 13.52 1 62 .001 

Family structure x child’s age 3.12 10 53 .003 

Family structure x SES 29.29 5 58 .001 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.50 0.24400 -26.68 .001 

Low SES 3.08 0.18900 16.27 .001 

Other married parents 1.24 0.30400 4.06 .001 

Unmarried parents 2.88 0.33500 8.58 .001 

Single parent with partner 2.26 0.36900 6.11 .001 

Single parent no partner 1.85 0.22100 8.37 .001 

No parent present 2.10 0.39000 5.39 .001 

1 child 0.09 0.17000 0.53 .601 

3 or more children 0.59 0.13100 4.48 .001 

Black 0.06 0.19500 0.30 .766 

Birth-5 years 0.54 0.23900 2.24 .029 

6-11 years 0.61 0.30500 2.01 .049 

Black x low SES -0.73 0.19900 -3.68 .001 

Other married parents x birth-5 years -0.45 0.40300 -1.12 .268 

Other married parentsx6-11 years -0.33 0.28800 -1.14 .260 

Unmarried parents x birth-5 years -1.38 0.36100 -3.81 .001 

Unmarried parentsx6-11 years -1.19 0.53900 -2.20 .031 

Single parent with partner x birth-5 years -0.10 0.33400 -0.30 .765 

Single parent with partner x 6-11 years 0.12 0.30900 0.39 .699 

Single parent no partner x birth-5 years -0.13 0.26400 -0.48 .630 

Single parent no partner x 6-11 years -0.29 0.30600 -0.94 .352 

No parent present x birth-5 years -0.29 0.38800 -0.75 .457 

E-28
 
Table E–19b. Continued 


 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

No parent present x 6-11 years -0.50 0.40400 -1.25 .216 

Other married parents x low SES -0.83 0.21900 -3.78 .001 

Unmarried parents x low SES -1.62 0.51200 -3.16 .002 

Single parent with partner x low SES -1.96 0.24400 -8.03 .001 

Single parent no partner x low SES -1.58 0.17300 -9.12 .001 

No parent present x low SES -2.57 0.31600 -8.13 .001 

E-29
 
 


 

Table E–20a. Model-fit Statistics for the Multi-factor Logistic Model Predicting Endangerment 

Standard Physical Neglect for Black and White Children Living With Parents 

Test F value Numerator df 

Denominator df p≤

Overall fit 191.43 35 31 .001 

SES 37.09 1 65 .001 

Family structure 12.69 4 62 .001 

Child’s age 1.80 2 64 .174 

Number of children 13.71 2 64 .001 

Parent’s employment 40.92 2 64 .001 

Race 6.31 1 65 .014 

SES x parent’s employment 36.96 2 64 .001 

Race x SES 14.22 1 65 .001 

Family structure x parent’s employment 2.46 8 58 .023 

Family structure x child’s age 3.52 8 58 .002 

Family structure x SES 21.56 4 62 .001 

Table E–20b. Model Parameters for the Multi-factor Logistic Model Predicting Endangerment 

Standard Physical Neglect for Black and White Children Living With Parents 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Intercept -6.66 0.27900 -23.84 .001 

Low SES 3.05 0.20700 14.78 .001 

Other married parents 1.11 0.34000 3.26 .002 

Unmarried parents 2.66 0.37200 7.15 .001 

Single parent with partner 2.28 0.37500 6.07 .001 

Single parent no partner 1.80 0.25500 7.06 .001 

Birth-5 years 0.55 0.24000 2.27 .026 

6-11 years 0.61 0.30700 2.00 .050 

1 child 0.05 0.18900 0.29 .774 

3 or more children 0.61 0.13400 4.52 .001 

Any parent unemployed 0.88 0.24500 3.59 .001 

Parent(s) not in labor force 2.42 0.36300 6.67 .001 

Black 0.06 0.19100 0.29 .771 

Low SES x any parent unemployed -0.48 0.30700 -1.57 .120 

Low SES x parent(s) not in labor force -1.66 0.20000 -8.29 .001 

Black x low SES -0.82 0.21600 -3.77 .001 

Other married parents x any parent 

unemployed 0.21 0.45400 0.45 .652 

Other married parents x parent(s) not in 

labor force 0.06 0.38200 0.17 .867 

E-30
 

 

Table E–20b. Continued 

Parameter 

Parameter 

Estimate 

Standard 

Error of 

Estimate Test for h0: p≤

Unmarried parents x any parent 

unemployed 0.60 0.44100 1.36 .179 

Unmarried parents x parent(s) not in labor 

force -0.98 0.43300 -2.27 .027 

Single parent with partner x any parent 

unemployed -0.06 0.28600 -0.20 .842 

Single parent with partner x parent(s) not 

in labor force -1.01 0.56500 -1.78 .079 

Single parent no partner x any parent 

unemployed 0.02 0.29900 0.06 .951 

Single parent no partner x parent(s) not in 

labor force -0.73 0.38500 -1.90 .062 

Other married parents x birth-5 years -0.47 0.38800 -1.21 .232 

Other married parents x 6-11 years -0.32 0.29200 -1.10 .278 

Unmarried parents x birth-5 years -1.40 0.38700 -3.62 .001 

Unmarried parents x 6-11 years -1.11 0.53900 -2.07 .042 

Single parent with partner x birth-5 years -0.12 0.34700 -0.35 .730 

Single parent with partner x 6-11 years 0.11 0.32100 0.34 .734 

Single parent no partner x birth-5 years -0.16 0.27000 -0.58 .567 

Single parent no partner x 6-11 years -0.30 0.30900 -0.96 .341 

Other married parents x low SES -0.79 0.22600 -3.50 .001 

Unmarried parents x low SES -1.46 0.52100 -2.80 .007 

Single parent with partner x low SES -1.79 0.25600 -6.99 .001 

Single parent no partner x low SES -1.42 0.17400 -8.17 .001 

E-31
 

 

1 

Appendix F 

Model-Based Marginal Probabilities and 95%-Confidence Intervals for Race-Related 

Findings for all Black and White Children 

Table F–1. Model-based Marginal Probabilities for the Race by SES Interaction Effect on Harm 

Standard Physical Abuse of All Black and White Children 

SES 

Black Children White Children 

Estimated p 

(95% C.I.) 

Estimated p 

(95% C.I.) 

Low .0062 

(.0041–.00083) 

.0053 

(.0040–.0066) 

Not Low .0039 

(.0030–.0048) 

.0021 

(.0020–.0021) 

F-1
 

Table F–2. Model-based Marginal Probabilities for the Race by SES Interaction Effect on All 

Endangerment Standard Maltreatment of All Black and White Children 

SES 

Black Children White Children 

Estimated p 

(95% C.I.) 

Estimated p 

(95% C.I.) 

Low .0520 

(0–.1540) 

.0557 

(0–.1648) 

Not Low .0322 

(0–0.0954) 

.0155 

(0–0.0458) 
Table F–3. Model-based Marginal Probabilities for the Race by Family Structure Interaction 

Effect on All Endangerment Standard Maltreatment of All Black and White Children 

Family Structure 

Black Children White Children 

Estimated p 

(95% C.I.) 

Estimated p 

(95% C.I.) 

Married Biological Parents .0217 

(.0158–.0275) 

.0257 

(.0199–.0315) 

Other Married Parents .0360 

(.0287–.0434) 

.0496 

(.0336–.0656) 

Unmarried Parents .0576 

(.0361–.0792) 

.0347 

(.0264–.0430) 

Single Parent with Partner .0912 

(.0534–.1291) 

.0470 

(.0329–.0611) 

Single Parent No Partner .0250 

(.0149–.0351) 

.0369 

(.0282–.0456) 

No Parent Present .0212 

(.0125–.0298) 

.0194 

(.0149–.0240) 

Table F–4. Model-based Marginal Probabilities for the Race by SES Interaction Effect on 

Endangerment Standard Physical Abuse of All Black and White Children 

 


 

SES 

Black Children White Children 

Estimated p 

(95% C.I.) 

Estimated p 

(95% C.I.) 

Low .0096

 (.0071–.0122) 

.0073 

(.0055–.0091) 

Not Low 0.0064 

(.0046–.0083) 

0.0026 

(.0020–.0031) 

F-2
 
 

Table F–5. Model-based Marginal Probabilities for the Race by Family Structure Interaction 

Effect on Endangerment Standard Physical Abuse of All Black and White Children 


 

Family Structure 

Black Children White Children 

Estimated p 

(95% C.I.) 

Estimated p 

(95% C.I.) 

Married Biological Parents .0036 

(.0019–.0052) 

.0029 

(.0019–.0040) 

Other Married Parents .0124 

(.0082–.0165) 

.0103 

(.0065–.0142) 

Unmarried Parents .0123 

(.0056–.0190) 

.0035 

(0–.0105) 

Single Parent with Partner .0124 

(.0079–.0169) 

.0065 

(0–.0184) 

Single Parent No Partner .0038 

(.0026–.0050) 

.0037 

(.0029–.0045) 

No Parent Present .0038 

(.0022–.0053) 

.0026 

(.0013–.0039) 

Table F–6. Model-based Marginal Probabilities for the Race by SES Interaction Effect on 

Endangerment Standard Emotional Maltreatment of All Black and White Children 

SES 

Black Children White Children 

Estimated p 

(95% C.I.) 

Estimated p 

(95% C.I.) 

Low .0266 

(.0189–.0343) 

.0283 

(.0226–.0340) 

Not Low .0125 

(.0078–.0171) 

.0054 

(.0041–.0067) 

F-3
 
Table F–7. Model-based Marginal Probabilities for the Race by Family Structure Interaction 

Effect on Endangerment Standard Emotional Maltreatment of All Black and White 

Children 


 

Family Structure 

Black Children White Children 

Estimated p 

(95% C.I.) 

Estimated p 

(95% C.I.) 

Married Biological Parents .0055 

(.0036–.0073) 

.0067 

(.0046–.0087) 

Other Married Parents .0115 

(.0081–.0148) 

.0229 

(.0156–.0302) 

Unmarried Parents .0384 

(.0181–.0587) 

.0195 

(.0146–.0244) 

Single Parent with Partner .0452 

(.0297–.0607) 

.0267 

(.0200–.0334) 

Single Parent No Partner .0092 

(.0046–.0138) 

.0171 

(.0120–.0223) 

No Parent Present .0074 

(.0032–.0116) 

.0083 

(.0053–.0113) 

Table F–8. Model-based Marginal Probabilities for the Race by SES Interaction Effect on 

Endangerment Standard Physical Neglect of All Black and White Children 

SES 

Black Children White Children 

Estimated p 

(95% C.I.) 

Estimated p 

(95% C.I.) 

Low .0170 

(.0125–.0214) 

.0319 

(.0246–.0391) 

Not Low .0081 

(.0053–.0109) 

.0077 

(.0048–.0105) 

F-4