Does a Standardized Spanish Translation of USDA’s U.S. 

Household Food Security Survey Module Affect Differential Item 

Functioning Between Hispanic and White Non-Hispanic 

Households? 

Matthew P. Rabbitt*1 and Alisha Coleman-Jensen1 

Economic Research Service 

U. S Department of Agriculture 

1400 Independence Avenue, Southwest 

Mailstop 1800 

Washington, DC 20250-0002 

*Contact Author: matthew.rabbitt@ers.usda.gov 

Phone: (202)-694-5593 

Fax: (202)-245-4779 

Proceeding of the 2015 Federal Committee on Statistical Methodology (FCSM) Research Conference 

Abstract 

This paper uses data from the 2009-2014 CPS-FSS to estimate difference-in-difference Rasch and logistic regression 

models of food security to examine whether the implementation of a standardized Spanish translation of the 

Household Food Security Survey Module (HFSSM) affected differential item functioning (DIF) between Hispanic 

and white, non-Hispanic households. A key assumption of the Rasch model, on which the HFSSM is based, is that 

the severity and discrimination of items are invariant across subpopulations. Violation of this assumption is referred 

to as differential item function. The practical effect of DIF is that severity of food security at a given raw score may 

not be the same in two subpopulations, and prevalence estimates based on classification by raw score may give a 

biased comparison between subpopulations. Separate Rasch models are estimated for white, non-Hispanic and 

Hispanic households interviewed before and after the Spanish translation was standardized. Comparisons of the 

item-severity parameters from the Rasch models suggest three items (and one frequency follow-up) exhibited DIF: 

Food bought did not last, Cut or skipped meals, and Ate less than felt should. However, DIF was small and all items 

were classified as “A” items according to Educational Testing Service guidelines. Logistic regression model results 

for the effect on the standardized Spanish translation on items that exhibited meaningful DIF were generally 

imprecisely estimated. The practical implications of DIF were assessed using bias estimates for the prevalence of 

food insecurity and very low food security. The USDA standardized Spanish translation may have reduced the bias 

on the prevalence of food insecurity by as much as 0.16 percentage points and increased the bias on very low food 

security by as much as 0.48 percentage points. 

Keywords: food security, Hispanics, Rasch model, differential item functioning 

1

 The views expressed in this paper are those of the authors and do not necessarily reflect those of the USDA or 

Economic Research Service. The Authors gratefully acknowledge Mark Nord, Paul De Boeck, Yan Zhang, and 

audience members at the 2015 FCSM research conference for helpful comments. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                            

Introduction 

The Economic Research Service (ERS) of the U.S. Department of Agriculture (USDA) measures the incidence and 

severity of food insecurity in U.S. households with the annual Current Population Survey Food Security Supplement 

(CPS-FSS). The Household Food Security Survey Module (HFSSM), administered as a part of the supplement, 

consists of a series of 18 questions about the conditions and behaviors characterizing households having difficulty 

meeting their basic food needs. Responses to these questions are used to construct the U.S. food security scale, 

which is based on the Rasch model (Rasch, 1960). A key assumption of the Rasch model is that the severity and 

discrimination of items are invariant across subpopulations. Violation of this assumption is referred to as differential 

item functioning (DIF). The practical effect of DIF is that severity of food insecurity at a given raw score (the count 

of affirmed food-insecure items) may not be the same in two subpopulations. 

Ideally respondents to Federal surveys understand survey items and respond to those items consistently regardless of 

their characteristics, or the survey context. However, differences between households or across survey 

administrations may affect responses to survey items. This analysis examines whether and to what extent a 

standardized Spanish translation of USDA’s HFSSM affects responses between Hispanic and white, non-Hispanic 

respondents. Separate Rasch models are estimated for white, non-Hispanic households and Hispanic households 

interviewed before and after the USDA’s standardization of the Spanish translation for the HFSSM. Rasch model 

item-severity parameters were compared using tables and figures to assess the extent of DIF between white, nonHispanic and Hispanic households. Logistic regression models were estimated for items that exhibited DIF based on 

the Rasch model analysis and Education Testing Service (ETS) guidelines for classifying DIF (Zwick, 2012) to 

explore what respondent characteristics may be related to differences between white, non-Hispanic and Hispanic 

households. Bias estimates for the prevalence of food insecurity and very low food security were also calculated 

based on the Rasch model analysis. 

Background 

USDA has measured the prevalence of food insecurity in U.S. households since 1995. Food-insecure households are 

those that had difficulty at some time during the year providing enough food for all their members due to a lack of 

resources. In 2014, 14.0 percent of U.S. households were food insecure (Coleman-Jensen et al., 2015). At USDA’s 

request, the Committee on National Statistics (CNSTAT) convened an expert panel to review the food security 

measure and offer recommendations for improving the measure and food security statistics (for more information, 

see National Research Council, 2006). One recommendation from the CNSTAT panel was to conduct analysis 

“fitting models that allow for different item parameters for households with and without children for the questions 

that are appropriate for all households in order to study the possibility and effects of differential item function” 

(National Research Council, 2006, p.98). As a response to that recommendation ERS conducted research to examine 

the extent to which responses differ among population subgroups, including Hispanic and non-Hispanic respondents 

(Nord, 2012). 

The underlying measurement theory behind the HFSSM is the Rasch model. The Rasch model is part of the family 

of Item Response Theory (IRT) models that originated in educational testing. The items used to assess household 

food security (10 items for adult only households, 18 items for households with children) are ordered in terms of 

severity. A greater number of affirmative responses to the items indicates a greater level of severity of food 

insecurity. The number of affirmative responses, or raw score on the scale, is used to assign household food security 

status. When developing the food security measure and with each subsequent year of data, analyses are conducted to 

ensure that the data fit the Rasch model (single-parameter logistic IRT measurement model) and that raw score is an 

adequate indicator of food security status2

. A key characteristic of the Rasch model is that the way households 

respond to the items is dependent only on the latent trait (food security), not the characteristics of the households. As 

explained succinctly by Nord (2012): 

“The multiple-item Rasch model, on which the U.S. Household Food Security Scale is based, assumes that 

the severity and discrimination of items are invariant across subpopulations. Violation of this assumption 

between two subpopulations is described as differential item function. The underlying cause of DIF could 

2 Under the assumptions of the Rasch model the raw score is a minimal sufficient statistic for the latent trait being 

measured. 
 

 

 

 

 

 

 

 

 

 

 

 

 

                                                            

 

be either that respondents in two subpopulations understand the question to refer to different objective 

conditions, or that the way the two subpopulations experience or manage food insecurity differs so that the 

relative severity of items differs between the subpopulations. The practical effect of DIF is that severity of 

food insecurity at a given raw score may not be the same in the two subpopulations, and prevalence 

statistics based on classification by raw score may give a biased comparison between the two 

subpopulations” (Nord, 2012, p. 59). 

Nord (2012) found that DIF was present for some items between Hispanic and white, non-Hispanic households with 

children. DIF by Hispanic origin was not found for households without children. Differential item function was not 

substantial but large enough that it could introduce some bias to comparisons of food insecurity prevalence in white, 

non-Hispanic and Hispanic households. The item Could not afford balanced meals was the item with the largest 

DIF. The estimated impact of the DIF was a 0.14 percentage point downward bias in the prevalence of food 

insecurity in Hispanic relative to white, non-Hispanic households. Adjusting or correcting for the inconsistencies 

between the two populations would not affect any substantive conclusions because the prevalence of food insecurity 

in Hispanic households is substantially higher than the prevalence of food insecurity in white, non-Hispanic headed 

households. 

Although many Hispanic respondents are English speakers, one potential explanation for differences between 

Hispanic and non-Hispanic respondents is linguistic issues. As ERS investigated potential reasons for DIF between 

Hispanic and white, non-Hispanic household reference persons, we learned that multi-lingual Census interviewers 

translate survey content “on-the-fly”. In an effort to standardize the implementation of Spanish-language interviews, 

ERS worked with Census to instrument both an English and Spanish language version of the HFSSM (see Appendix 

A). This Spanish translation was first developed by Harrison and colleagues (2003) and then revised by USDA 

researchers and multi-lingual Census interviewers. The Spanish language version of the food security questionnaire 

was first implemented in CPS-FSS interviews in 2012. In 2012 and 2013, a paper copy of the Spanish translation of 

the food security questions was provided to multi-lingual Census interviewers that they could read from. The 

computer instrument of the CPS-FSS was only available in English. In 2014, the Spanish language version of the 

full Food Security Supplement questionnaire was incorporated into the computer interview instrument. Interviewers 

could use either the English or Spanish version of the interview instrument. This paper is the first analysis of 

responses obtained through this standardized translation. The motivation is to examine DIF between Hispanic and 

white, non-Hispanic households with the implementation of the Spanish-language module. 

Data 

The analyses use data from the 2009-2014 Current Population Survey Food Security Supplement (CPS-FSS). The 

CPS is the official source of government statistics on employment status and poverty. Approximately 55,000 

households are interviewed each month with data collected on labor force participation status, income, household 

demographics, and state identifiers. The CPS is representative of the state- and national-levels of the civilian, 

noninstitutionalized population after weighting. 

The Food Security Supplement is conducted as a supplement to the CPS for the Economic Research Service (ERS) 

of the U.S. Department of Agriculture (USDA). The purpose of the CPS-FSS is to estimate the prevalence and 

severity of food insecurity in U.S. households. Each year, ERS estimates national prevalence rates of food insecurity 

in its Household Food Security in the United States series (for example, see Coleman-Jensen et al., 2015). 

Households are asked questions about their food expenditures, basic food needs, and participation in public- and 

private-food assistance programs. To reduce respondent burden, households with income above 185 percent of the 

Federal poverty line3

 that showed no signs of food stress were not asked the food security questions. 

Dependent Variables 

The analyses examine responses to a series of food security questions taken from the HFSSM as dependent 

variables. The HFSSM consists of a series of 18 questions about the conditions and behaviors characterizing 

households having difficulty meeting their basic food needs. All households are asked the first 10 question about 

food needs among the households and adults. If children are present in the household, then an additional 8 questions 

3

 The Federal poverty line was $24,008 for a family of four (two adults and two children) in 2014. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                            

are asked about the food needs of children. The severity of food hardships experienced by the household ranges 

from anxiety over food running out to shortages of the amounts and kinds of foods eaten to episodes of adults and 

children (if present) going without food for an entire day. All of the questions reference the previous 12 months and 

are framed in terms of either shortages of money or affordability. For a complete listing of the English and Spanish 

versions of the food insecurity questions and the methods used to convert them into binary indicators see Appendix 

B. 

The 18 questions that comprise the HFSSM form the basis of the U.S. household food security scale. This scale 

consist of 18 items, including 8 adult and household items, 7 child items, and 3 follow up (2 adult/household items 

and 1 child item). The analyses accounted for dependencies between follow-up and base items by modeling them as 

ordered polytomous items rather than as two independent items. Analyses were restricted to the 10-item (commonly 

referred to as the adult scale) U.S. food security scale to mitigate concerns about bias due to a departure from 

unidimensionality in the food security scale due to the presence of children (Nord and Coleman-Jensen, 2014) and to 

reduce the likelihood of detecting DIF between households with and without children unrelated to the language of 

interview (Wilde, 2004; Nord, 2012). 

Independent Variables 

The logistic regression analyses include additional controls for respondent’s demographics, household 

characteristics, and household resources to explain the sources of DIF. The principle explanatory variables are an 

indicator for a Hispanic household reference person, the household’s Rasch score, and interactions with indicators 

for the time periods pre- and post-USDA standardization of the HFSSM Spanish translation, where the pre- and 

post-USDA standardization time periods are characterized by the years 2009-2011 and 2012-20144

, respectively. 

Additional control variables were included in the logistic regression models to explain sources of DIF. An indicator 

for households in which Spanish was the only language spoken by adults age 15 and older is included to control for 

linguistic differences between Hispanic and white, non-Hispanic households. The analyses also controlled for 

respondents who reported they were non-citizen immigrants and the number of years since they entered the U.S. 

interacted with the indicator for non-citizen immigrant. Citizenship status and the number of years since entry into 

the U.S. are likely highly correlated with acculturation. The analyses also include controls for the proportion of 

adults who are female (a proxy for female respondent), age of the oldest adult (and it’s square), income relative to 

the federal poverty line (and it’s square), educational attainment of the most highly educated adult in the household, 

metropolitan residence status, and region- and time- fixed effects. These controls are commonly found to be 

associated with food security status (Coleman-Jensen et al., 2015). 

Analysis Sample 

The analyses consider households with a Hispanic or white, non-Hispanic reference person and incomes below 185 

percent of the federal poverty line. The majority of households with incomes above 185 percent of the federal 

poverty line were screened out of the food security questions. Households with incomplete or missing responses to 

any of the food security questions were omitted from the analysis sample. Additionally, households with extreme 

raw scores (0 or 10) on the 10-item U.S. food security scale were omitted from the sample because households with 

these raw scores cannot be identified in the Conditional Maximum Likelihood (CML) Rasch model, resulting in a 

sample of 23,257 households. 

Households were disaggregated into three mutually exclusive and exhaustive samples for the Rasch DIF analyses 

based on Hispanic ethnicity of the household reference person and whether or not the household was interviewed 

before or after USDA standardized the HFSSM Spanish translation. The first subsample consisted of households 

with a white, non-Hispanic reference person interviewed in 2009-2014, which will serve as the control group in the 

analyses. White, non-Hispanic households were not further disaggregated into pre- and post-implementation groups 

because the food security scale for white, non-Hispanic households is relatively consistent over time and they are 

unlikely to be affected by standardization of the standardized Spanish translation. The second sample includes 

4 Additional analysis not shown examined DIF for Hispanics interviewed in 2012/2013 and 2014 because of 

differences in the implementation of the standardized Spanish translation. No substantive differences were found. 

All Hispanic interviews from 2012, 2013, and 2014 are pooled for analyses. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



households with a Hispanic reference person interviewed in 2009-2011. These households represent the pretreatment group since they include Hispanic households prior to USDA’s implementation of the standardized 

Spanish translation and will be used to establish a baseline food security scale for Hispanic households. The final 

group includes households with a Hispanic reference person interviewed in 2012-2014. Hispanic households 

interviewed in 2012-2014 would have been affected by the USDA’s implementation of the Spanish translation and 

are considered the post-treatment group. 

The final sample sizes for the Rasch analyses were 23,257 households, including 17,095 white, non-Hispanic 

households, and 3,113 and 3,049 Hispanic households interviewed before and after standardized the Spanish 

translation, respectively. 

Data on Hispanic households at all income levels interviewed in 2009-2014 are used to construct a reference 

distribution of households across all raw scores for the food insecurity and very low food security prevalence 

estimate bias calculations. The sample consisted of 24,638 Hispanic households. 

Econometric Methods 

The U.S. household food security scale is based on an IRT model known as the Rasch model (Rasch, 1960). The 

Rasch model assumes multiple observable outcomes (such as food hardships) all derive from a single underlying 

variable, such as food security. Let household i’s underlying continuous index of food insecurity be denoted by θi, 

with the property that higher values of the index correspond to greater levels of hardship. While the researcher is 

unable to observe θi directly, suppose he has j continuous indicators, Yij*

, which are related to θi such that each 

depends on the index and some random measurement error, νj. The relationship between the observable indicators 

and the underlying latent index can be expressed as 

* Y =θ +ν , (1) ij i j 

which describes a factor analytic relationship in which the food-insecurity index, θi, is the underlying factor and the 

factor loadings (discrimination parameters) are constrained to be equal across all items and normalized to one. 

Currently, the model is expressed in terms of a set of continuous indicators of food insecurity (the Yij*

’s); however, 

the U.S. food security scale consists of a series of binary variables. The Rasch model assumes the continuous 

indicators, Yij*

, are related to the binary responses of survey respondents as follows: 



* 1 if   Yij  j Yij   * , (2) 

0 if Y   

 ij j 

where δj is the severity threshold (calibration) parameter. Equation (2) specifies the same relationship between the 

latent continuous indicators and the observed categorical responses as that in standard probit and logistic models. 

The severity thresholds (δj) are estimated as part of the multivariate model and take on different values for each 

food-insecure condition. Higher values of the severity thresholds are associated with items that capture greater 

severity of food insecurity. Given equations (1) and (2), and the assumption that random measurement error (νj) 

follows a logistic distribution, the probability that household i’s respondent affirms the jth food-insecure condition is 

exp  

P Y  1| , 

i  j

  , (3) ij i j 1 exp i    j 

where exp( ) is the exponential function. 

The Rasch model assumes the errors in the responses are conditionally independent, which implies the probability of 

an affirmative response to a given food-insecure condition for a value of θi, the latent trait, does not depend on the 

response to another question. This conditional independence assumption implies the conditional probability of a 

given response vector is the product of the probabilities for each item. By stacking the household’s responses (Yij) 

into a vector, Yi, the probability of observing a given response pattern is given by 
 

 

 

 

 

 

 

                                                            

ij 1 Y ij 

J  exp      exp   j 

Y 

  



i j i  i  i i , PY y|  j     1  , (4) 

j 1 1 exp     1 exp 



   i j    i  j 

  

where j runs over the number of food-insecure conditions for each household. Assuming observations are 

independent and identically distributed, the likelihood function is the product of the probabilities of observing a 

given response pattern for all observations and can be estimated via maximum likelihood methods. Rasch models for 

the analyses were estimated via Conditional Maximum Likelihood (CML) using SAS programs developed by ERS. 

The programs model items with follow-up questions as trichotomies and account for internal screening in the 

HFSSM. 

Assessing Differential Item Functioning in the Rasch Model 

Another key assumption of the Rasch model is parameter invariance, which assumes the severity and discrimination 

of items are invariant across subpopulations. When this assumption is violated for the severity thresholds, δj, the 

model will exhibit uniform DIF, or more formally, 

δj= δj+αjG, (5) 

where G is an indicator for membership in a specific subpopulation and αj, an unknown parameter to be estimated, is 

the jth item specific effect of belonging to subpopulation group G compared to a reference subpopulation. If, after 

estimation, the αj’s are not statistically significantly different from zero, then membership in a subpopulation does 

not differentially impact the probability of affirming the food-insecurity items and the items do not exhibit DIF. 

However, if the αj’s can be distinguished from zero, then group membership explains latent food insecurity and the 

items exhibit DIF. 

While numerous methods exist for detecting DIF (i.e., logistic regression, mixed logistic regression, MantelHaenszel chi-square statistic, etc.) (De Ayala, 2013; Van den Noortgate and De Boeck, 2005), the current analyses 

use CML Rasch models, estimated separately, for white non-Hispanic households, and Hispanics households before 

and after standardization of the Spanish translation. The result of estimating Rasch models for each subsample is 

three sets of item-severity parameters and their standard errors. However, the severity parameter estimates are not 

directly comparable because of differences in scaling. The analyses adjusted for this prior to making comparisons 

using a linear transformation that equated the mean and standard deviation of the Hispanic scales to the white, nonHispanic scale. After equating the scales, estimates of the αj’s can be obtained by subtracting the severity thresholds 

(δj’s) for white, non-Hispanics households from the severity thresholds for Hispanics households. 

For the estimates of DIF to be meaningful, the differences in severity thresholds for the two groups being compared 

must be statistically significantly different from zero. To test for the presence of differences, the analyses use 

Welch’s t-test, which is calculated as follows for item j. 

δ - δ j, Hispanic j, WNH t= , (6) 

where δj, Hispanic and δj, WNH are the severity thresholds for Hispanic and white, non-Hispanic households, respectively. 

The corresponding standard errors for the severity thresholds are given by SEj, Hispanic and SEj, WNH. 

Even small differences in severity parameters can be detected for subpopulations if sample sizes are large enough. 

Because of this, the National Center for Education Statistics (NCES) and ETS5

 have adopted classification rules 

based on (Petersen, 1988) to help researchers identify meaningful DIF. Items are classified into one of three 

categories (A, B, and C) based on the magnitude and statistical significance of the estimate of DIF. An “A” item is 

5

 For a review of DIF classification procedures see Zwick (2012). 

   

j 

SE + SE j, Hispanic j, WNH 
 

 

 

 

 

where θi is the household’s food insecurity measure, Gi is an indicator for Hispanic group membership, and Xi is a 

matrix of control variable that includes respondent- and household-characteristics and region fixed effects, including 

a constant, and an error term, ei, which is distributed logistically. The presence of uniform DIF may occur if, α, the 

group membership parameter is nonzero. Non-uniform DIF may be detected if an interaction between the group 

membership indicator (G) and the household’s food insecurity measure (θi) is nonzero. 

 

 

 

 

 

 

where i, j, and t are indices for the household, item, and year. The dummy variable Postt is equal to 1 for households 

surveyed in 2012-2014. Gi and Xi are defined above, τt represents year fixed-effects, and eijt is the error term. The 

                                                            

 

one in which the estimate of DIF is not significant at the 5 percent level or better or the magnitude of the DIF 

estimate is smaller than 0.43 logits6

 in absolute value. Items in category “A” exhibit no or negligible DIF. For an 

item to be classified as a “C” item, the estimate of DIF must be statistically significantly greater than 0.43 logits in 

absolute value at the 5 percent level or better and are larger than 0.64 logits in absolute value. These items indicate

moderate or large DIF. Other items are categorized as “B” items, which are greater than 0.43 logits, but less than 

0.64 logits, in absolute value and statistically distinguishable from zero. 

Standards for identifying meaningful magnitudes of DIF vary from 0.4 to 0.6 logits (Draba, 1977; Longford et al., 

1993; Scheuneman and Subhiyah, 1998; Wang, 2000; Paek, 2002; Elder et al., 2003). For the purposes of this 

analysis, meaningful DIF is defined by the ETS classification rules. 

Explaining Differential Item Functioning 

Logistic regression models are used in the DIF literature to detect and explain DIF. Under this approach, household 

i’s response to the jth food-insecurity condition is modeled as 

1 if + G +    +X +e  0 i i i i i Yij   , (7) 

 0 otherwise 

The sources of uniform- and non-uniform-DIF may be explained in this framework using a series of logistic 

regression models. The researcher will first estimate a baseline model that only includes the household’s food 

insecurity measure, an indicator for Hispanic group membership, and their interaction. A second model is then 

estimated that builds on this baseline model by adding controls for the household respondent’s demographics and 

household characteristics. Any changes in the Hispanic group membership variable and it’s interaction with the 

household’s food insecurity measure between the baseline and adjusted model indicate proportion of variation in 

uniform- and non-uniform-DIF that is explained by these additional characteristics. 

The researcher must overcome two challenges to estimate the logistic model specified in equation (7). First, the 

food insecurity measure (θi) is an unobservable construct. A common solution to this problem is to use the 

household’s raw food insecurity score (i.e., count of affirmed items.) as a proxy variable. However, this approach 

may be affected by multicollinearity. Therefore, the analyses use the household’s Rasch score. 

The second challenge that must be overcome in this analysis is the fact that Hispanics self-select into the 

standardized HFSSM Spanish translation because of observable and unobservable differences between Hispanic 

households or Census interviewers elect to administer the standardized translation for reasons that are unobservable 

to the researcher. The current analyses addresses this potential source of bias by implementing a difference-indifferences logistic regression model. Under this new parameterization, equation (7) is now 

1 if  G Post +   G Post θ + Post + +τ θ +α G +γ θ G +X β +e >0 1 i t 1 i t i t i 0 i 0 i 1 ij t t ijt Y=  , (8) ijt  0 otherwise 

6

 The classification procedures proposed by Petersen (1988) and used the National Center for Education Statistics 

and Educational Testing Service use delta units because it uses the Mantel-Haenszel delta difference. One logit is 

equal to 2.35 deltas. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

effect of administering the USDA standardized HFSSM translation will be unbiased as long as unobservable 

characteristics are time invariant. 

Estimating the Effect of Differential Item Functioning on Food Security Prevalence Estimates 

The extent of bias due to DIF between Hispanic and white, non-Hispanic households on the prevalence estimates of 

food insecurity and very low food security was assessed based on the methodology outlined in Nord (2012), which 

used the item severity parameters and household measures estimated separately for the populations of interest 

(Hispanic and white, non-Hispanic households in the current analysis) and then adjusted to a common scale using a 

linear transformation. 

Nord calculated the bias on the prevalence of food insecurity (and very low food security) using a multistep iterative 

procedure. The steps for this procedure are as follows. 

1. A reference distribution across food security raw scores was calculated using data for Hispanic households, 

including extreme scores (0 and 10) on the 10-item food security scale and all income levels. The observed 

(measured) prevalence of food insecurity (very low food security) in the reference distribution was 

calculated by determining the percentage of the sample with a raw score of 3 (6) or higher. 

2. An initial value for the threshold for food insecurity (very low food security) was selected using the 

midpoint of the mean severity of raw scores 2 and 3 (5 and 6). 

3. The proportion of households in each raw score group with “true” severity higher than the initial value of 

the threshold (i.e., truly food insecure (very low food secure) was calculated using the household 

parameters for white, non-Hispanic households and a normal distribution with mean and standard deviation 

corresponding to those estimated for that raw score group. Households in raw score group 0 were assumed 

to be food secure and households parameters for households with raw score 10 were calculated as if the raw 

score was 9.5. 

4. The proportion of “truly” food insecure (very low food secure) in each raw score group were weighted by 

the proportion of the reference distribution with that raw score. 

5. The threshold was then iteratively adjusted (repeating steps 3-5) until the “true” prevalence equaled the 

observed prevalence, which is the threshold at which there is zero measurement bias. 

6. Step 3 was repeated for Hispanic households using their household parameters. 

7. The proportion of “truly” food insecure (very low food secure) in each raw score group were weighted by 

the proportion of the reference distribution with that raw score. The weighted sum across raw scores 

represented the “true” prevalence of food insecurity (very low food security) in Hispanic households using 

the threshold at which measurement bias was zero for white, non-Hispanic households. 

8. The difference between the observed prevalence of food insecurity (very low food security) and the true 

prevalence of food insecurity (very low food security) in Hispanic households is an estimate of the bias of 

measured food insecurity (very low food security) in Hispanic households relative to white, non-Hispanic 

households. 

The analyses employed the procedure above to determine how standardization of the HFSSM Spanish translation 

affected food insecurity and very low food security prevalence estimates. Bias for the prevalence of food insecurity 

and very low food security were calculated, separately, using the samples of Hispanic households before and after 

standardization of the Spanish translation. 

Results 

Item-severity parameters from the CML Rasch models, estimated separately for white, non-Hispanic and Hispanic 

households before and after USDA standardized the HFSSM Spanish translation are listed in Table 1. The top panel 

contains item-severity parameters while the bottom panel lists the mean and standard deviation of the estimated 10-

item food security scale. Column one reports Rasch model estimates for the samples of white, non-Hispanic 

households interviewed in 2009-2014. The remaining columns contain Rasch model item-severity parameter 

estimates for the samples of Hispanic households who were interviewed before and after the USDA implemented 

the standardized Spanish translation of the HFSSM. 

[Table 1 about here.] 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

The relative severity of the items in the 10-item U.S. food security scale is as expected and similar for white, nonHispanic and Hispanic households. Comparisons of the item-severity parameters between white, non-Hispanic and 

Hispanics households suggest, Worried food would run out, Food bought didn’t last, Adult cut or skipped meals (1 

or 2 vs. 0), Adult cut or skipped meals (2 vs. 0 or 1), and Ate less than felt should differed in severity between the 

two groups, regardless of which Hispanic household sample was used (pre- and post-USDA standardization). All 

other differences in item-severity parameters cannot be statistically distinguished from zero. When factoring in the 

classification guidelines proposed by ETS and adopted by NCES, the differences in item-severity parameters 

between white, non-Hispanic and Hispanic households interviewed before standardization of the Spanish translation 

fall in the “A” item grouping. Items in the “A” group typically exhibit little or no meaningful level of DIF. The 

items Worried food would run out and Food bought did not last were relatively more severe while the items Adult 

cut or skipped a meal (1 or 2 vs. 0), Adult cut or skipped a meal (2 vs. 0 or 1), and Ate less than felt should were less 

severe for white, non-Hispanics compared to Hispanics interviewed before standardization. 

The classification of differences in item-severity parameters between white, non-Hispanic and Hispanic households 

interviewed after the USDA standardized the Spanish translation generally followed the patterns described above for 

white, non-Hispanics and Hispanics interviewed before the USDA standardization of the Spanish translation, with 

one exception. The difference in the item-severity parameter of Adult cut or skipped meals (1 or 2 vs. 0) for white, 

non-Hispanics and Hispanics interviewed after the USDA standardized the Spanish translation is now classified as a 

“B” item, rather than an “A” item, however, the difference-in-difference (i.e., change in DIF before and after 

standardization) for this item is not statistically significantly different from zero. Items within this group are 

characterized by weak DIF. 

The effect of the USDA standardization on DIF between white, non-Hispanic and Hispanic households is assessed 

in the far right column of Table 1. This column represents the difference in DIF before and after the USDA 

standardized the Spanish translation. Intuitively, this is equivalent to a difference-in-difference Rasch model where 

the control group (white, non-Hispanics) is assumed to be unaffected by the treatment (the USDA’s standardization 

of the Spanish translation). While this may appear to be a strong assumption, the U.S. food security scale is 

remarkably consistent over time, especially for white, non-Hispanic households. The item Food bought did not last 

is the only item where the difference in DIF was statistically significant, albeit at the 10 percent level. The difference 

in DIF estimate for this item suggests DIF increased by 0.13 logits in absolute magnitude and decreased in severity 

relative to white, non-Hispanics as a result of the USDA’s standardization. Even with this increase in DIF the item 

remains classified as an “A” item, albeit within one standard deviation of being considered a “B” item. 

The bottom panel of Table 1 presents the mean and standard deviation of the 10-item food security scale for white, 

non-Hispanic and Hispanic households. The standard deviations for Hispanics interviewed before and after the 

USDA standardized the Spanish translation are 17 percent and 15 percent larger, respectively, than in white, nonHispanic households when all models were estimated on a logistic metric (discrimination parameters equal to 1.0). 

This indicates a stronger fit of the data to the Rasch model for Hispanic households, that is, moderately higher 

average discrimination of items. Parameters were adjusted for this difference prior to comparison using a linear 

transformation. 

Items may differ in severity and/or discrimination between white, non-Hispanic and Hispanic households. Any 

potential concerns about DIF in discrimination (non-uniform DIF) are relieved by item-infit statistics. Item 

discrimination estimates may be obtained by estimating 2-parameter Rasch models, however, the current analysis 

does not consider these models because the aim of this analysis was to keep the modelling strategies as close as 

possible to the existing methodology used to construct the U.S. food security scale. Item-infit statistics provide a 

proxy (although inversely) for item discrimination. Table 2 presents item-infit statistics from CML Rasch models 

estimated separately for white, non-Hispanic and Hispanic households interviewed before and after USDA 

standardized the Spanish translation of the HFSSM. 

[Table 2 about here.] 

Item-infit statistics were generally similar for white, non-Hispanic and Hispanic households, regardless of which 

Hispanic sample was used. Ideally, all item-infit statistics should be 1.0, indicating all items discriminate equally 

well, as assumed by the Rasch model. In practice, item-infit statistics ranging from 0.7 to 1.3 are generally 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

                                                            

 

considered to indicate an acceptable fit of the Rasch model. Household’s responses generally fit the Rasch model 

well, with the majority of item-infit statistics ranging from 0.9 to 1.3, with the exception of Adult cut or skipped 

meals (overall), which had an item-infit of 1.39. Because the item-infit statistic is a chi-square-like statistic, higher 

values indicate the item is more weakly (i.e., poorly discriminates) associated with latent food insecurity. 

Difference-in-difference logistic regression models for food insecurity items that exhibited meaningful DIF were 

estimated to assess the extent to which the standardized Spanish translation and other respondent- and householdcharacteristics explain DIF between white, non-Hispanic and Hispanic households. Table 3 contains logistic 

regression coefficients and standard errors from models for the items Food bought did not last, Adult cut or skipped 

meals (1 or 2 vs. 0), Adult cut or skipped meals (2 vs. 0 or 1)7

, and Ate less than felt should. The top panel contains 

estimates for uniform DIF coefficients, while the middle and bottom panels list estimates for non-uniform DIF and 

respondent/household characteristic coefficients, respectively. Unadjusted models include controls for uniform- and 

non-uniform-DIF and time fixed effects. The adjusted models build upon the unadjusted models by adding controls 

for respondent and household characteristics (see the data section for a listing of the control variables), and region 

fixed effects. 

[Table 3 about here.] 

Uniform DIF, represented by the indicator for a household with a Hispanic reference person, was detected for all 

items and all specifications. Households headed by a Hispanic reference person appear to be less likely to affirm 

each item compared to households headed by white, non-Hispanics. For each item, the coefficient on Hispanic 

reference person interacted with the post-USDA standardization time period is imprecisely estimated. The second 

panel lists coefficients and standard errors that control for non-uniform DIF. Non-uniform DIF is captured by 

including a control for the interaction between the indicator for households with a Hispanic reference person and the 

household’s Rasch score. Non-uniform DIF was detected for all items with the exception of Adult cut or skipped 

meals (1 or 2 vs. 0). Since the USDA standardized Spanish translation may also have an effect on non-uniform DIF, 

the analyses included an interaction between Hispanic reference person, the post-USDA standardization time period, 

and the household’s Rasch score, which was insignificant for all items and specifications, with the exception of the 

item Ate less than felt should. After controlling for respondent- and household- characteristics, the USDA 

standardized Spanish translation was associated with a reduction in the probability of affirming Ate less than felt 

should at different values of the household’s Rasch score compared to white, non-Hispanic households. 

Controlling for respondent and household characteristics increased uniform DIF between Hispanics and white, nonHispanics by 14.8 percent for the item Food bought did not last, while decreasing DIF for Adult cut or skipped 

meals (1 or 2 vs. 0), Adult cut or skipped meals (2 vs. 0 or 1), and Ate less than felt should by 17.4 percent, 5.1 

percent, and 1.9 percent, respectively. In the cases of Adult cut or skipped meals (1 or 2 vs. 0) and Ate less than felt 

should, the decline in the uniform DIF was accounted for mainly by educational attainment of the highest educated 

person in the household. For Food bought did not last, the increase in uniform DIF was almost entirely accounted 

for by educational attainment of the highest educated adult and households with children. The decline in uniform 

DIF for Adult cut or skipped meals (2 vs. 0 or 1) was strongly associated with the female headed households. 

Differences in items severity for Food bought did not last, Cut or skipped meals, and Ate less than felt should for 

white, non-Hispanic and Hispanic households may bias the prevalence of food insecurity and very low food 

security. The bias for food insecurity prevalence estimates is expected to be upwards because of the lower severity 

of Food bought did not last in Hispanic households relative to white, non-Hispanic households (Figure 1). The 

USDA’s classification system for a household’s food insecurity (very low food security) status is based on a raw 

score of three or more (six or more). The items in question are the second, fourth, fifth, and sixth on the U.S. food 

security scale in order of severity. 

[Figure 1 about here.] 

The prevalence of very low food security is expected to be biased downwards for Hispanic households relative to 

white, non-Hispanic households because of the higher severity of Cut or skipped meals and Ate less than felt should 

7 Ordered logistic models were also estimated for Adult cut or skipped meals to model the dependencies between the 

base and follow-up question, however, the results produced very similar results. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

in Hispanic households relative to white, non-Hispanic households. Two of the items in question, Cut or skipped 

meals and Ate less than felt should, are close to the threshold and will likely be the strongest influences on the bias 

for very low food security prevalence estimates. These items are the fourth, fifth, and sixth on the U.S. food security 

scale based on severity. 

The estimated bias on the prevalence of food insecurity is in the opposite direction in spite of the lower severity of 

Food bought did not last, regardless of which Hispanic household parameters were used. The bias analysis was 

conducted based on the mean and standard deviation of household measures for Hispanic households interviewed 

before and after standardization of the Spanish translation. For Hispanic households interviewed before the Spanish 

translation was standardized, the prevalence of food insecurity was biased downwards by 0.62 percentage points 

(2.8 percent) for Hispanic households relative to white, non-Hispanic households. The downwards bias on the 

prevalence of food insecurity was smaller for Hispanics interviewed after standardization. Specifically, the 

prevalence of food insecurity was downwards biased by 0.46 percentage points (2.06 percent) for Hispanic 

households relative to white, non-Hispanics. Differencing the bias estimates using the household measures of 

Hispanics interviewed before and after standardization suggests the standardization of the Spanish translation may 

have reduced the bias on food insecurity induced by DIF between Hispanics and white, non-Hispanics by as much as 

0.16 percentage points. 

Bias estimates on the prevalence of very low food security are consistent with expectations. When the household 

measures is used for Hispanics interviewed before standardization of the Spanish interview, the prevalence of very 

low food security is downwards biased by 0.38 percentage points (4.9 percent). However, the downwards bias on 

very low food security roughly doubles to 0.86 percentage points (11.2 percent) when using household measures 

from Hispanics interviewed after standardization. While at face value the standardized Spanish translation appears to 

bias very low food insecurity prevalence estimates, these findings are similar to the results reported in Nord (2012). 

In his analysis he estimated that the measured prevalence of very low food security for Hispanic households with 

children was biased downwards by 0.72 percentage points or 14 percent. After differencing the bias estimates using 

the household measures of Hispanics interviewed before and after standardization, the USDA’s standardization of 

the Spanish translation appears to have increased the bias on very low food insecurity induced by DIF between 

Hispanics and white, non-Hispanics by as much as 0.48 percentage points. 

Conclusion 

This analyses use nationally representative data from the 2009-2014 CPS-FSS to examine whether a standardized 

Spanish translation of the HFSSM affects DIF between Hispanic and white, non-Hispanic households. Comparisons 

of Rasch model item-severity parameters suggest DIF exists between Hispanic and white, non-Hispanic households. 

Small differences in item-severity parameters were detected for Worried food would run out, Food bought didn’t 

last, Adult cut or skipped meals (at the different thresholds), and Ate less than felt should, however, none of the 

items exhibited meaningful levels of DIF according to the guidelines proposed by ETS and used by NCES. Effect 

sizes of DIF for each item resulted in the majority of items being classified as “A” items. Under ETS guidelines, 

“A” items exhibit no DIF. 

The analyses employed a difference-in-difference approach to estimate the effect of the USDA’s implementation of 

a standardized Spanish translation of HFSSM on DIF between Hispanic and white, non-Hispanic households. While 

the Rasch results suggest DIF exists between Hispanics and white, non-Hispanics, differences in DIF before and 

after the standardization were imprecisely estimated for all items except Food bought did not last. For this item, 

standardization of the Spanish translation increased DIF by 0.13 logits. While standardization of the Spanish 

translation increased the effect size of DIF for this item, it remains classified as an “A” item. 

Results from the logistic models for items that exhibited meaningful DIF consistently indicated standardization of 

the Spanish translation had no effect on uniform DIF. While the standardized Spanish translation does not appear to 

have had an effect on uniform DIF, respondent- and household-characteristics explained nearly one eight and one 

fifth of DIF for Food bought did not last and Adult cut or skipped meals. Non-uniform DIF was detected in the 

logistic regression models for Hispanics relative to white, non-Hispanics households, however, standardization of 

the Spanish translation had little to no effect on non-uniform DIF for the items except for Ate less than felt should. 
 

 

 

 

 

 

 

 

While the results suggest modest DIF exists between Hispanic and white, non-Hispanic households, it is important 

to assess the practical implications of these findings. The implication of DIF on the measurement of food insecurity 

in these subpopulations appears to be rather minimal. To place this in perspective, the estimated bias on the 

prevalence of food insecurity ranges from -0.46 (2.8 percent) to -0.62 (2.1 percent) percentage points for Hispanic 

households relative to white, non-Hispanic households. The lower end estimate of bias is associated with the 

interview period after the USDA standardized the Spanish translation, and suggests standardization may have 

reduced the bias on the prevalence of food insecurity by as much as 0.16 percentage points. 

Standardization of the Spanish translation of the HFSSM has important practical effects for the measurement of very 

low food security. Bias for the prevalence of very low food security ranges from -0.38 percentage points (4.9 

percent) to -0.86 percentage points (-11.2 percent) when using the household measures for Hispanics interviewed 

before and after standardization, respectively. Bias on the prevalence of very low food security appears to have 

increased by 0.48 percentage points as a result of the USDA’s standardization of the Spanish translation. The 

increase in bias for the prevalence of very low food security is likely being caused by positive DIF for Adult cut or 

skipped meals and Ate less than felt should, which are the fourth, fifth, and sixth items on the U.S. food security 

scale and fall directly below the threshold for very low food security. Overall, these bias estimates are relatively 

small compared to the most recent prevalence estimates when one considers that 22.4 percent of all Hispanic 

households were food insecure compared to 10.5 percent of white, non-Hispanic households in 2014 (ColemanJensen et al., 2015). In that same year 6.9 percent and 4.5 percent of Hispanic and white, non-Hispanic households 

experienced very low food security, respectively. 
 

 

 

 

 

 

 

 

 

 

 

 

 

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Coleman-Jensen, Alisha, Matthew P. Rabbitt, Christian Gregory, and Anita Singh. 2015. Household Food Security 

in the United States in 2014. ERR-194. U.S. Department of Agriculture, Economic Research Service. 

De Ayala, Rafael. J. (2013). The Theory and Practice of Item Response Theory. New York, NY. Guilford 

Publications. 

Draba, R. E. (1977). The Identification and Interpretation of Item Bias. Research Memorandum, (25). 

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Kilanowski, Jill. F., and Li Lin. 2012. Rasch Analysis of US Household Food Security Survey Module in Latino 

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National Research Council. 2006. Food Insecurity and Hunger in the United States: An Assessment of the Measure. 

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Behavioral and Social Sciences and Education. Washington, DC: The National Academies Press. 

Nord, Mark. 2012. Assessing Potential Technical Enhancements to the U.S. Household Food Security Measures. 

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Nord, Mark, and Coleman-Jensen, A. (2014). Improving Food Security Classification of Households with Children. 

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Paek, I. (2002). Investigations of Differential Item Functioning: Comparisons Among Approaches, and Extension to 

a Multidimensional Context. University of California, Berkeley. 

Petersen, N. (1988). DIF Procedures for Use in Statistical Analysis. Unpublished Memorandum. 

Rasch, Georg. 1960. Studies in Mathematical Psychology: I. Probabilistic Models for Some Intelligence and 

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Scheuneman, Janice D., and Subhiyah, R. G. (1997). Evidence for the Validity of a Rasch Model Technique for 

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Van den Noortgate, Wim, and Paul De Boeck. 2005. Assessing and Explaining Differential Item Functioning Using 

Logistic Mixed Models. Journal of Educational and Behavioral Statistics, 30(4), 443-464. 

Wang, W. C. (1999). Modeling Effects of Differential Item Functioning in Polytomous Items. Journal of Applied 

Measurement, 1(1), 63-82. 
 

 

Wilde, P. E. (2004). Differential Response Patterns Affect Food-Security Prevalence Estimates for Households with 

and without Children. The Journal of Nutrition, 134(8), 1910-1915. 

Zwick, Rebecca. (2012). A Review of ETS Differential Item Functioning Assessment Procedures: Flagging Rules, 

Minimum Sample Size Requirements, and Criterion Refinement. ETS Research Report Series, 2012(1), i30. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Tables 

Table 1: CML Rasch Model Item Severity Parameters Estimated in Separate Models for Hispanic and White Non-Hispanic Households Pre- and PostUSDA Standardization of the HFSSM Spanish Translation 

Hispanic households

White nonHispanic Pre-USDA Standardized Post-USDA Standardized 

households Spanish Translation Spanish Translation 

Difference Difference 

from White from White 

Severity Severity non-Hispanic Severity non-Hispanic Difference-inItem parameter parameter households parameter households Difference 

Worried food would run out 4.01 3.77 -0.24*** 3.75 -0.26*** -0.02 

(0.067) (0.065) (0.087) 

Food bought did not last 4.97 4.74 -0.23*** 4.61 -0.36*** -0.13* 

(0.056) (0.057) (0.074) 

Could not afford balanced meals 5.07 5.10 0.03 5.00 -0.07 -0.10 

(0.055) (0.055) (0.072) 

Adult cut or skipped meals (1 or 2 vs. 0) 6.39 6.71 0.32*** 6.90 0.50*** 0.19 

(0.094) (0.097) (0.126) 

Adult cut or skipped meals (2 vs. 0 or 1) 6.84 7.03 0.19* 7.24 0.39*** 0.21 

(0.109) (0.106) (0.143) 

Ate less than felt should 6.43 6.69 0.26*** 6.80 0.37*** 0.12 

(0.059) (0.060) (0.078) 

Hungry but did not eat 8.10 8.18 0.08 8.11 0.01 -0.07 

(0.073) (0.072) (0.096) 

Lost weight 8.96 8.98 0.02 8.97 0.01 -0.01 

(0.087) (0.088) (0.116) 

Adult did not eat for whole day (1 or 2 vs. 0) 9.50 9.32 -0.18 9.22 -0.28 -0.10 

(0.191) (0.191) (0.255) 

Adult did not eat for whole day (2 vs. 0 or 1) 9.73 9.49 -0.24 9.41 -0.32 -0.08 

(0.236) (0.241) (0.391) 

Mean—all items 7.00 7.00 7.00 

Std. deviation—all items 1.90 1.90 1.90 

Discrimination parameter 1.00 1.17 1.15 

Number of cases 17,095 3,113 3,049 

Note: CML Rasch models estimated using weighted household data from the 2009-2014 CPS-FSS. Standard errors appear in parenthesis. All models were estimated on a logistic 

metric (discrimination parameter = 1.00). The discrimination parameter above for Hispanic and White, non-Hispanic households are those required to equate the standard deviation 

to be equivalent in Hispanic and White, non-Hispanic households for the purposes of that comparison. Severity parameters for the trichotomous items, Adult cut or skipped meals 

and Adult did not eat for whole day, are the “Rasch-Thurstone” or “50-percent probability” values. 

* Significant at the 0.10 level. ** Significant at the 0.05 level. *** Significant at the 0.01 level. 
 

 

 

 

 

 

 

 

 

 

 

 

 

Table 2: CML Rasch Model Item-Infit Statistics for Separate Models for Hispanic and White Non-Hispanic 

Households 

Hispanic Households 

Pre-USDA Post-USDA 

White non- Standardized Standardized 

Hispanic Spanish Spanish 

Item households Translation Translation 

Worried food would run out 0.96 1.00 0.97 

Food bought did not last 0.94 0.89 0.88 

Could not afford balanced meals 1.22 1.16 1.21 

Adult cut or skipped meals (1 vs. 0) 0.98 1.06 0.96 

Adult cut or skipped meals (2 vs. 1) 1.15 1.24 1.30 

Adult cut or skipped meals (overall) 1.15 1.39 1.31 

Ate less than felt should 0.75 0.70 0.76 

Hungry but did not eat 0.78 0.85 0.80 

Lost weight 0.91 0.87 0.86 

Adult did not eat for whole day (1 vs. 0) 1.07 0.98 0.91 

Adult did not eat for whole day (2 vs. 1) 1.04 1.13 1.31 

Adult did not eat for whole day (overall) 1.07 1.12 1.25 

Number of cases 17,095 3,113 3,049 

Note: CML Rasch models estimated using weighted household data from the 2009-2014 CPS-FSS. Fit statistics for the 

trichotomous items, Adult cut or skipped meals and Adult did not eat for whole day, were calculated from mean square 

differences between observed responses and the expected mean response that the response was in one of the two categories of 

that threshold. Overall fit statistics for trichotomous items were based on observed value (0, 1, or 2) versus expected value in the 

0-2 range. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3: Difference-in-Difference Logistic Regression Models of Responses to Items that Exhibit Meaningful Differential Item Functioning for Hispanic 

and White Non-Hispanic Households 

Adult cut or skipped meals Adult cut or skipped meals 

Food bought did not last (1 or 2 vs. 0) (2 vs. 0 or 1) Ate less than felt should 

Unadjusted Adjusted Unadjusted Adjusted Unadjusted Adjusted Unadjusted Adjusted 

Uniform differential item functioning parameters: 

Hispanic reference person interacted with post- -0.094 -0.067 -0.215 -0.206 0.862 0.837 0.867 0.884 

USDA standardization of Spanish translation (0.340) (0.341) (0.821) (0.822) (0.883) (0.885) (0.612) (0.612) 

Hispanic reference person -0.824*** -0.967*** -1.215** -1.035* -1.611** -1.533** -1.722*** -1.690*** 

(0.243) (0.249) (0.547) (0.551) (0.642) (0.648) (0.445) (0.450) 

Post-USDA standardization of Spanish translation 0.145 0.174 -0.809* -0.846* -0.254 -0.272 -0.465 -0.465 

(0.179) (0.180) (0.444) (0.445) (0.469) (0.470) (0.326) (0.326) 

Non-uniform differential item functioning parameters: 

Hispanic reference person interacted with post-USDA 0.049 0.048 0.003 -0.009 -0.183 -0.181 -0.192 -0.198* 

 standardization of Spanish translation and Rasch score (0.101) (0.101) (0.155) (0.155) (0.145) (0.146) (0.118) (0.118) 

Hispanic reference person interacted with Rasch score 0.396*** 0.395*** 0.124 0.125 0.230** 0.229** 0.292*** 0.292*** 

(0.071) (0.071) (0.104) (0.105) (0.106) (0.106) (0.087) (0.087) 

Rasch score 0.808*** 0.813*** 1.594*** 1.604*** 1.488*** 1.492*** 1.246*** 1.253*** 

(0.030) (0.030) (0.056) (0.056) (0.053) (0.053) (0.041) (0.041) 

Post-USDA standardization of Spanish translation 0.008 0.006 0.132 0.141* 0.033 0.034 0.067 0.068 

 interacted with Rasch Score (0.042) (0.042) (0.084) (0.084) (0.075) (0.075) (0.059) (0.059) 

Respondent/household characteristics: 

Respondent is a non-citizen immigrant 0.219 -0.324 -0.167 -0.089 

(0.151) (0.215) (0.224) (0.186) 

Non-citizen immigrant interacted with years since -0.004 0.010 0.012 -0.002 

U.S. entry (0.007) (0.010) (0.010) (0.009) 

Spanish is the only languages spoken by all adults -0.041 -0.062 0.059 0.025 

(0.124) (0.168) (0.177) (0.146) 

Household with child 0.208*** -0.023 -0.097 0.165** 

(0.060) (0.085) (0.085) (0.074) 

Proportion of adults who are female 0.117 0.064 0.307*** -0.086 

(0.084) (0.118) (0.116) (0.103) 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 3 (Cont.): Difference-in-Difference Logistic Regression Models of Response to Items that Exhibit Meaningful Differential Item Functioning for 

Hispanic and White Non-Hispanic Households 

Adult cut or skipped meals Adult cut or skipped meals 

Food bought did not last (1 or 2 vs. 0) (2 vs. 0 or 1) Ate less than felt should 

Unadjusted Adjusted Unadjusted Adjusted Unadjusted Adjusted Unadjusted Adjusted 

Income to poverty ratio -0.318 0.273 0.531 -0.149 

(0.242) (0.341) (0.340) (0.297) 

Income to poverty ratio, squared 0.084 -0.058 -0.260 0.106 

(0.120) (0.172) (0.173) (0.150) 

Age of oldest adult 0.024** -0.026* 0.006 -0.010 

(0.010) (0.014) (0.014) (0.012) 

Age of oldest adult, squared -0.000* 0.000 -0.000 0.000 

(0.000) (0.000) (0.000) (0.000) 

Most highly educated adult less than high school 0.097 -0.123 -0.064 0.024 

(0.080) (0.115) (0.116) (0.099) 

Most highly educated adult some college, less than -0.179*** 0.164* 0.076 0.126 

bachelor’s degree (0.066) (0.094) (0.095) (0.082) 

Most highly educated adult bachelor or 4-year degree -0.388*** 0.392*** 0.052 0.215* 

(0.101) (0.146) (0.149) (0.128) 

Most highly educated adult graduate or -0.375** 0.453* 0.180 0.209 

professional degree (0.175) (0.257) (0.260) (0.226) 

Resident in principal city of metropolitan -0.065 -0.096 -0.180* 0.065 

statistical area 

(0.072) (0.102) (0.104) (0.089) 

Resident in metropolitan statistical area -0.086 -0.011 -0.074 0.189* 

not identified (0.082) (0.118) (0.117) (0.103) 

Resident outside of metropolitan statistical area -0.015 -0.154 -0.126 0.080 

(0.076) (0.109) (0.110) (0.095) 

Constant -2.625*** -3.203*** -8.184*** -7.540*** -8.971*** -9.410*** -6.512*** -6.304*** 

(0.129) (0.304) (0.297) (0.485) (0.331) (0.518) (0.225) (0.407) 

Year fixed effects Yes Yes Yes Yes Yes Yes Yes Yes 

Region fixed effects No Yes No Yes No Yes No Yes 

Log-Likelihood -4,194.157 -4,155.258 -2,250.262 -2,226.626 -2,204.574 -2,192.293 -2,898.414 -2,887.090 

N 23,257 23,257 23,257 23,257 23,257 23,257 23,257 23,257 

Note: Logistic models were estimated using weighted household data for households with income below 185% of the Federal poverty line from the 2009-2014 CPS-FSS. Standard 

errors appear in parenthesis. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table 4: Bias for the Estimated Prevalence of Food Insecurity and Very Low Food Security of Hispanic and White Non-Hispanic Households Due to 

Differential Item Functioning 

Bias, 

Bias, White non-Hispanic versus 

True Prevalence Measured versus True Hispanic

 White non- White non- Percent of Percent of 

Method and Characteristic 

Measured 

Prevalence 

Hispanic 

Household 

Hispanic 

Household

Hispanic 

Household 

Hispanic 

Household

All 

Households 

Observed 

Prevalence 

- - - - - - - - percent - - - - - - - - - percentage points - - - - percent - - -

Pre-USDA Standardized Spanish Translation 

Food Insecurity 22.15 22.15 22.77 0.00 -0.62 -0.62 -2.80 

Very Low Food Security 7.77 7.77 8.15 0.00 -0.38 -0.38 -4.89 

Post-USDA Standardized Spanish Translation 

Food Insecurity 22.15 22.15 22.61 0.00 -0.46 -0.46 -2.06 

Very Low Food Security 7.77 7.77 8.64 0.00 -0.86 -0.86 -11.19 

Note: CML Rasch models estimated using weighted household data from the 2009-2014 CPS-FSS. 
 

     

   

     

       

   

   

     

     

         

         

     

         

Figures 

Figure 1: CML Rasch Model Item-Severity Parameter Comparison, Hispanic versus White, non-Hispanic 

Households 

Worried found would

not run out

Food did not last

Could not afford balanced meal

Cut/skipped meal, 0/1

Cut/skipped meal, 1/2

Ate less than should

Hungry, did not eat

Lost weight

Did not eat whole day, 0/1 Did not eat whole day, 1/2

3

4

5

6

7

8

9

10

11

12

3 4 5 6 7 8 9 10 11 12

Item Severity, Hispanic

Item Severity, White non‐Hispanic

Pre‐USDA Standardized Translation Post‐USDA Standardized Translation Equal Severity

Note: Item-severity parameters were estimated from separate CML Rasch models for Hispanic and White, non-Hispanic 

households using data from the 2009-2014 CPS-FSS. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix A. Analysis of Differential Item Functioning between Hispanic and White Non-Hispanic Households with and without Children 

Table A.1: CML Rasch Model Item Severity Parameters Estimated in Separate Models for Hispanic and White Non-Hispanic Households without 

Children Pre- and Post-USDA Standardization of the HFSSM Spanish Translation 

Hispanic households

White nonHispanic Pre-USDA Standardized Post-USDA Standardized 

households Spanish Translation Spanish Translation 

Difference Difference 

from White from White 

Severity Severity non-Hispanic Severity non-Hispanic Difference-inItem parameter parameter households parameter households Difference 

Worried food would run out 4.23 3.91 -0.31*** 3.93 -0.30*** 0.01 

(0.110) (0.101) (0.147) 

Food bought did not last 5.02 4.72 -0.29*** 4.71 -0.31*** -0.01 

(0.097) (0.092) (0.131) 

Could not afford balanced meals 4.77 4.96 0.19** 4.75 -0.01 -0.21 

(0.095) (0.091) (0.129) 

Adult cut or skipped meals (1 or 2 vs. 0) 6.40 6.71 0.31** 6.86 0.46*** 0.15 

(0.158) (0.152) (0.214) 

Adult cut or skipped meals (2 vs. 0 or 1) 6.81 7.06 0.25 7.26 0.44*** 0.20 

(0.174) (0.158) (0.231) 

Ate less than felt should 6.47 6.64 0.17* 6.76 0.28 0.11 

(0.098) (0.095) (0.133) 

Hungry but did not eat 8.18 8.25 0.07 8.14 -0.04 -0.10 

(0.114) (0.109) (0.155) 

Lost weight 8.90 8.95 0.05 8.80 -0.10 -0.15 

(0.128) (0.124) (0.175) 

Adult did not eat for whole day (1 or 2 vs. 0) 9.50 9.28 -0.22 9.29 -0.21 0.02 

(0.254) (0.282) (0.371) 

Adult did not eat for whole day (2 vs. 0 or 1) 9.72 9.51 -0.21 9.50 -0.23 -0.02 

(0.320) (0.336) (0.454) 

Mean—all items 7.00 7.00 7.00 

Std. deviation—all items 1.90 1.90 1.90 

Discrimination parameter 1.00 1.07 1.06 

Number of cases 10,645 1,027 1,068 

Note: CML Rasch models estimated using weighted household data from the 2009-2014 CPS-FSS. Standard errors appear in parenthesis. All models were estimated on a logistic 

metric (discrimination parameter = 1.00). The discrimination parameter above for Hispanic and White, non-Hispanic households are those required to equate the standard deviation 

to be equivalent in Hispanic and White, non-Hispanic households for the purposes of that comparison. Severity parameters for the trichotomous items, Adult cut or skipped meals 

and Adult did not eat for whole day, are the “Rasch-Thurstone” or “50-percent probability” values. 

* Significant at the 0.10 level. ** Significant at the 0.05 level. *** Significant at the 0.01 level. 
 

 

 

 

 

 

 

 

 

 

 

 

 

Table A.2: Bias for the Estimated Prevalence of Food Insecurity and Very Low Food Security of Hispanic and White Non-Hispanic Households without 

Children Due to Differential Item Functioning 

Bias, 

Bias, White non-Hispanic versus 

True Prevalence Measured versus True Hispanic

 White non- White non- Percent of Percent of 

Method and Characteristic 

Measured 

Prevalence 

Hispanic 

Household 

Hispanic 

Household

Hispanic 

Household 

Hispanic 

Household

All 

Households 

Observed 

Prevalence 

- - - - - - - - percent - - - - - - - - - percentage points - - - - percent - - -

Pre-USDA Standardized Spanish Translation 

Food Insecurity 19.61 19.61 19.90 0.00 -0.29 -0.29 -1.46 

Very Low Food Security 7.95 7.95 8.41 0.00 -0.46 -0.46 -5.79 

Post-USDA Standardized Spanish Translation 

Food Insecurity 19.61 19.61 19.79 0.00 -0.17 -0.17 -0.88 

Very Low Food Security 7.95 7.95 8.72 0.00 -0.77 -0.77 -9.69 

Note: CML Rasch models estimated using weighted household data from the 2009-2014 CPS-FSS. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table A.3: CML Rasch Model Item Severity Parameters Estimated in Separate Models for Hispanic and White Non-Hispanic Households with 

Children Pre- and Post-USDA Standardization of the HFSSM Spanish Translation 

Hispanic households

White nonHispanic Pre-USDA Standardized Post-USDA Standardized 

households Spanish Translation Spanish Translation 

Difference Difference 

from White from White 

Severity Severity non-Hispanic Severity non-Hispanic Difference-inItem parameter parameter households parameter households Difference 

Adult/Household Food Security Items: 

Worried food would run out 2.64 2.48 -0.16** 2.38 -0.27*** -0.10 

(0.074) (0.075) (0.105) 

Food bought did not last 3.85 3.60 -0.25*** 3.34 -0.51*** -0.26*** 

(0.065) (0.067) (0.094) 

Could not afford balanced meals 4.44 4.08 -0.36*** 3.96 -0.49*** -0.12 

(0.064) (0.066) (0.092) 

Adult cut or skipped meals (1 or 2 vs. 0) 5.34 5.99 0.64*** 6.17 0.83*** 0.18 

(0.111) (0.116) (0.161) 

Adult cut or skipped meals (2 vs. 0 or 1) 5.78 6.30 0.52*** 6.49 0.72*** 0.20 

(0.126) (0.135) (0.185) 

Ate less than felt should 5.35 6.03 0.68*** 6.16 0.81*** 0.13 

(0.068) (0.073) (0.100) 

Hungry but did not eat 6.79 7.62 0.83*** 7.61 0.82*** -0.01 

(0.086) (0.0.91) (0.125) 

Lost weight 7.78 8.53 0.75*** 8.77 0.99*** 0.24 

(0.104) (0.117) (0.156) 

Adult did not eat for whole day (1 or 2 vs. 0) 8.16 8.90 0.74*** 8.72 0.56** -0.18 

(0.268) (0.240) (0.360) 

Adult did not eat for whole day (2 vs. 0 or 1) 8.36 9.01 0.65** 8.89 0.53* -0.13 

(0.308) (0.313) (0.439) 

Mean—all items 7.00 7.00 7.00 

Std. deviation—all items 2.38 2.38 2.38 

Discrimination parameter 1.00 0.98 0.98 

Number of cases 7,378 2,383 2,113 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table A.3 (Cont.): CML Rasch Model Item Severity Parameters Estimated in Separate Models for Hispanic and White Non-Hispanic Households with 

Children Pre- and Post-USDA Standardization of the HFSSM Spanish Translation 

Hispanic households

White nonHispanic Pre-USDA Standardized Post-USDA Standardized 

households Spanish Translation Spanish Translation 

Difference Difference 

from White from White 

Severity Severity non-Hispanic Severity non-Hispanic Difference-inItem parameter parameter households parameter households Difference 

Child Food Security Items: 

Relied on few kinds of low-cost food to feed 4.54 4.07 -0.47*** 4.14 -0.40*** 0.07

 child(ren) (0.064) (0.066) (0.092) 

Couldn’t feed child(ren) balanced meals 5.88 5.42 -0.46*** 5.43 -0.45*** 0.01 

(0.067) (0.070) (0.097) 

Child(ren) were not eating enough 7.89 6.76 -1.13*** 7.00 -0.89*** 0.24** 

(0.080) (0.086) (0.118) 

Cut size of child(ren)’s meals 8.98 8.15 -0.84*** 8.26 -0.73*** 0.11 

(0.104) (0.112) (0.153) 

Child(ren) were hungry 9.24 9.15 -0.09 9.21 -0.03 0.07 

(0.127) (0.138) (0.188) 

Child(ren) cut or skipped meals (1 or 2 vs. 0) 9.33 9.00 -0.33 8.85 -0.48 -0.15 

(0.278) (0.312) (0.418) 

Child(ren) cut or skipped meals (2 vs. 0 or 1) 9.45 9.18 -0.27 8.99 -0.46 -0.19 

(0.372) (0.392) (0.541) 

Children did not eat for whole day 12.18 11.73 -0.45 11.62 -0.56 -0.11 

(0.358) (0.360) (0.508) 

Mean—all items 7.00 7.00 7.00 

Std. deviation—all items 2.38 2.38 2.38 

Discrimination parameter 1.00 0.98 0.98 

Number of cases 7,378 2,383 2,113 

Note: CML Rasch models estimated using weighted household data from the 2009-2014 CPS-FSS. Standard errors appear in parenthesis. All models were estimated on a logistic 

metric (discrimination parameter = 1.00). The discrimination parameter above for Hispanic and White, non-Hispanic households are those required to equate the standard deviation 

to be equivalent in Hispanic and White, non-Hispanic households for the purposes of that comparison. Severity parameters for the trichotomous items, Adult cut or skipped meals, 

Adult did not eat for whole day, and Children cut or skipped meals, are the “Rasch-Thurstone” or “50-percent probability” values. 

* Significant at the 0.10 level. ** Significant at the 0.05 level. *** Significant at the 0.01 level. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

Table A.4: Bias for the Estimated Prevalence of Food Insecurity and Very Low Food Security of Hispanic and White Non-Hispanic Households with 

Children Due to Differential Item Functioning 

Bias, 

Bias, White non-Hispanic versus 

True Prevalence Measured versus True Hispanic

 White non- White non- Percent of Percent of 

Measured Hispanic Hispanic Hispanic Hispanic All Observed 

Method and Characteristic Prevalence Household Household Household Household Households Prevalence 

- - - - - - - - percent - - - - - - - - - percentage points - - - - percent - - -

Pre-USDA Standardized Spanish Translation 

Food Insecurity 29.50 29.50 28.30 0.00 1.20 1.20 4.06 

Very Low Food Security 13.78 13.78 14.77 0.00 -0.99 -0.99 -7.20 

Post-USDA Standardized Spanish Translation 

Food Insecurity 29.50 29.50 27.96 0.00 1.54 1.54 5.21 

Very Low Food Security 13.78 13.78 15.33 0.00 -1.55 -1.55 -11.25 

Note: CML Rasch models estimated for the 18-item U.S. food security scale using weighted household data from the 2009-2014 CPS-FSS. 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix B. U.S. Adult Household Food Security Survey Module Questions 

Questions asked of all households: 

USDA English Adult Household Food Security Scale USDA Standardized Spanish Adult Household Food 

Module Security Scale Module 

“We worried whether our food would run out before 

we got money to buy more.” Was that often, 

sometimes, or never true in the last 12 months? 

“The food that we bought just didn’t last and we didn’t 

have money to get more.” Was that often, sometimes, 

or never true for you in the last 12 months? 

“We couldn’t afford to eat balanced meals.” Was that 

often, sometimes, or never true for you in the last 12 

months? 

“In the last 12 months, did you or other adults in the 

household ever cut the size of your meals or skip meals 

because there wasn’t enough money for food? 

(Yes/No) 

[If yes above, ask] How often did this happen—almost 

every month, some months but not every month, or in 

only 1 or 2 months? 

In the last 12 months, did you ever eat less than you 

felt you should because there wasn’t enough money for 

food? (Yes/No) 

In the last 12 months, were you ever hungry, but didn’t 

eat because there wasn’t enough money for food? 

(Yes/No) 

In the last 12 months, did you lose weight because 

there wasn’t enough money for food? (Yes/No) 

In the last 12 months did you or other adults in your 

household ever not eat for a whole day because there 

wasn’t enough money for food? (Yes/No) 

[If yes above, ask] How often did this happen—almost 

every month, some months but not every month, or in 1 

or 2 months? 

Note: “Affirmative” responses indicated in bold (Bickel et al., 2000). 

The La primera situación es “(Me preocupó / Nos 

preocupamos) que la comida se podía acabar antes de 

tener dinero para comprar más.” (Para Ud. / En su 

hogar), ¿ésto ocurrió frecuentemente, a veces, o nunca 

en los últimos 12 meses? 

La comida que (compré / compramos) no rindió lo 

suficiente, y (no tenía / no teníamos) dinero para 

comprar más." (Para Ud. / En su hogar), ¿ésto ocurrió 

frecuentemente, a veces, o nunca en los últimos 12 

meses? 

“(No tenía / No teníamos) recursos suficientes para 

comer comida variada y nutritiva.” (Para Ud. / En su 

hogar), ¿ésto ocurrió frecuentemente, a veces, o nunca 

en los últimos 12 meses? 

En los últimos 12 meses, ¿(Ud. / Ud. u otro adulto del 

hogar) redujo alguna vez la cantidad de sus comidas o 

dejó de desayunar, almorzar o cenar porque le faltaba 

dinero para alimentos? (Sí,No) 

[If SÍ above, ask] ¿Con qué frecuencia sucedió esto? 

Casi todos los meses, algunos meses pero no todos, o 

solamente en 1 ó 2 meses? 

En los últimos 12 meses, ¿comió Ud. alguna vez menos 

de lo que pensaba que debía comer porque le faltaba 

dinero para alimentos? (Sí,No) 

En los últimos 12 meses, ¿Tuvo Ud. hambre alguna vez 

pero no comió porque le faltaba dinero para alimentos? 

(Sí,No) 

En los últimos 12 meses, ¿Perdió Ud. peso porque no 

comió los alimentos suficientes por falta de dinero para 

comida? (Sí,No) 

En los últimos 12 meses, ¿alguna vez no comió (Ud. / 

Ud. u otro adulto del hogar) en todo el día porque le 

faltaba dinero para comida? (Sí,No) 

[If SÍ above, ask] ¿Con qué frecuencia sucedió esto? 

Casi todos los meses, algunos meses pero no todos, o 

solamente en 1 ó 2 meses? 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Appendix C: Characteristics of All Households 

Table C.1: Means of Analysis Variables for Households with Income Less Than 185% of the Federal Poverty 

Threshold and No Extreme Responses the U.S. Adult Household Food Security Scale 

Pre-USDA Standardized Post-USDA Standardized 

Spanish Translation Spanish Translation 

White non- White nonAll Hispanic Hispanic Hispanic Hispanic 

Households Households Households Households Households 

Respondent is a non-citizen 0.149 0.017 0.426*** 0.018 0.399*** 

 immigrant (0.003) (0.002) (0.10) (0.002) (0.010) 

Non-citizen immigrant interacted 2.307 0.224 6.475*** 0.213 6.529*** 

with years since U.S. entry (0.054) (0.031) (0.193) (0.031) (0.201) 

Spanish only language spoken by 0.082 0.003 0.264*** 0.003 0.221***

 all household members (0.002) (0.001) (0.009) (0.001) (0.008) 

Proportion of adults who are female 0.585 0.584 0.574 0.590 0.586 

(0.002) (0.004) (0.006) (0.004) (0.006) 

Age of oldest adult 50.476 50.872 48.757*** 51.768 48.769*** 

(0.129) (0.219) (0.331) (0.216) (0.337) 

Income/poverty ratio 0.968 1.002 0.893*** 0.996 0.920***

(0.003) (0.006) (0.009) (0.006) (0.009) 

Household with child 0.480 0.405 0.665*** 0.386 0.637***

(0.004) (0.006) (0.009) (0.006) (0.010) 

Most highly educated adult less than 0.200 0.142 0.338*** 0.133 0.310*** 

high school (0.003) (0.004) (0.009) (0.004) (0.009) 

Most highly educated adult high 0.353 0.371 0.342* 0.356 0.323** 

 school diploma (reference) (0.003) (0.006) (0.009) (0.006) (0.009) 

Most highly educated adult some 0.334 0.363 0.245*** 0.379 0.276*** 

 college, less than bachelor (0.003) (0.006) (0.008) (0.006) (0.009) 

Most highly educated adult bachelor 0.089 0.098 0.062*** 0.101 0.072*** 

or other 4-year degree (0.002) (0.004) (0.009) (0.004) (0.005) 

Most highly educated adult graduate 0.024 0.026 0.013*** 0.031 0.019** 

or professional degree (0.001) (0.002) (0.002) (0.002) (0.003) 

Resident in principal city of metro- 0.281 0.190 0.465*** 0.187 0.465*** 

politan statistical area (0.003) (0.005) (0.010) (0.005) (0.010) 

Resident in metropolitan statistical 0.339 0.344 0.333 0.334 0.346 

 area, not principal city (reference) (0.004) (0.006) (0.009) (0.006) (0.009) 

Resident in metropolitan statistical 0.162 0.196 0.107*** 0.185 0.104*** 

 area, not identified (0.003) (0.005) (0.006) (0.005) (0.006) 

Resident outside of metropolitan 0.218 0.270 0.095*** 0.294 0.085***

 statistical area (0.003) (0.005) (0.007) (0.005) (0.005) 

Northeast (reference) 0.156 0.158 0.147 0.156 0.160

(0.003) (0.005) (0.007) (0.005) (0.008) 

Midwest 0.212 0.283 0.074*** 0.275 0.079*** 

(0.003) (0.005) (0.005) (0.005) (0.005) 

South 0.376 0.371 0.378 0.383 0.369

(0.004) (0.006) (0.010) (0.006) (0.009) 

West 0.256 0.188 0.400*** 0.185 0.391*** 

(0.003) (0.005) (0.09) (0.005) (0.009) 

N 23,257 8,509 3,113 8,586 3,049 

Note: Means and standard deviations (in parenthesis) estimated using weighted household data from the 2012-2014 CPS-FSS. 

Stars indicate statistically significant differences of means for Hispanics relative to White, non-Hispanics in each time period. 

* Significant at the 0.10 level. ** Significant at the 0.05 level. *** Significant at the 0.01 level.