Weighting and Estimation Research Methodology and

Results From the American Community Survey

Family Equalization Project

Mark E. Asiala

US Census Bureau 

DSSD, CENHQ RM 4H057, 4600 Silver Hill Rd, Washington DC 20233 

mark.e.asiala@census.gov

Abstract

Historically the American Community Survey (ACS) has produced inconsistent estimates of households and householders 

and inconsistent estimates of husbands and wives in married couple households even though logically these estimates should be 

equal. In the 2005 ACS, the size of these inconsistencies at the national level was approximately 3.7 million more householders 

than households and approximately 1.8 million more spouses than married-couple households. Likewise, for unmarried-partner 

households there are approximately 176,000 more unmarried-partners than unmarried-partner households. The cause of these 

data inconsistencies was rooted in the person weighting methodology used prior to 2006 which was independent of the housing 

unit weighting and did not consider relationship to the householder. This paper describes the current weighting methodology 

and changes introduced to reduce these data inconsistencies while having a minimal impact on other estimates and on the 

variances of the estimates. A three-dimensional raking methodology is used where the marginal control totals are derived 

from the survey itself rather than an independent source for the frst two dimensions that are related to equalizing spouses 

and householders. Changes in the estimation of housing unit characteristics are also discussed. Empirical results from the 

implementation of this new methodology are presented based on the 2004 and 2005 ACS data. 

Background

The American Community Survey (ACS) is part of the Census Bureau’s plans for a re-engineered 2010 Census. 

The ACS will collect long-form (sample) data on an annual basis in order to produce single and multi-year estimates. Specifcally, the 5-year estimates are comparable to the long-form estimates traditionally produced after each 

decennial census. 

The ACS collects information on a wide variety of topics including housing, household, family, and person characteristics. The existing weighting methodology produces two weights to tally characteristics for all domains: a housing 

unit weight which was used for housing, household, and family characteristics and a person weight which was used 

for person characteristics including householder characteristics. Prior to the 2006 ACS, the weighting methodology 

produced these weights semi-independently with no method to try to ensure consistency between the weights. Because of this, some signifcant data inconsistencies were present in the ACS data prior to 2006. The largest was 

the inconsistency between the estimate of householders and the estimate of households. Logically, this should be 

a one-to-one relationship. However, in 2005 the ACS estimate for householders was 114.8 million but the estimate 

of households was only 111 million. Similarly, there should be a one-to-one relationship between the number of 

spouses in households and the number of married-couple households. Again in the 2005 ACS, there were 57.1 million 

This report is released to inform interested parties of ongoing research and to encourage discussion of work in progress. The views

expressed on statistical issues are those of the author and not necessarily those of the U.S. Census Bureau.
spouses but only 55.2 million married-couple households. These inconsistencies did not exist in the unweighted data 

so clearly the weighting methodology was responsible for the observed dierences in the estimates. In each of the 

examples given, the frst estimate (householders, spouses) was tabulated from the person weights and the second 

estimate (households) was tabulated from the housing unit weights. These dierences were of great concern to data 

users both external and internal to the Census Bureau. 

Previous Attempts to Address the Problem

The frst attempt to address the dierence between the estimate of householders and households was in 2002. The 

solution was to use the person weight of the householder to tabulate estimates for households rather than the housing 

unit weight. This led to consistency between the estimates of householders and households but introduced a new 

inconsistency between the estimate of households and occupied housing units which should also have a one-to-one 

relationship. There were also other undesirable impacts on other estimates which led to abandoning this method 

and returning to using the housing unit weight to tabulate households. 

Our second attempt to address these data inconsistencies borrowed from the weighting methodology of the New York 

City Housing Vacancy Survey (NYCHVS) conducted by the Census Bureau (Navarro et al., 2004). The NYCHVS 

methodology defnes the fnal person weight of the householder and of the spouse to be equal to the housing unit 

weight. The person post-stratifcation adjustment to the independent population controls is amended so that the 

householder and spouse by default always get an adjustment equal to 1 and the balance of the sample persons 

must account for the entire dierence between the pre-controlled estimates and the population controls. While this 

achieves the data consistencies desired at the record level, it does so at high cost. By forcing the balance of the 

sample persons to account for all of the relative coverage dierence, the comparatively larger adjustment factors 

leads to increased variances in the estimates. The method can also lead to negative weights which must be handled 

through an increased amount of collapsing of the post-stratifcation cells. This in turn leads to a greater bias in the 

estimates as the controls are applied to broader cells. We determined that while this method works for the NYCHVS 

which is concerned primarily with housing units, it was not appropriate for the ACS with its wide range of estimates 

for housing units and persons and so it, too, was abandoned. 

Research Goals

Based on our experience from the early attempts, the primary goal for the family equalization project was more 

modest than the record-level consistency achieved using the NYCHVS method. We defned our objective to simply 

reduce but not necessarily eliminate the inconsistencies at the weighting area level which for the ACS is either a 

county or a collection of counties. By weakening the objective to the weighting area, we could still obtain our overall 

goal for most of the estimates but the expectation was that we could do so without the large impact on variances we 

observed in the NYCHVS method. 

It was also recognized that if we achieve success in closing the 3.7 million gap between the estimate of householders 

and households, that additional person weight would be shifted to other members of the household in an uncontrolled 

fashion. In order to avoid this potential problem we expanded our goals for the project to the following: 

1. To reduce the inconsistency between the estimates of householders and households. 

2. To reduce the inconsistency between the estimates of spouses and married-couple households. 

3. To reduce the inconsistency between the estimates of unmarried partners and unmarried-partner households. 

4. To reduce the inconsistency between the estimates of spouses in subfamilies and married-couple subfamilies. 

5. To improve the estimate of vacant housing units. 

6. To accomplish the above while not causing unintended impacts on other estimates or variances. 

The frst four goals directly address the data inconsistencies described previously. Goal #5 was added to the project 

as the result of another concern about the vacancy rate of the ACS. The source of this concern is described in more 
detail in the next section. Lastly, the sixth goal was there to explicitly evaluate the impact of the weighting changes 

on other estimates and to recognize that achieving these data consistencies at the expense of substantial increase in 

variances or changing other estimates in a manner that we could not support would not be acceptable. 

Before describing the methodology developed to accomplish these goals, we give a quick overview of the ACS weighting 

methodology as it applies to the project. 

Methodology Prior to 2006

The weighting methodology for the ACS is a ratio-estimation method involving several steps. We present here a 

high-level overview with some additional detail given concerning the person weighting and the fnal steps of the 

housing unit weighting. For a more detailed description of the existing weighting methodology prior to 2006, see US 

Census Bureau (2006). 

The weighting methodology produces two sets of weights: a housing unit weight and a person weight. The basic 

steps of the housing unit weighting are as follows: 

1. Calculate the base weights defned as the inverse of the probability of selection. 

2. Apply the Variation in Monthly Sample adjustment to smooth month to month response variation. 

3. Apply a set of non-interview adjustments. 

4. Apply a housing-unit post-stratifcation adjustment to control the estimate of total housing units. 

5. Perform the person weighting [see below]. 

6. Apply the Principal Person adjustment. 

7. Reapply the housing-unit controls via a second housing-unit post-stratifcation adjustment. 

The person weighting was a one-step process. The initial person weight was equal to the housing unit weight after 

step (4) above and then a person post-stratifcation adjustment was performed after classifying persons into cells 

based on race, ethnicity, age, and sex. While the intermediate housing unit weight from step (4) is used as an 

initial person weight, the methodology prior to 2006 had no mechanism in place to ensure the type of consistency 

between the fnal housing unit weight and the fnal person weight to avoid the data inconsistencies described in the 

Background section. It is this fact that is the principal cause of the data inconsistencies. 

One housing unit weight step of note is step (6) where the person weighting informs the housing unit weighting 

through the principal person adjustment. The principal person of the household is defned to be the female spouse of 

the householder, if she exists. Otherwise, the principal person is simply defned to be the householder. The principal 

person adjustment in the housing unit weighting defnes the housing unit weight for all occupied housing units to be 

equal to the weight of the principal person, eectively incorporating the person post-stratifcation adjustment of the 

principal person into the housing unit weight. The purpose of this adjustment is to correct for dierential household 

coverage and net household coverage under the assumption that the only manner in which the principal person can 

be missed is if the entire household is not included in or missed by the survey. 

The impact of the principal person adjustment, however, is a net increase in occupied housing units. In addition, the 

total number of housing units increased and so step (7) is necessary in order to make the estimate of total housing 

units to once again agree with the independent controls. The impact of the principal person adjustment on the fnal 

housing unit weights still increases the estimate of occupied units but it also decreases the vacancy rate. Analysts

in our Housing and Household Economics Statistics division were concerned that the result of this weighting step 

artifcially depressed the ACS estimate of the vacancy rate further away from the Census Bureau’s oÿcial vacancy 

rate estimate obtained through the Housing Vacancy Survey (a supplement to the Current Population Survey). While 

there are structural dierences between the two surveys, the ACS estimate of 10.4% (±0.2%) was signifcantly lower 

than the oÿcial estimate of 12.8% (±0.1%). Because of this, we added Goal #5 above to see if we could address this 

issue at the same time we were addressing Goals #1–#4. 
Proposed Methodology

The initial proposed methodology involved changes to the person weighting, the housing unit weighting, and also 

the estimation. All three parts had to work together in order to address all the goals listed including Goal #6 which 

was to make these changes without having unintended impacts elsewhere on other estimates or variances. 

Weighting steps (1)–(4), listed earlier, were not changed in the proposed methodology. All changes to the weighting 

aected only steps (5)–(7). 

Person Weighting Changes. The change to the person weighting is to introduce a raking-ratio estimation 

procedure by which we can reduce the data inconsistencies described previously. The Census 2000 sample weighting 

methodology used a similar approach but it also had the beneft of 100% Census counts for detailed demographics by 

householder/non-householder, spouses, and the like. While the ACS population controls do not include additional 

detail, we were able to design a more detailed raking matrix that used ACS estimates in the marginals in order to 

carry out the raking methodology. 

The raking matrix is defned with three dimensions. The frst dimension carries out the spousal/unmarried-partner 

equalization. The second dimension carries out the householder/household equalization. The third, and fnal, 

dimension applies the same demographic controls in the same fashion as the person post-stratifcation adjustment 

did in the original methodology. The geographic scope of the matrix is our weighting area which is defned to be a 

county or collection of counties. The order of the dimensions refects the relative importance of each goal. Consistency 

with the controls has the highest priority and thus is the fnal step in the raking to ensure exact agreement with the 

controls as we have had in the past. The second to last step is the householder/household equalization step which 

was identifed as a higher priority over the spousal equalization. 

The spouse equalization dimension is defned as having 3 cells: 

• Householder with spouse/unmarried-partner present 

• Spouse/unmarried-partner of the householder 

• Balance of sample persons 

The frst two cells are constrained to be equal to the estimate of married-couple or unmarried-partner households 

which is tabulated using the housing unit weight from step (4). The third cell is then constrained to be equal to 

the total population from the independent control minus the sum of the control totals for the frst two cells. In this 

manner, total population is always controlled to the independent population control. 

A second variation of this raking dimension included the married-couple subfamilies. To accomplish this, the subfamily head was added to the frst cell and the subfamily spouse was added to the second cell. The constraint for 

the frst and second cells for this variation are the estimate of married-couple or unmarried partner households plus 

the total number of married-couple subfamilies using the same housing unit weight as above. The third cell is then 

constrained to the residual of the total population as was calculated earlier. 

The householder equalization dimension is defned as having 2 cells: 

• Householders 

• Non-householders (balance of sample persons) 

The frst cell is constrained to be equal to the estimate of occupied housing units and hence the estimate of households. 

The second cell is then constrained to be equal to the total population control minus the marginal control for the 

frst cell. 

The demographic dimension is defned as having up to 156 cells per weighting area obtained from multiplying the 
number cells for race/ethnicity (6) by age (13) by sex (2). In practice, collapsing of small cells typically makes the 

actual number of cells fewer than 156. 

Each step, or dimension, in the raking is applied in series to make up one iteration, always ending with the demographic dimension. For the research, the raking was repeated for 10 iterations for every weighting area. No additional 

convergence criterion was used. 

Housing Unit Weighting Changes. The frst proposed change to the housing unit weighting methodology was

to remove steps (6) and (7) from the list given in the earlier section. This was to accomplish two things. The frst 

is that it removed the source of the depressed vacancy rate. The second is that this allows the person weighting to 

use the fnal housing unit weight as the initial person weight. This avoids the possibility that additional steps in the 

housing unit weighting may adversely aect the consistency gained through the raking done in the person weighting. 

Estimation Changes. The fnal change planned was in the estimation of household characteristics. By removing 

the principal person adjustment from the housing unit weighting methodology, the housing unit weight will no 

longer contain this adjustment for dierential coverage of households which could negatively impact the estimates 

for characteristics of households particularly when broken out by the race of the householder. 

To account for the dierential coverage, we planned to use the weight of the householder for tabulating estimates 

for households rather than using the weight of the housing unit. This would have two impacts. The frst is that 

the tabulated estimates of householders and households would be exactly equal and the tabulated estimates of 

householders and occupied housing units would be equal to the extent that the raking is successful in the second 

dimension. The second impact is that using the householder weight would capture the dierential household coverage 

while essentially assuming that the net household undercoverage is zero (because we are trying to equalize it to our 

initial estimate of occupied housing units). Our expectation was that the dierence between occupied housing units 

and households should be small for tabulated areas which are at the county level or aggregations of counties. 

Final Methodology

The fnal methodology was changed slightly from the proposed methodology outline above because of the discovery 

of some unintended consequences in our review of the data. The problems occurred in a set of housing unit tables 

that were crossed by person or household characteristics. This is discussed in more detail in the Results section. The 

methodology was changed from above to include one additional step in the housing unit weighting. This step makes 

the weight of an occupied housing unit to be equal to the weight of its householder. The weight of vacant housing 

units remain unchanged by this step. 

This guarantees agreement between estimates of occupied housing units, households, and householders. It also 

makes the change in the weight used to tabulate estimates of household characteristics unnecessary since both the 

householder weight and the housing unit weight are equal. 

Results

The methodology described above was used to produce two alternative sets of weights using the 2004 ACS data. 

The frst set included the spouses in subfamily equalization and the second set did not. A total of 313 tables were 

then created using these two sets of weights and we compared the estimates from each to the production 2004 ACS 

estimates. Our objective was then to determine which of the two methods performed best overall at achieving the 

goals laid out including not introducing any unintended consequences with regards to the estimates and variances. 

The most important goal was the equalization of householders and households. For the 2004 production data, the 

estimate of householders was 3.5 million greater than the estimate of households. For both alternative estimates (with 

and without subfamilies), that dierence was reduced to approximately 70,000 nationally with the new methodology. 

This dierence was also investigated at other levels of geography and the improvement was consistently demonstrated 

at all levels of county and above. 

With our highest priority (and easiest to check) goal achieved, the remaining results examine the consistency between 
household type and relationship and our review of other estimates including the household and housing unit estimates. 

Household Type and Relationship

There were three goals to check for consistency between household type and relationship: spouses and married-couple 

households, unmarried partners and unmarried-partner households, and spouses in sub-families and married-couple 

subfamilies. Since these were all directly addressed in the raking methodology, the results here are a check on how 

compatible these goals were within the raking matrix. One primary objective in evaluating the results of these 

tables was to develop a recommendation on whether to include the equalization of married-couple subfamilies in the 

methodology or not based on the review of the estimates. 

The goal of reducing the dierence between the estimates of married-couple households and spouses had the highest 

priority because it is the largest group of the three. Table 1 shows the ACS 2004 production estimate, alternative 

estimate including the subfamily methodology, and the alternative estimate which does not include the subfamily 

methodology. The results in the table show that the alternative estimate reduces the dierence between the estimate 

of spouses and married-couple households from 3.2% to 0.6% and 0.3% for the methods with and without marriedcouple subfamilies respectively. For context, the dierence for the Census 2000 sample data is also shown. Both 

of the alternative estimates bring the dierence between the number of married-couple households and the number 

of spouses to within sampling error unlike the ACS 2004 production which was highly signifcantly dierent. For 

comparing the two methods, we can disregard the sampling error on the dierence between the estimate of spouses 

and married-couple households since the dierence is due entirely to the person weighting methodology and not the 

data itself where the unweighted dierence is zero. Thus, this data shows that the alternative estimate without 

subfamilies was more eective at reducing this dierence than the method that included married-couple subfamilies 

and is more eective at the national level than the Census 2000 sample data which used a more complex raking 

methodology. 

Table 1: Estimates of Married-Couple Households and Spouses with 90% Margin of Error 

Type of Household and ACS 2004 Alternative Estimate Alternative Estimate Census 2000 

person-level estimate Production with subfamilies without subfamilies Sample 

Married-couple households 

Number of households 55,223,574 55,313,723 55,132,899 55,458,451 

(±290, 689) (±306, 626) (±286, 942) (±17, 035) 

Number of spouses 57,012,791 55,645,486 55,273,347 55,731,406 

(±180, 015) (±236, 542) (±237, 369) (±22, 199) 

Dierence (Spouses-Households) 

Number 1,789,217 331,763 140,448 272,955 

(±341, 914) (±387, 262) (±372, 397) (±27, 982) 

Percent (Di/households) 3.24 0.60 0.25 0.49 

(±0.62) (±0.70) (±0.68) (±0.05) 

The goal of reducing the dierence between the estimates of unmarried-partner households and unmarried partners 

had a similar priority to the married-couple household goal although it is a much smaller group. Table 2 shows 

the equivalent results for the unmarried partners as the previous table did for spouses. While the improvements in 

the percent dierence is not as large as for spouses in married-couple households, the dierence from production is 

reduced from 3.3% to 1.7% and 1.3% for the methods with and without subfamilies in the methodology respectively. 

Like the married-couple households, the dierences for each alternative method is now smaller than the sampling 

error associated with them. Again, the method which does not include the equalization for married-couple subfamilies 

performs the best. 

The goal of reducing the dierence between the estimates of married-couple subfamilies and spouses in subfamilies (a 

one-to-two relationship) had a lower priority than the other two household type and relationship equalization goals. 

This was because of the relatively small size of the estimate of married-couple subfamilies, the lower prominence of 

the two estimates (they are not shown in the main data profles, for example), and because the ACS does not directly 
Table 2: Estimates of Unmarried-Partner Households and Unmarried Partners with 90% Margin of Error 

Type of Household and ACS 2004 Alternative Estimate Alternative Estimate Census 2000 

person-level estimate Production with subfamilies without subfamilies Sample 

Unmarried-partner households 

Number of households 5,840,833 5,663,939 5,637,879 5,230,703 

(±80, 009) (±81, 432) (±80, 604) (±7, 404) 

Number of partners 6,035,051 5,758,810 5,713,906 5,318,070 

(±83, 677) (±78, 340) (±77, 826) (±5, 978) 

Dierence (Partners-Households) 

Number 194,218 94,871 76,027 87,367 

(±115, 773) (±112, 997) (±112, 044) (±9, 516) 

Percent (Di/households) 3.33 1.68 1.35 1.67 

(±1.98) (±2.00) (±1.99) (±0.18) 

Table 3: Estimates of Married-Couple Subfamilies and Spouses in Subfamilies with 90% Margin of Error 

Type of Household and ACS 2004 Alternative Estimate Alternative Estimate Census 2000 

person-level estimate Production with subfamilies without subfamilies Sample 

Married-couple subfamilies 

Number of subfamilies 891,721 882,490 883,028 940,784 

(±25, 481) (±26, 055) (±25, 955) (±3, 242) 

Number of spouses 1,907,217 2,045,164 2,348,755 1,868,518 

(±56, 736) (±60, 860) (±73, 178) (±4, 770) 

Ratio spouses/subfamilies 2.14 2.32 2.66 1.99 

(±0.09) (±0.10) (±0.11) (±0.01) 

capture the subfamily information (it is constructed through an edit). For these reasons it was viewed as a worthy 

yet expendable goal if it had an adverse or suboptimal impact on the other goals. Table 3 shows the relevant data 

for the consistency between the estimates of married-couple subfamilies and spouses in married-couple subfamilies. 

The logical ratio of spouses to married-couple subfamilies is exactly two and the table shows that both alternative 

methods actually increase the ratio away from 2.0 and away from the 2004 production estimate of 2.14. All three 

estimates are statistically signifcant from 2.0. 

While the method that includes subfamilies does perform better than the method without subfamilies (2.32 versus 

2.66), the subject-matter experts agreed that the better performance for subfamilies was not great enough to oset 

the gains that the method without subfamilies had for married-couple and unmarried-partner households. Thus, 

based on the estimates the subject-matter experts recommended the method which did not include subfamilies over 

the method which included subfamilies. 

Other Population Characteristics

We also reviewed other key population characteristics across 34 person-based tables. Our objective was to note the 

number of signifcant dierences between the production and the two alternative estimates, check for demographic 

consistency, and to compare the variance properties. 

The number of signifcant dierences between production and the two alternative estimates were principally concentrated in national-level estimates for relationship and marital status. At the state level, only approximately two 

percent of the changes in the estimates were statistically signifcant and at the county level only about 0.4 percent 

of the changes in the estimates were signifcant. 
A non-parametric Friedman test was used to compare the variance properties for groups of similar characteristics 

between the two alternative methodologies and each alternative methodology as compared to the production variance estimates. This test showed no signifcant dierences between the variance estimates for the two alternative 

methodologies. For the population characteristics, the only group that showed signifcant dierences between the 

production and alternative methods was for the relationship and marital status tables. 

The analysis based on all three criteria led to the same conclusion that apart from the household-type and relationship tables, both methods could be supported equally. Given the fndings detailed above, this solidifed the 

recommendation of the method which did not include subfamilies over the method which did. Further, the population 

subject-matter experts were able to fully recommend the implementation of the new weighting methodology. 

Housing Units and Household Characteristics

Given the changes in the estimation procedure for households and the removal of the principal person adjustment 

from the housing unit weighting, much of our attention was on the housing unit and household characteristics tables. 

These tables made up 279 of the 313 tables studied. 

Like the other population characteristics, the housing unit and household characteristic tables were checked to note 

the number of statistical dierences and the variance properties for each of the alternative methodologies as compared 

to the 2004 production. In general, both analyses supported the two methods equally, however, both analyses noted 

problems in a subset of the housing unit tables which had a large number of signifcant dierences and a signifcant 

increase in the variances. Further investigation revealed that while the new housing unit weight produced acceptable 

results for estimates of pure housing unit characteristics, those tables which crossed housing characteristics by person 

or householder characteristics showed a number of dierences which were deemed unacceptable by the housing unit 

and household subject-matter experts. This dierence had to be fxed in order to get their approval of the new 

methodology regardless of the benefts demonstrated for the person tables. 

Table 4 shows the dierences between estimates of households in the production and the alternative estimate. These 

estimates can be found both in a table of total occupied housing units by race of householder (ACS Table B25006) 

and in the race-iterated versions of the basic tenure table (ACS Table B25003A–B25003I). Because of this, these 

estimates are tabulated using the housing unit weight rather than the householder weight. The table shows the 

impact of having removed the principal person adjustment from the housing unit weight. Whites and American 

Indian or Alaskan Native (AIAN) show the greatest gains which are two groups that the ACS historically has had 

the strongest coverage relative to the population controls. The other groups all have substantial drops in their 

estimates. 

The results of composite tables like these led to the exploration of other possible changes to the methodology 

specifcally for housing unit tables which are crossed by household or householder characteristics. 

Composite Housing Unit Tables and Vacancy

The frst proposal for the composite housing unit tables was to use the person weight of the householder (the same 

weight used for the household tables) to tabulate all composite housing unit tables. To test this, the methodology for 

the alternative estimates without the use of subfamilies was applied using the 2005 ACS data and the 153 housing 

unit tables were tabulated using two sets of weights: one using the housing unit weight and one using the householder 

weight (for occupied housing units only). The estimates and variances from each run were compared to the 2005 

production values. The results confrmed that the weight of the householder produced estimates for the composite 

tables that were more consistent with the 2005 production both with respect to the estimates and the variances. 

However, this introduced the possibility that tables like tenure could be tabulated using one weight for the normal 

tabulation of occupied/owned/rented housing units and a dierent weight for the same tabulation when crossed by 

the race of householder. This was recognized as simply transferring the original consistency problem of householders 

and households to a new area. 

In reviewing all the data, however, it was found that using the weight of the householder also produced both acceptable 

estimates for the pure housing unit tables (those not crossed by any household or householder characteristics) while 

also having lower variances than using the alternative housing unit weight. After carefully reviewing all the housing 
Table 4: Households by Race of Householder with 90% Margin of Error 

Households by ACS 2004 Alternative Percent Change 

Race of Production estimate without from 2004 

Householder Estimate Subfamilies Production 

All Households 109,902,090 109,569,818 -0.30% 

(±238, 125) (±271, 588) (±0.33%) 

White 86,665,334 87,319,418 0.75% 

(±227, 636) (±364, 930) (±0.50%) 

Black 12,963,975 12,293,076 -5.18% 

(±56, 710) (±216, 644) (±1.73%) 

AIAN 770,686 808,937 4.96% 

(±21, 505) (±94, 425) (±12.57%) 

Asian 3,966,989 3,800,053 -4.21% 

(±34, 570) (±68, 807) (±1.94%) 

NHPI 116,315 111,589 -4.06% 

(±8, 302) (±11, 457) (±12.17%) 

Some other race 4,053,538 3,901,153 -3.76% 

(±64, 684) (±101, 175) (±2.96%) 

Two or more races 1,365,253 1,335,592 -2.17% 

(±39, 758) (±37, 939) (±4.03%) 

unit tables, the subject-matter experts recommended that the weight of the householder be used to tabulate all 

housing unit estimates for occupied housing units. This would ensure that the same weight is used to tabulate 

occupied housing units, households, and householders completely eliminating this data inconsistency. 

The simplest way to accomplish this is to simply set the housing unit weight for all occupied units to be equal to 

the person weight of the householder, much in the way that was done for the principal person. The dierence now is 

that the total person weight of the householders after the raking should be much closer to the original total housing 

unit weight for occupied housing units so the vacancy rate would not be impacted to the degree that it was with the 

principal person adjustment. This left the question of how to estimate the vacant housing units. In the methodology 

prior to 2006, a fnal ratio adjustment to the independent housing unit controls had been done to assure that the 

estimate of total housing units would be controlled. To use that method now would break consistency between the 

weight of the householder and the weight of the occupied housing unit. This left two choices: to back into the 

estimate of vacant housing units by subtraction of the estimate of occupied housing units from the total housing unit 

control or to leave the weight of the vacant housing units unchanged allowing the estimate of total housing units to 

foat. 

The latter choice would change what had been an objective of the ACS, that is, produce consistent estimates of total 

housing units with the Population Estimates Program (PEP), the Census Bureau’s oÿcial source of total housing 

unit estimates. After internal discussions within the Census Bureau, it was agreed that since the raking would assure 

that the ACS and PEP housing unit estimates would be very close the decision should be made based on the quality 

of the vacant housing unit estimates produced by each method. 

Figure 1 compares the the estimate of vacant housing units compared with ACS 2005 production by state. The graph 

is ordered from largest to smallest eect for the method which keeps the vacant housing units independent of the 

person weighting. Note that the largest dierence using the 2005 data is for Montana with an increase of 7.5% in the 

number of vacant housing units to a slight decline for North Dakota. The highest percent dierences are found in 

small states with the exception of California and the two lines generally follow each other. Overall, the independent 

vacant method causes a 2.3% increase in the estimate of vacant housing units nationally and the subtraction vacant 

method causes a 1.6% increase. Since the view of the subject-matter experts was that the ACS was underestimating 

the number of vacant housing units, the relatively higher estimate of vacant units in the independent vacant method 
Figure 1: Dierences in Vacant Housing Unit Estimates Compared with ACS 2005 Production, By State 

-1%

0%

1%

2%

3%

4%

5%

6%

7%

8%

Montana

New Mexico

Rhode Island

Delaware

Alaska

Louisiana

California

Wyoming

Oklahoma

Georgia

Texas

Kentucky

Vermont

New York

Arkansas

Oregon

Connecticut

Washington

Utah

Illinois

Colorado

Missouri

Ohio

South Carolina

Mississippi

Tennessee

Alabama

Arizona

Maryland

West Virginia

Maine

Virginia

Kansas

Nebraska

New Hampshire

Iowa

Michigan

Nevada

Pennsylvania

DC

Idaho

Florida

South Dakota

Massachusetts

Hawaii

New Jersey

North Carolina

Indiana

Minnesota

Wisconsin

North Dakota

Percent Difference

Independent Weighting Subtraction Method

led to their recommendation of that method over the subtraction vacant method. 

Since the independent method would cause the estimate of total housing units to no longer agree with the controls, 

this estimate was also investigated. Figure 2 shows the dierences in total housing units from the controls by state. 

Again the states are ordered from largest positive eect to the lowest negative eect. Most states show a small 

increase in the estimate of total housing units with just a few small states showing an increase of 0.15% or more. 

Nationally, the dierence is approximately 0.08% or about 97,000 housing units. This data acted to confrm that the 

small trade-o in the dierence between the estimate of total housing units and the controls was worth the beneft 

in the improved estimates of vacant units. With these changes, the housing and household subject-matter experts 

were able to fully recommend the implementation of the new weighting methodology. 

Implications and Conclusions

With the fnal methodology in place, all of the goals were met with the exception of the married-couple subfamilies. 

In the end the improvements gained toward the other goals without including the portion of the methodology 

that addressed the married-couple subfamilies outweighed the gains by including it. This new methodology was 

implemented in the 2006 ACS weighting released in the summer of 2007. 

To summarize the results along the lines of the goals outlined in the Research Goals section: 
Figure 2: Dierences in Total Housing Unit Estimates Compared with ACS 2005 Production, By State 

-0.05%

0.00%

0.05%

0.10%

0.15%

0.20%

0.25%

0.30%

Montana

Vermont

Oklahoma

DelawareWyoming

N Hampshire

Oregon

Illinois

Connecticut

Texas

Ohio

Iowa

Washington

Utah

Rhode Island

Maine

Nebraska

South Dakota

New Mexico

Missouri

South Carolina

Alabama

Alaska

Kansas

Mississippi

Kentucky

Michigan

Nevada

Idaho

Colorado

Arkansas

California

New York

Minnesota

Tennessee

Georgia

Massachusetts

Pennsylvania

Wisconsin

Virginia

Louisiana

New Jersey

Arizona

West Virginia

North Dakota

Florida

DC

Maryland

Hawaii

North Carolina

Indiana

Percent Difference

1. The estimate of householders will be exactly equal to the estimate of households (which is exactly equal to the 

estimate of occupied housing units). 

2. The dierence between the estimates of spouses and married-couple households was cut from 3.6% to 0.3% 

based on 2004 data. 

3. The dierence between the estimates of unmarried partners and unmarried-parter households was cut from 

3.3% to 1.3% based on 2004 data. 

4. We expect that the dierence between the estimate of married-couple subfamilies and spouses in subfamilies to 

be no larger than the empirical results shown with the 2004 data.

5. The overall estimate of vacant housing units should rise approximately 2.3% nationally based on 2005 data. 

6. There should not be any systematic signifcant changes to other tables neither in their estimates nor in their 

variances with the exception of total housing units which will no longer be exactly equal to the controls at the 

weighting area level or higher (including states). There will be a small margin of error associated with this 

estimate to refect the fact that the fnal estimate of total housing units is no longer controlled. 

Based on these results for the 2004 and 2005 data, we expected that the impacts on the 2006 data to be similar. 

Given that the impacts above are substantial, the plans for the implementation of this methodology were shared 

through various user groups and a user note was drafted to accompany the 2006 data release. Overall, we received 

very positive feedback from users concerning our plans. 
We also examined how eÿciently the raking matrix was performing for the 2006 weighting. Using the adopted 

methodology, we used 19 iterations everywhere based on identifying the point at which nationally the data inconsistencies cease to improve and actually begin to worsen. Our plan is to automate the process of determining how 

many iterations to use by adding a convergence criterion possibly at the weighting area level rather than the national 

level. A topic for future research is to see if we can collapse the raking down to two dimensions in place of three. 

Our initial work shows that the raking could converge both more quickly and closer to the control totals using two 

dimensions in place of three. Before implementing such a change, however, we would need to repeat our analysis 

that changing the number of dimensions would not cause an adverse impact on either the estimates or the variances. 

In particular, we are concerned that the variances could increase using this method. 

References

Alexander, C. & Roebuck, M. (1986). Comparison of Alternative Methods for Household Estimation, Proceedings 

of the 1986 American Statistical Association, American Statistical Association, Alexandria, VA. 

Navarro, A., Albright, K. & Asiala, M. (2004). An Alternative to the Principal Person Method for Weighting in the 

American Community Survey, Proceedings of the 2004 Joint Statistical Meetings, American Statistical Association, 

Alexandria, VA. 

Navarro, A., Griÿn, R., & Bates, L. (1990). Family Estimates Empirical Study, Proceedings of the 1990 Meetings 

of the American Statistical Association, American Statistical Association, Alexandria, VA. 

US Census Bureau (2006). Design and Methodology: American Community Survey, US Government Printing Oÿce, 

Washington DC.