Attachment W - A nonresponse Bias Study of the CE for the Ten Year Period 2010-2019

A Nonresponse Bias Study of
the Consumer Expenditure
Survey for the Ten-Year Period
2010-2019

May 9, 2022
Barry Steinberg, Sharon Krieger, Brett McBride, Brian Nix,
Michael Sverchkov, Daniel Yang
Consumer Expenditure Surveys Program Report Series

Table of Contents
1. Introduction........................................................................................................................... 2
2. Background and Approach....................................................................................................... 2
3. Methodology ......................................................................................................................... 6
3.1. Data ............................................................................................................................... 6
3.2. Sample Design and Weighting............................................................................................ 6
3.3. Significance tests for one-way and two-way socio-demographic comparisons............................ 7
3.4. Significance tests for linear regression analysis ..................................................................... 8
4. Individual studies to determine MCAR ...................................................................................... 8
4.1. Comparison of CE respondents to external data..................................................................... 8
4.2. Comparison of response rates across subgroups: General information......................................13
4.2.1. Interview Survey: Comparison of response rates across subgroups ......................................14
4.3 Models for determining MCAR..........................................................................................15
5. Calculating Relative Nonresponse Bias.....................................................................................15
5.1. OMB nonresponse bias equation........................................................................................15
6. Description of the Four Methods Used in Calculation of Relative Bias ..........................................17
6.1. Method 1 .......................................................................................................................17
6.2. Method 2 .......................................................................................................................17
6.3. Method 3 .......................................................................................................................18
6.4. Method 4 .......................................................................................................................19
6.5. Results Using the Four Methods to Quantify Relative Bias ....................................................19
7. Conclusion ...........................................................................................................................22
Appendices ..............................................................................................................................24
Appendix A..........................................................................................................................24
Appendix B..........................................................................................................................25
Appendix C..........................................................................................................................26
Appendix D..........................................................................................................................28
Appendix E ..........................................................................................................................29
Appendix F ..........................................................................................................................30
Appendix G..........................................................................................................................31
Appendix H..........................................................................................................................32
Appendix I ...........................................................................................................................33
Appendix J ...........................................................................................................................35
Appendix K..........................................................................................................................36

1. Introduction
The Consumer Expenditure (CE) Surveys are nationwide household surveys sponsored by the U.S.
Bureau of Labor Statistics to determine how U.S. consumers spend their money. There are two distinct
CE Surveys, a quarterly Interview Survey and a two-week Diary Survey. The Interview Survey provides
detailed information on large expenditures such as property, automobiles, and major appliances, as well
as on recurring expenditures such as rent, utilities, and insurance premiums. By contrast, the Diary Survey
provides detailed information on the expenditures of small, frequently purchased items such as food and
apparel. The data from the two surveys are then integrated to provide a complete picture of consumer
expenditures in the United States.
Over the past ten years (2010-2019), the response rates for both surveys decreased by about 20 percentage
points, from 73 percent to 53 percent in the Interview Survey, and from 71 percent to 52 percent in the
Diary Survey. These decreases are a concern because respondents and nonrespondents may have different
expenditure patterns, and if so, there may be a bias in the survey estimates, with decreasing response rates
increasing the amount of bias.
The Office of Management and Budget (OMB) which makes and enforces rules governing the collection
of all data in federally sponsored surveys, encourages all federal surveys to study their nonresponse bias
and requires such a study of all federal surveys whose response rates are below 80 percent. Both the CE
Interview and Diary Surveys have response rates below 80 percent, so a nonresponse bias study is
required of them. OMB’s directive requires an analysis of nonresponse to determine whether the
unreported data are “missing completely at random” (MCAR; see “Studies to determine MCAR
status,” later in this text, for a definition), and another analysis to estimate the amount of nonresponse
bias in the survey’s estimates. Both analyses are summarized in this report. 1
The analyses in this report show lower-income households are over-represented and higher-income
households are under-represented in both CE Surveys. The analyses also show response rates are higher
for rural households than for urban households in both CE Surveys; higher for homeowner households
than for renter households in the Diary Survey; and lower for homeowner households than for renter
households in the Interview Survey. Moreover, some of these relationships are changing over time. Taken
together, all of these findings indicate that the unreported data in the two CE surveys are not MCAR.
These over- and under-representations generally lead to nonresponse bias estimates of 0.0 percent to -2.0
percent in the Interview Survey and 0.0 percent to +3.5 percent in the Diary Survey.
2. Background and Approach
As mentioned above, over the ten-year period 2010-2019, the response rate for the Interview Survey
decreased from 73.4 percent to 53.7 percent, and the response rate for the Diary Survey decreased from
71.5 percent to 52.8 percent. (See Table 1.) This decrease is a concern because it may affect the accuracy
of CE’s expenditure estimates if the respondents and nonrespondents have different expenditure patterns.

1

OMB’s standards and guidelines for statistical surveys were originally published in 2006 and have been modified
periodically since then. The requirement that federal surveys with response rates below 80 percent conduct a
nonresponse bias study can be found in the September 2006 version (guideline 3.2.9 on page 16) and the October
2016 version (question 66 on page 60), and guidelines for conducting a nonresponse bias study can be found in the
September 2006 version (guideline 3.2.9 on page 16) and the October 2016 version (question 71 on page 64).

2

This report examines the possibility of respondents and nonrespondents having different expenditure
patterns by examining the surveys’ nonrespondents and determining whether their unreported data are
MCAR. The research presented in this report updates and expands the research performed in 2008 by CE
program staff, which found that expenditure estimates from the Interview Survey did not have a
significant amount of nonresponse bias even though the respondents and nonrespondents had different
characteristics, and even though the unreported data were not MCAR. 2
Table 1. Unweighted Response Rates for the CE Interview and Diary Surveys, 2010-2019

CE Interview Survey
Total
Collection
Type A 3
Complete
Eligible
Year
Noninterviews Interviews
Cases
2010
38,718
10,289
28,429
2011
38,348
11,358
26,990
2012
38,835
11,842
26,993
2013
39,142
13,034
26,108
2014
39,003
13,095
25,908
2015
36,692
13,118
23,574
2016
40,375
14,934
25,441
2017
40,193
15,714
24,479
2018
40,366
17,207
23,159
2019
40,389
18,688
21,701

CE Diary Survey
Total
Response
Type A
Complete
Eligible
Rate
Noninterviews Interviews
Cases
73.4% 19,988
5,692
14,296
70.4% 19,823
5,898
13,925
69.5% 20,298
6,537
13,761
66.7% 20,296
7,961
12,335
66.4% 20,476
7,170
13,306
64.2% 20,517
8,676
11,841
63.0% 20,391
8,839
11,552
60.9% 20,110
8,452
11,658
57.4% 20,133
9,054
11,079
53.7% 20,244
9,562
10,682

Response
Rate
71.5%
70.2%
67.8%
60.8%
65.0%
57.7%
56.7%
58.0%
55.0%
52.8%

This report contains a summary of four studies undertaken with more recent data to determine whether
CE’s data are MCAR, and four studies to estimate the amount of nonresponse bias in CE’s expenditure
estimates. The four MCAR studies are:
•
•
•
•

Study 1: A comparison of CE’s respondent demographic characteristics to those of the
American Community Survey (ACS).
Study 2: A comparison of response rates between subgroups of CE’s sample.
Study 3: A linear regression analysis of CE’s response rate trends and demographic
characteristic trends over the ten-year period 2010-2019.
Study 4: A logistic regression analysis of CE’s response rates using socio-demographic
variables that are available for both respondents and nonrespondents.

And the four nonresponse bias studies are:

2

See the August 2008 study “Assessing Nonresponse Bias in the CE Interview Survey: A Summary of Four
Studies,” by Boriana Chopova, Jennifer Edgar, Jeffrey Gonzalez, Susan King, Dave McGrath, and Lucilla Tan.

3

A Type A interview occurs when the survey’s field representative finds an occupied housing unit but is unable to
contact an eligible household member or is unable to convince a reluctant household member to participate in the
survey.

3

•
•
•
•

Study 1: A comparison of expenditure estimates from the survey’s respondents weighted two
different ways – with unadjusted base weights and with base weights adjusted to account for
nonresponse.
Study 2: A comparison of expenditure estimates identical to Study 1 except the base weights
are adjusted in a different way.
Study 3: A comparison of expenditure estimates identical to Studies 1 and 2 except the base
weights are adjusted in a third way.
Study 4: A comparison of expenditure estimates between two different subsets of CE’s
respondents, “pseudo respondents” and “pseudo nonrespondents.” (See Section 6.4, “Method
4” for definitions.),

All four MCAR studies conclude that the nonrespondents’ unreported data in both surveys are not
MCAR. Study 1 and Study 3 show the distributions of various socio-demographic characteristics differ
between the CE Surveys and the ACS, and the relationships between some of them are changing over
time. Study 2 and Study 3 show the response rates among various subgroups of the CE’s sample differ
from each other and the relationships between some of them are changing over time as well. And Study 4
shows CE’s response rate is affected by the demographic composition of the survey’s sample. All four of
these studies show different subgroups of the survey’s sample respond to the CE Surveys at different
rates, which means their patterns of missingness are not MCAR.
All four nonresponse bias studies conclude that nonresponse bias is small. Three of the four studies
compare the average annual expenditure per household computed with base weights to the average annual
expenditure per household computed with base weights adjusted for nonresponse. Study 1 uses the
nonresponse adjustment used in production which is a traditional cell adjustment method, while Study 2
and Study 3 use the weight of each household adjusted according to its probability of responding to the
survey using a logistic regression model. And Study 4 compares the average annual expenditure per
household for respondents that are easy to contact (require few contact attempts) to that of all respondents
(both those that are easy to contact and those that are hard to contact). All four of these studies show
nonresponse bias for the total expenditures summary variable ranges from approximately 0.0 percent to 2.0 percent in the Interview Survey, and from 0.0 percent to +3.5 percent in the Diary Survey, which
means CE’s nonresponse bias is small.
The report will describe each study and provide tables and graphs highlighting the magnitude of the bias
and the trends over the ten-year period.
Studies to determine MCAR status
To determine whether the missing values in the two CE Surveys are “missing completely at random”
(MCAR), the four studies described above were performed. Details of each are below. But before
proceeding, the term “MCAR” needs to be defined. The generally accepted definition comes from
Roderick Little and Donald Rubin (2002). According to them, data are MCAR if the mechanism that
produces the missing values is unrelated to the values of the data themselves and independent of any other
characteristics as well. 4 The question of whether the data are MCAR is important because nonresponse
bias is often associated with the data not being MCAR.

4

For more details, see Roderick J.A. Little and Donald B. Rubin, “Statistical Analysis with Missing Data,” 2002,
second edition.

4

In practical terms, this definition means CE’s data are MCAR if the difference in amount spent between
survey’s respondents and nonrespondents for the same set of goods and services is not statistically
significant (i.e., the pattern of missingness is independent of the data’s actual values), and if every
demographic subgroup of the survey’s sample has, statistically speaking, the same response rate (i.e., the
pattern of missingness is independent of any other characteristics). Since the expenditures of
nonrespondents are unknown, examining the response rates among different demographic subgroups is
one of the primary methods of determining whether a survey’s data are MCAR, and it is one of the
methods used in this report. 5
The first study examines whether the data are MCAR by comparing the distribution of socio-demographic
characteristics of the survey’s respondents to those of a recent census or a “gold standard” survey. The
American Community Survey (ACS) can be thought of as a “gold standard” survey because it has a large
sample size, a high response rate, a high coverage rate, and a reputation for accuracy. 6 Any differences
between the current survey and the gold standard survey suggest that the two surveys have different
response mechanisms, and since the gold standard survey is presumed to have a response mechanism
closer to that of an MCAR process, the other survey is presumed to have a response mechanism further
from that of an MCAR process, which means its missingness pattern is probably not independent of the
data themselves.
The second study examines whether the data are MCAR by comparing the survey’s respondents and
nonrespondents on several socio-demographic variables that are available for both groups. Any
differences between them indicate that the pattern of missingness is not independent of other variables,
and therefore the missing data are not MCAR. Despite the limited number of variables that can be used in
this analysis, it is another standard method of figuring out whether the data are MCAR, and it is used in
this study.
The third study looks at ten-year trends in response rate and demographic characteristic “relativities”
using simple linear regressions to determine whether the relationships of the response rates to each other
and the demographic characteristics to the ACS (the gold standard survey) are changing over time. In the
case of response rates, the relativity of interest is the ratio of response rate for a subgroup in CE to the
overall response rate. For example, the ratio of the response rate in the Northeast region to the response
rate for the whole country. In the case of demographic characteristics, the ratio of interest is the
proportion of CE’s respondents in a specific demographic subgroup to the proportion of the population in
the same demographic subgroup according to the ACS.

5

For those who like formal logic, the following may be helpful. Start by recalling that these two statements are
logically equivalent: “MCAR ⇔ A and B” and “~MCAR ⇔ ~A or ~B.” The key difference between these two
statements is that one has the word, “and” which means two things have to be demonstrated, while the other has the
word “or” which means only one thing has to be demonstrated. Thus, two things need to be demonstrated to show
the data are MCAR (the pattern of missing-ness is independent of the data’s actual values and the values of any
other variables), but only one thing needs to be demonstrated to show the data are not MCAR (the pattern of
missing-ness is not independent of the data’s actual values or the values of any other variables). Thus, we only need
to show that the pattern of missing-ness is not independent of the values of any other variables to show that the data
are not MCAR. We do not need to show anything about the unobservable expenditures of the survey’s
nonrespondents, hence demonstrating that the data are not MCAR is easier than demonstrating that they are MCAR.

6

The ACS Survey is sent to over 3.5 million housing units per year, which is a large sample size, and in 2016 its
response rate (94.7 percent and its coverage rate (91.9 percent) were both high.

5

Finally, the fourth study uses logistic regressions to examine whether the surveys’ response rates are
associated with certain socio-demographic characteristics. A logistic regression is a model of the
outcomes of a binary process, such as whether a sample household participates in the CE Survey. It has a
specific algebraic form that ensures its numeric values are between 0 and 1, which makes it suitable for
modeling probabilities.
3. Methodology
3.1. Data
For comparability of results, the analyses for the Interview and Diary Surveys both used the same ten
years of data, January 2010 through December 2019. The unit of analysis in these studies was generally
the consumer unit (CU), but a mixture of information about the CU and individual members was used for
the analyses comparing CE’s demographic characteristics to those of the ACS. CUs are similar, but not
identical to, households. 7 Nevertheless, most households comprise only one CU, so the terms are used
interchangeably herein.
3.2. Sample Design and Weighting
The CE Surveys’ sample design is a nationwide probability sample of addresses. That means a random
sample of addresses is selected to represent the addresses of all CUs in the nation. Most addresses have
only one CU living therein, hence the terms “address” and “CU” are used interchangeably in this report.
The CE Surveys actually have a two-stage sample design in which a random sample of geographic areas
called Primary Sampling Units (PSUs) is selected for the survey, and then a random sample of CUs is
selected within those PSUs to represent them. The Bureau of Labor Statistics (BLS) selects the sample of
PSUs and the U.S. Census Bureau selects the sample of CUs.
Each interviewed CU represents itself plus a number of other CUs that were not interviewed for the
survey. Therefore, each interviewed CU must be weighted to properly account for the proportion of the
population it represents. The weighting process starts with a “base weight,” which is the number of CUs
in the nation the CU selected for the sample represents. It is equal to the inverse of the CU’s probability
of selection, and since every CU in a PSU has the same probability of selection every CU selected in a
PSU has the same base weight.
Then, BLS makes three types of adjustments to the base weights: an adjustment in the rare situation
where a field representative finds multiple housing units where only a single housing unit was expected; a
nonresponse adjustment to account for CUs that were selected for the survey but did not participate in it;
and a calibration adjustment to account for nonresidential and other out-of-scope addresses in the
sampling frame, as well as sampling frame under-coverage. 8 These weight adjustments are made to each

7

A CU is a group of people living together in a housing unit who are related by blood, marriage, adoption, or some
other legal arrangement; who are unrelated but pool their incomes to make joint expenditure decisions; or is a person
living alone or sharing a housing unit with other people but who is financially independent of the other people. A
household consists of one or more people who live in the same dwelling and may consist of a single family or
another group of people.

8

Since invalid addresses are available for selection, this is accounted for during the calibration adjustment process.

6

individual CU that participated in the survey, hence each respondent CU has its own unique
“nonresponse-adjusted weight” and “final calibration weight.” All of the studies in this report use base
weights, except for the study comparing CE respondents to external data which uses final calibration
weights.
3.3. Significance tests for one-way and two-way socio-demographic comparisons
Respondents and nonrespondents were compared on several categorical socio-demographic
characteristics to ascertain whether the two groups had the same distribution of characteristics, and
whether those characteristics were correlated with the likelihood of responding to the survey. For these
comparisons, the Rao-Scott chi-square statistic was used, which is a design-adjusted version of the
Pearson chi-square statistic involving differences between observed and expected frequencies. For oneway comparisons, the null hypothesis was that the respondents in the CE Surveys and the ACS had the
same distribution of characteristics. And for two-way comparisons, the null hypothesis was that the
response status (interview or noninterview) of CUs in the CE Survey was independent of their sociodemographic characteristics.
Ten years of data were analyzed in this study (2010-2019), with a separate analysis done for each year.
The Rao-Scott chi-square statistic was generated for each comparison, with one statistic generated for
each year, and the results of those ten yearly analyses were summarized by counting the number of times
statistically significant results were obtained. For one-way comparisons, a difference in distribution was
considered to be “strongly significant” if statistically significant differences (p<0.05) were found in 5 or
more years analyzed, “moderately significant” for significant differences in 3 or 4 years, and “not
significant” otherwise. For example, the difference between CE’s and ACS’s “education” distributions
were statistically significant in 8 of the 10 years for the Interview Survey and in all 10 years for the Diary
Survey, so both cases were considered to be “strongly significant” (see Appendix B).
For two-way comparisons, the scoring system was similar to the one-way comparisons. For each
comparison, a net difference was calculated as the number of years the first subgroup listed had a
statistically significantly higher response rate than the second subgroup listed (p<0.05) minus the number
of years it had a statistically significantly lower response rate (p<0.05). In other words, for each year, if
the first subgroup listed had a statistically significantly higher response rate than the second subgroup
listed, then it was given a score of “+1”; if it had a statistically significantly lower response rate, then it
was given a score of “–1”; and if there was no statistically significant difference, then it was given a score
of “0.” Then the ten scores for the ten years were summed, giving an overall score between –10 and +10.
The difference between the two subgroups was then categorized as “strongly significant” if the overall
score was greater than or equal to +5 or less than or equal to –5; “moderately significant” if it was equal
to ±3 or ±4; and “not significant” if it was equal to ±2, ±1, or 0. Table 2 shows an example comparing the
response rates for the South region to the West region of the country:

7

Table 2. Example comparing the response rates for the South region to the West region, 2010-2019

Category
South’s response rate is significantly higher than the West’s
response rate
South’s response rate is significantly lower than the West’s
No significant difference between the South’s and West’s response
t
Overall
Score

# Years

Total Score
= # Years *
Score

3 years

3*(+1) =+3

0 years
7 years

0*(–1) = 0
7*( 0) = 0
+3

The overall score was +3, which was in the 3 or 4 range, hence the South’s response rates were higher
than the West’s response rates, and the difference was “moderately significant.”
3.4. Significance tests for linear regression analysis
For tests of significance pertaining to response rate subgroups, the ratio of each demographic subgroup’s
response rate to the overall response rate was calculated each year for the ten years analyzed. Then an
ordinary least squares (OLS) regression line Y = β0 + β1 X was fit to the data where the x-variable was the
year in which the data were collected, and the y-variable was the ratio of response rates for that year.
After fitting the line, a t-test was performed to determine whether its slope differed from zero. That is, the
two-sided hypothesis test of the slope was this:
H0 : β1 = 0
Ha : β1 ≠ 0
A level of significance of α=0.05 was used, so if p<0.05 for the t-test on the slope coefficient, then the
ratio of response rates is linearly increasing over time if the slope coefficient is positive, and linearly
decreasing over time if the slope is negative.
4. Individual studies to determine MCAR
4.1. Comparison of CE respondents to external data
As mentioned above, a common approach to analyzing the effect of nonresponse on a survey’s estimates
is to compare the distribution of socio-demographic characteristics of the survey’s respondents to that of a
recent census or other “gold standard” survey (Groves, 2006). If they are the same then the
nonrespondents are likely MCAR, but if they are different then the nonrespondents are most likely not
MCAR.
Appendix A for the Interview Survey and Appendix D for the Diary Survey show a 2019 comparison of
the distribution of selected socio-demographic characteristics between the CE and the ACS. Calibrationweighted respondents for CE are used in the comparisons between the CE survey and the ACS. The
characteristics compared are sex, age, race, education, CU size, housing tenure, number of rooms in a
housing unit, owner-occupied housing value, monthly rent, and CU income. Housing information about
the number of rooms in a housing unit, the housing unit’s market value, and the housing unit’s rental

8

value are available from the Interview Survey only. Tables for all years were produced but showing one
year provides information to get a sense for the work that was done.
Comparing the distribution for a particular characteristic in the CE data to its distribution in the ACS data
falls into the framework of a one-way chi-square goodness-of-fit test. The Rao-Scott chi-square statistic
described above is used to find out whether a characteristic’s distribution in the CE Survey and the ACS
are the same or different. 9 For both surveys, statistically significant differences (p < 0.05) were found for
many of the socio-demographic characteristics. Table 3 below summarizes these results.
Table 3. Summary of Comparison of Socio-demographic Characteristics in the CE Survey and ACS
Calibration-weighted CE respondents versus ACS

“Strongly Significant”
Differences

CE Interview Survey
Gender
Race
Education
CU size
No. rooms in housing unit
Owner-occupied housing value
Monthly rent
CU income

“Moderately Significant”
Differences

CE Diary Survey
Race
Education

CU income
Gender
CU size

Not Significant

It should be pointed out that there are factors beyond the characteristics of the respondents in these two
surveys that make differences likely to be statistically significant. First, the CE and the ACS differ in both
their data collection modes and question wording. And second, for some of the CU-level variables
examined, the definitional difference between CUs in the CE Surveys and households in the ACS may
impact the results even though most of the time they are the same. As a result, the strength of the
comparison of CE data with ACS data is limited by the extent to which the survey designs are truly
comparable.
Further analysis was done to observe trends over time for the CE data compared to the ACS data by using
linear regression analysis over the ten-year period from 2010 to 2019. The goal of this analysis is to
determine whether the CE and ACS have the same distributions of socio-demographic characteristics, and

9

For these comparisons, the Rao-Scott Chi-square test with the BRR variance method is used to reflect CE’s sample
design. The chi-square test is included for all socio-demographic characteristics listed, except for age and housing
tenure. The reason for excluding comparisons for these two variables is that they are used in calibration, meaning
their replicate weights and final weight in the BRR procedure create design correction factors that are zero or very
close to zero. This causes the resulting test statistics to become extremely large and their associated p-values to
become extremely small. Therefore, the comparison of CE’s distribution to ACS’s distribution for these two
variables is not practical.

9

if they are different whether they are moving towards each other or moving away from each other over
time. In other words, whether the CE/ACS ratio is moving towards 1.00 or moving away from 1.00. The
ten yearly CE/ACS relativities over the ten-year period 2010-2019 are plotted and analyzed to determine
whether their relationships are changing or holding steady over time.
CE-to-ACS comparison for the Interview Survey
As mentioned above, several of the characteristics have different distributions in the two surveys. Some
of the differences are rather small and statistically significant but a few of them have noticeable patterns
in which some socio-demographic subgroups are systematically over-represented or under-represented
relative to the ACS. Characteristics with noticeable patterns include the market value of owner-occupied
housing units, the monthly rent of rental housing units, and especially CU income (Figure 1). The graphs
below show the patterns of over-representation or under-representation for CU income. The graphs show
the socio-demographic subgroups along the horizontal axis, then above them there are ten circles showing
the CE/ACS relativities for those subgroups for each of the ten years, and a solid line connecting the
average value of the CE/ACS relativities to show the patterns.
Figure 1 shows the patterns of over-representation and under-representation for CUs’ by ranges of annual
incomes (less than $0 to $200,000+) in the Interview Survey. 10 The graph shows that CUs with incomes
below $50,000 are over-represented in the CE Interview Survey relative to the ACS, while CUs with
incomes of $50,000 or higher are under-represented. Specifically, CUs with incomes below $50,000 are
over-represented by 5 to 20 percent, while CUs with incomes of at least $50,000 are under-represented by
5 to 20 percent. Furthermore, for CUs with higher incomes (i.e., at least $50,000), the underrepresentation grows with their incomes, so that, for example, the $100,000-$149,999 subgroup is underrepresented in the CE Survey by about 10 percent, the $150,000-$199,999 subgroup is under-represented
by about 15 percent, and the $200,000+ subgroup is under-represented by about 20 percent. For the Diary
Survey, the patterns of over-representation and under-representation are similar to what is shown for the
Interview Survey in Figure 1.

10

The lowest income group (“Less than $15,000”) includes CUs with negative incomes. [Negative incomes can
occur when they have large capital losses, such as when they sell a house for less than its purchase price.] WORD
DOES NOT ALLOW COMMENTS IN FNs, so note the “Negative incomes” sentence is incorrect, plus the addition
of new text here: Negative incomes can occur when consumer units incur losses via self-employment or rental
property income. In addition to the “Less than $15,000” range, the other ranges are: $15,000 – $X; $X+1 to $Y;
…, and $200,000+. ALTERNATIVE: Since the authors use microdata, it is plausible that they excluded the
negative incomes. If that is the case, I suggest: In standard publications, the lowest income group (“Less than
$15,000”) includes CUs with negative incomes. (Negative incomes can occur when consumer units incur losses via
self-employment or rental property income.) However, we have excluded negative incomes from this analysis, so
that the minimum possible value is $0. In addition to the “$0 to $15,000” range, the other ranges we examine are:
$15,000 – $X; $X+1 to $Y; …, and $200,000+

10

Figure 1. CE-to-ACS Relativities for CU Income Subgroups in the Interview Survey, 2010-2019

These patterns for income are a problem because incomes are correlated with expenditures Therefore,
their patterns suggest that CUs with higher expenditures are under-represented in CE Surveys, which may
lead to bias.
Regression Analysis for the Interview Survey
In the previous two sections, we looked at the distributions of various socio-demographic characteristics
among CE’s respondents relative to the ACS. The next two sections look at how those distributions
changed over the ten-year period. The graphs show the ten-year period (2010-2019) on the horizontal
axis, and the yearly “relativities” of selected socio-demographic characteristics on the vertical axis. Each
graph also has a linear regression line showing how the relativities changed over time. The regression
lines are trend lines as opposed to a formal time series analysis.

11

Appendix C shows the following socio-demographic characteristics have statistically significant trends
(based on the coefficient for year) for one or more subgroups: age, race, education, CU size, monthly rent,
owner-occupied housing value, and CU income.
CU Income. For the Interview Survey, the subgroups with incomes less than $15,000, $15,000 to
$24,999, and $25,000 to $34,999 have regression lines with statistically significant slopes. Their p-values
were p=0.007, p<0.001, and p=0.008, respectively, for the calibration-weighted data. All three subgroups
have regression lines with CE/ACS relativities that start between 1.09 and 1.12 and increase to between
1.18 and 1.30. That means CUs in these subgroups were over-represented by 9 percent to 12 percent
relative to the ACS at the beginning of the ten-year period (i.e., in 2010) and they were over-represented
by 18 percent to 30 percent at the end of the ten-year period (i.e., in 2019). Since movement towards 1.00
is desirable, these subgroups are moving in the wrong direction. The less than $15,000 subgroup is shown
in Figure 2.
Figure 2. Lowest CU income group over-represented in the CE Interview Survey

Also, for the Interview Survey, the subgroups with incomes between $150,000 to $199,999 and
$200,000+ have regression lines with slightly positive slopes, but they are not statistically significant.
Their regression lines are well below the preferred ratio of 1.00 throughout the ten-year period. The CUs
in these subgroups were under-represented by about 10 to 20 percent relative to the ACS throughout the
ten-year period. These results are consistent with other recent research findings that show high-income
CUs are under-represented in the CE Interview Survey and that CE’s weighting procedures do not fix the
problem. 11 The $200,000+ subgroup is shown in Figure 3.

11

John Sabelhaus, David Johnson, Stephen Ash, David Swanson, Thesia Garner, and Steve Henderson, Is the
Consumer Expenditure Survey Representative by Income?, (NBER Working Paper No. 19589, October 2013).

12

Figure 3. Highest CU income group under-represented in the CE Interview Survey

Summary. The graphs in this section highlight two points, one being that the CE Interview Survey and
the ACS have different distributions for several socio-demographic characteristics, and the other being
that the relationships between some of those distributions are changing over time. Assuming ACS’s
distributions are more accurate than CE’s distributions, both of these findings/results suggest that the CE
Interview Survey’s data are not MCAR. Furthermore, the difference in the distribution of CU incomes
from the ACS distribution is growing over time for low-income CUs. Low-income CUs are overrepresented in the CE Interview Survey relative to the ACS and their over-representation is growing over
time, and high-income CUs are under-represented in the CE Interview Survey relative to the ACS and
their under-representation is relatively unchanged over time. This is a concern since CE is a survey about
spending, and the over-representation of low-income/under representation of high-income CUs may result
in CE’s expenditure estimates being under-estimated, and with the under-estimation growing over time.
This will be discussed later in the report.
Just like in the Interview Survey, Appendix E shows the results of the regression analysis from 2010 to
2019 for all subgroups in the Diary Survey, with statistically significant test results highlighted in gray.
The results relative to statistically significant trends for CU income in the Diary Survey are fairly
consistent with those of the Interview Survey.
4.2. Comparison of response rates across subgroups: General information
This study examined the response rates by socio-demographic characteristics among subgroups for which
such characteristics could be identified for both respondents and nonrespondents. Any differences
between them indicate that the pattern of missingness is not independent of other variables, and therefore
the missing data are not MCAR. As mentioned above, such comparisons are usually limited in scope
because little is known about the nonrespondents since they do not respond to the survey. Consequently,
the variables examined for them are often limited to a small number of variables on the sampling frame
and maybe a few other variables that data collectors are able to collect for every sample unit regardless of
their participation in the survey. For this reason, the subgroups analyzed were limited to region of the

13

country (Northeast, Midwest, South, West), “urbanicity” (urban, rural), PSU size class, housing tenure
(owner or renter), and housing values for owners and renters. 12
Base-weighted response rates were calculated for these subgroups separately for both the Diary Survey
and the four waves of the Interview Survey. 13 As a reminder, base weights are the inverse of a sample
address’s probability of selection. Base-weighted response rates answer the question “What percent of
the survey’s target population do the respondents represent?” Base-weighted response rates are defined as
the sum of base-weighted interviewed units divided by the sum of base-weighted interviewed units plus
the base-weighted Type A noninterviews units. Type A noninterviews occur when no interview is
completed at an occupied eligible housing unit.
Base-weighted response rate =
•
•
•

∑𝑖𝑖∈𝐼𝐼 𝑤𝑤𝑖𝑖
where:
∑𝑖𝑖 ∈𝐼𝐼 𝑤𝑤𝑖𝑖+ ∑𝑖𝑖∈𝐴𝐴 𝑤𝑤𝑖𝑖

wi = base weight for the ith CU.
“I” is the set of all CUs that completed an interview; and
“A” is the set of all CUs that are Type A noninterviews.

4.2.1. Interview Survey: Comparison of response rates across subgroups
Interview Survey response rates were examined across socio-demographic subgroups for the ten-year
period (2010-2019) and their results are summarized in Appendix F, Appendix G, and Appendix H.
Appendix F shows response rates for each subgroup and the nation by wave. Only results for 2019 are
shown to keep the report more condensed. Appendix G summarizes the test results from the Rao Scott
chi-square tests for each of the subgroup comparisons only for Wave 4, again to keep the report more
condensed. And Appendix H shows response rate relativities for each of the subgroups relative to the
nation by year and wave. Examples of these subgroup comparisons include the Northeast vs. Nation,
Midwest vs. Nation, South vs. Nation, and West vs. Nation. The response rate relativities are then used to
create the regression lines that demonstrate the statistical significance of the slope. For each of the four
interview waves, all possible pairs of subgroups within the six categories were examined over the ten-year
period.
Using a level of significance α=0.05, a t-test of slope coefficients from linear regression is used to find
whether the slope of the ten-point regression line (each point represents one year) differs from zero. For
example, if the slope is 0.0038 (i.e., the response rate relativity increases 0.0038 per year) and the

12

The information on housing values is from the 2000 decennial census for CUs that were in the sample in 2010
through 2014, and it is from the 2010 decennial census for CUs that were in the sample in 2015 through 2019. This
means the information is available for every CU, both respondents and nonrespondents, but it is out-of-date.
13

If a household is selected to participate in the Interview Survey, that address will be scheduled to have four
interviews, one every three months, over the course of a ten-month period. The interview number (from 1 to 4), also
called the wave, will be used to identify which visit in the sequence it represents. For example, if the household is
scheduled for interviews in February, May, August, and November then the February interview would be Wave 1,
the May interview would be Wave 2, the August interview would be Wave 3, and the November interview would be
Wave 4.

14

standard error of the slope is 0.0016, then it has a t-statistic of 2.38 (= (0.0038 – 0.0000)/0.0016), which
means the slope is statistically different from zero at α=0.05 level of significance.
The two-way comparisons show that there are many statistically significant differences in response rates
for every subgroup and since there is not a trend for convergence for the overwhelming majority of these
comparisons, this strongly demonstrates that the data are not Missing Completely at Random for the
Interview Survey.
The Diary Survey response rates analyses were examined across socio-demographic subgroups in a
similar fashion to the Interview Survey and their results are summarized in Appendix I, Appendix J, and
Appendix K. Much like the Interview Survey, response rate differences within the subgroups suggest that
the data are not MCAR because the respondent and nonrespondent CUs are not simple cross sections of
the original sample.
4.3 Models for determining MCAR
In this study a model of the probability of a sample household participating in the CE Survey is
developed. It is a logistic regression model where the independent variables are chosen from a list of
geographic and housing characteristics that are available for every household on the sampling frame, and
the dependent variable is the household’s probability of participating in the survey. The purpose of the
model is to determine whether there is a relationship between these geographic and housing
characteristics and a household’s probability of participating in the survey. If there is a relationship, then
the nonrespondents’ missing data is not MCAR.
The variables were chosen for the model with a forward stepwise selection process, and then after the
main effect variables were chosen the interaction terms were evaluated and chosen. Separate models were
generated for the Interview and Diary Surveys using all ten years of data. The two models were nearly
identical to each other, with region of the country (Northeast, Midwest, South, West), urbanicity (urban or
rural), and household tenure (homeowner or renter) as the main effect variables, and many of their twoand three-way combinations as the interaction terms. The small p-values on the individual variables in the
models and the high overall goodness-of-fit statistics on the models indicate that there is a relationship
between the variables and a household’s probability of participating in the survey. That means the
nonrespondents’ missing data is not MCAR.

5. Calculating Relative Nonresponse Bias
5.1. OMB nonresponse bias equation
To estimate nonresponse bias, OMB (2006) provided a specific formula for computing the nonresponse
bias of the respondent sample mean. This is given by:

where:

𝐵𝐵 (𝑦𝑦�𝑅𝑅 ) = 𝑦𝑦�𝑅𝑅 − 𝑦𝑦�𝑇𝑇 = �

15

𝑛𝑛𝑁𝑁𝑁𝑁
� (𝑦𝑦�𝑅𝑅 − 𝑦𝑦�𝑁𝑁𝑁𝑁 )
𝑛𝑛








𝐵𝐵(𝑦𝑦�𝑅𝑅 ) is the nonresponse bias of the respondent sample mean;
𝑦𝑦�𝑅𝑅 is the mean based only on respondent cases;

𝑦𝑦�𝑇𝑇 is the mean based on all sample cases;

𝑛𝑛𝑁𝑁𝑁𝑁 is the number of nonrespondent cases in the sample; and

𝑛𝑛 is the number of cases in the sample; and

𝑦𝑦�𝑁𝑁𝑁𝑁 is the mean based only on nonrespondent cases.

Slight modifications to the nonresponse bias formula were necessary because relevant data (e.g.,
expenditures) were not available for the CE nonrespondents. After the modifications (described later in
Section 6.1 through 6.4) were made, the application of the formula to CE expenditure data becomes:

where:




𝐵𝐵 (𝑍𝑍̅𝑅𝑅 ) = 𝑍𝑍̅ 𝑅𝑅 − 𝑍𝑍̅𝑇𝑇 = �

𝑁𝑁𝑁𝑁𝑁𝑁
�(𝑍𝑍̅𝑅𝑅 − 𝑍𝑍̅ 𝑁𝑁𝑁𝑁 )
𝑁𝑁

𝐵𝐵(𝑍𝑍̅ 𝑅𝑅 ) is the nonresponse bias in the base-weighted respondent sample mean.

𝑍𝑍̅𝑅𝑅 is the base-weighted mean of expenditures for all respondent CUs (this estimate excludes

pseudo nonrespondent CUs, defined below, from the calculation);
𝑍𝑍̅𝑇𝑇 is the base-weighted mean of expenditures for all CUs (this estimate includes all CUs,
respondents and pseudo nonrespondents);





𝑁𝑁𝑁𝑁𝑁𝑁 is the base-weighted number of pseudo nonrespondent CUs;

𝑁𝑁 is the base-weighted number of CUs; and

𝑍𝑍̅𝑁𝑁𝑁𝑁 is the base-weighted mean of expenditures for all pseudo nonrespondent CUs;

Pseudo nonrespondents are respondents with low contact rates. “Harder-to-contact” respondents are
considered as proxy nonrespondents. It draws on a theory known as the ‘continuum of resistance’ to
identify appropriate respondents to serve as proxy nonrespondents. This theory suggests that sample units
can be ordered across a continuum by the amount of interviewer effort exerted in order to obtain a
completed interview (Groves, 2006). Their difficulty in being contacted makes them similar to
nonrespondents in terms of their low probability of participating in the survey, and it is assumed that they
are similar to nonrespondents in other ways as well, such as in the expenditures they make.
For the estimates of nonresponse bias in the pseudo nonrespondent study, we computed relative
nonresponse bias, instead of the absolute nonresponse bias described in the formula above. The reason is
that the dollar amounts vary substantially across expenditure categories, making comparisons difficult.
For example, a nominal difference in dollars could be considered large for a lower expenditure variable
but small for a high expenditure variable. Therefore, a relative bias percentage is a more appropriate
statistic for comparisons across categories. The relative nonresponse bias is a percentage calculated by
dividing the nonresponse bias by the adjusted base-weighted mean expenditures of all CUs and is shown
below:

16

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 (𝑍𝑍𝑅𝑅̅ ) =

(𝑍𝑍̅𝑅𝑅 − 𝑍𝑍̅𝑇𝑇 )
× 100%
𝑍𝑍̅𝑇𝑇

As a final point of clarification, the above formula was applied separately for each method. For Method 1,
𝑍𝑍̅𝑅𝑅 represents the base-weighted respondent mean and 𝑍𝑍̅ 𝑇𝑇 represents the final calibration weighted
respondent mean, for Methods 2 and 3, 𝑍𝑍̅ 𝑅𝑅 represents the base-weighted respondent mean and 𝑍𝑍̅ 𝑇𝑇
represents the Propensity-weighted respondent mean (see sections 6.2 and 6.3), and for Method 4, 𝑍𝑍̅ 𝑅𝑅
represents the base-weighted “pseudo respondent” mean and 𝑍𝑍̅ 𝑇𝑇 represents the all base-weighted
respondents’ mean.

6. Description of the Four Methods Used in Calculation of Relative Bias
The following four methods were used to estimate the amount of nonresponse bias in the CE Surveys.
The exact amount of nonresponse bias is unknown, so four methods of estimating it were developed to
generate a range of plausible values for the true but unknown amount but taken together they give a good
idea of the amount of nonresponse bias in the CE Surveys.
6.1. Method 1
Method 1 calculates nonresponse bias as the difference between the weighted estimate of the population
mean prior to any nonresponse adjustment and the weighted estimate of the mean after nonresponse
adjustment. “Base” weights were used for the weights prior to nonresponse adjustment, and “final”
weights were used for the weights after nonresponse adjustment. The final weights include adjustments
for both nonresponse and calibration, but the nonresponse adjustment is its largest component. This
estimate of nonresponse bias assumes the nonresponding CUs are MAR, and the nonresponse adjustment
factor in the final weights is a reasonable estimate of the inverse of each CU’s response probability.
This method uses the general bias formula, 𝐵𝐵(𝑦𝑦�) = 𝐸𝐸 (𝑦𝑦�) − 𝑦𝑦�, where 𝑦𝑦� =

∑𝑖𝑖 ∈𝑅𝑅 𝑤𝑤𝐵𝐵
𝑖𝑖 𝑦𝑦𝑖𝑖
∑𝑖𝑖∈ 𝑅𝑅 𝑤𝑤𝐵𝐵
𝑖𝑖

is a weighted

estimate of the population mean expenditure ignoring nonresponse, 𝑤𝑤𝑖𝑖𝐵𝐵 is the base-weight of the i-th CU,
and R denotes the set of all respondents. 𝐸𝐸(𝑦𝑦�) can be estimated by 𝑦𝑦�, and 𝑦𝑦�, can be estimated by an
unbiased (or consistent) estimate that takes into account nonparticipation and more specifically,
nonresponse. Assuming that the final calibration weighted estimate accounts for nonresponse, 𝑦𝑦� can be
∑ 𝑤𝑤𝐹𝐹21 𝑦𝑦
estimated by 𝑦𝑦� = 𝑖𝑖∈𝑅𝑅 𝑖𝑖 𝐹𝐹21 𝑖𝑖 , where 𝑤𝑤𝑖𝑖𝐹𝐹21 is the final calibration weight. This estimate assumes that
∑𝑖𝑖∈𝑅𝑅 𝑤𝑤𝑖𝑖

response is MAR and response correction to the final calibration weight is a reasonable estimate to the
� 𝐹𝐹21(𝑦𝑦�) =
inverse of the response probability. Therefore, the nonresponse bias can be estimated by 𝐵𝐵
𝐵𝐵
𝐹𝐹21
∑𝑖𝑖∈𝑅𝑅 𝑤𝑤𝑖𝑖 𝑦𝑦𝑖𝑖
∑𝑖𝑖∈𝑅𝑅 𝑤𝑤𝑖𝑖 𝑦𝑦𝑖𝑖
(𝑍𝑍�𝑅𝑅 −𝑍𝑍�𝐹𝐹 )
̅
× 100% where 𝑍𝑍̅𝑅𝑅 is the base-weighted
𝐵𝐵 −
𝐹𝐹21 where 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 (𝑍𝑍𝑅𝑅 ) =
∑𝑖𝑖∈𝑅𝑅 𝑤𝑤𝑖𝑖

∑𝑖𝑖∈𝑅𝑅 𝑤𝑤𝑖𝑖

mean and 𝑍𝑍̅𝐹𝐹 is the final calibration weighted mean.

𝑍𝑍�𝐹𝐹

6.2. Method 2

Method 2 calculates the difference between the weighted estimates of the population mean before any
nonresponse adjustments minus the propensity-weighted estimate. This propensity-weighted estimate is
developed using a logistic regression model that contains socio-demographic variables. Initial research

17

showed that the surveys’ response rates are affected by certain socio-demographic variables. Those
variables were household tenure, urbanicity, region of residence, and many of their two-way interaction
terms. Further research showed that CU size was also a good variable to use and was therefore added to
the current model.
The selected Interview Survey model was:
𝑳𝑳𝑳𝑳 (𝒑𝒑/(𝟏𝟏 − 𝒑𝒑)) = 𝜷𝜷𝟎𝟎 + 𝜷𝜷𝟏𝟏 I(Rural) + 𝜷𝜷𝟐𝟐 𝐈𝐈(Renter) + 𝜷𝜷𝟑𝟑 I(Tenure Other) + 𝜷𝜷𝟒𝟒 𝐈𝐈(Midwest) + 𝜷𝜷𝟓𝟓 𝐈𝐈(South) +
𝜷𝜷𝟔𝟔 𝐈𝐈(West) + 𝜷𝜷𝟕𝟕 𝐈𝐈(CU Size 1) + 𝜷𝜷𝟖𝟖 𝐈𝐈(CU Size 2) + 𝜷𝜷𝟗𝟗 𝐈𝐈(CU Size 3 or 4) + 𝜷𝜷𝟏𝟏𝟏𝟏 (Percentage of
Noncontacts) + 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Rural∗ Midwest) + 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Rural ∗ South) + 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Rural ∗
West)+ 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Renter ∗ Midwest) + 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Renter ∗ South) + 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Renter ∗
West) + 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Tenure Other ∗ Midwest) + 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Tenure Other ∗ South) + 𝜷𝜷𝟏𝟏𝟏𝟏 𝐈𝐈(Tenure Other∗
West) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 1*Rural) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 2*Rural) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 3 or 4 * Rural) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU
Size 1 * Renter) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 1 * Tenure Other) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 2 * Renter) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 2 *
Tenure Other) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 3 or 4 * Renter) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 3 or 4 * Tenure Other) + 𝜷𝜷𝟐𝟐𝟐𝟐 𝐈𝐈(CU Size 1
* Midwest) + 𝜷𝜷𝟑𝟑𝟑𝟑 𝐈𝐈(CU Size 1 * South) + 𝜷𝜷𝟑𝟑𝟑𝟑 𝐈𝐈(CU Size 1 * West) + 𝜷𝜷𝟑𝟑𝟑𝟑 𝐈𝐈(CU Size 2 * Midwest) +
𝜷𝜷𝟑𝟑𝟑𝟑 𝐈𝐈(CU Size 2 * South) + 𝜷𝜷𝟑𝟑𝟑𝟑 𝐈𝐈(CU Size 2 * West) + 𝜷𝜷𝟑𝟑𝟑𝟑 𝐈𝐈(CU Size 3 or 4 * Midwest) + 𝜷𝜷𝟑𝟑𝟑𝟑 𝐈𝐈(CU Size 3
or 4 * South) + 𝜷𝜷𝟑𝟑𝟑𝟑 𝐈𝐈(CU Size 3 or 4 * West) where 𝒑𝒑 is the probability of response.

The Interview Survey and Diary Survey have similar models with the only difference being the exclusion
of a few interaction terms not being used in the Diary Survey model because they were not statistically
significant.
As a reminder, logistic regression is a model of the probability of outcomes of a binary process, such as
whether a sample household participates in the CE Surveys.
To estimate nonresponse bias, Method 2 estimates 𝑦𝑦� using the estimate of the CU’s probability of
responding:
� 𝑃𝑃𝑃𝑃𝑃𝑃𝑃𝑃 (𝑦𝑦�) =
𝐵𝐵

∑𝑖𝑖∈𝑅𝑅 𝑤𝑤𝐵𝐵
𝑖𝑖 𝑦𝑦𝑖𝑖
∑𝑖𝑖∈𝑅𝑅 𝑤𝑤𝐵𝐵
𝑖𝑖

−

∑𝑖𝑖 ∈𝑅𝑅(𝑤𝑤𝐵𝐵
𝑖𝑖 /𝑝𝑝𝑖𝑖 )𝑦𝑦𝑖𝑖
∑𝑖𝑖∈ 𝑅𝑅(𝑤𝑤𝐵𝐵
𝑖𝑖 /𝑝𝑝𝑖𝑖)

where 𝑝𝑝𝑖𝑖 =

1

1+𝑒𝑒−�𝛽𝛽0+𝛽𝛽1 𝑥𝑥1 +𝛽𝛽2 𝑥𝑥2 +⋯+𝛽𝛽𝑛𝑛 𝑥𝑥𝑛𝑛 +𝜀𝜀 �

is the estimate of the CU’s response probability (propensity score), assuming that the non-response is
MAR and 𝑝𝑝𝑖𝑖is a reasonable estimate of probability to respond. The resulting propensity scores will have a
score between 0.0 and 1.0 and the reciprocal of this propensity will be multiplied by the current base(𝑍𝑍� −𝑍𝑍� )
weight to get the adjusted base-weight. Relative bias can then be estimated by (𝑍𝑍̅𝑅𝑅 ) = 𝑅𝑅𝑍𝑍� 𝐹𝐹 × 100%
𝐹𝐹
where 𝑍𝑍̅ 𝑅𝑅 is the base-weighted mean and 𝑍𝑍𝑝𝑝̅ is the propensity adjusted base-weighted mean.
6.3. Method 3

Method 3 is nearly identical to Method 2 except that it contains a contact history variable (noncontact
percentage) in the logistic regression model in addition to all of the socio-demographic variables
discussed in Method 2. This contact history variable was calculated as the percent of noncontacts during
the interview process and was found to have a strong relationship to propensity to respond. Having this
variable in the model resulted in a much wider range of propensity scores than for those in Method 2.
When the resulting propensity adjusted base-weighted means were calculated, there was noticeably more
variance of the relative bias. Therefore, the model with this variable included was analyzed separately.
Everything else pertaining to Method 2 described above also applied to Method 3.

18

6.4. Method 4
For Method 4, responders were divided into “pseudo responders” and “pseudo nonresponders” based on
contact history. Responders who have high contact rates were treated as pseudo responders while those
with low contact rates were treated as pseudo nonresponders since they were harder-to-contact. We
assume that the pseudo nonresponders from the real respondent part of the sample behave like real
nonrespondents regarding expenditure patterns. While not directly verifiable, this assumption is based on
the theory known as the “continuum of resistance” to identify certain respondents to serve as pseudo
nonrespondents. The theory suggests that sampling units can be ordered by the amount of interviewer
effort needed to obtain a completed interview (Groves 2006) and was used in the previous nonresponse
bias study. 14
Using data collected in the Interview Survey Contact History Instrument (CHI), respondents were defined
to be “harder to contact” when greater than 50 percent of the contact attempts resulted in noncontacts. The
only exception was if there were two contact attempts resulting in one contact, these CUs were also
considered “harder to contact” and were treated as pseudo nonresponders. This cut-off was selected to
yield a response rate that coincided with the observed response rates during the 2010-2019 period covered
by the data that ranged from the 53.7 percent 73.4 percent.
The formula used to calculate the relative bias was similar to those mentioned above except the numerator
is the difference between the base-weighted mean of the pseudo respondents and the base-weighted mean
of all respondents divided by the base-weighted mean of all respondents. It can be shown as follows:
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 (𝑋𝑋�𝑅𝑅 ) =
Where:

(𝑋𝑋�𝑅𝑅 − 𝑋𝑋�𝑇𝑇 )
× 100%
𝑋𝑋�𝑇𝑇

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝐵𝐵𝐵𝐵𝐵𝐵𝐵𝐵 (𝑋𝑋�𝑅𝑅 ) is the relative nonresponse bias % of the weighted sample mean,

𝑋𝑋�𝑅𝑅 is the weighted mean of the pseudo respondent expenditures.
𝑋𝑋�𝑇𝑇 is the weighted mean of all respondent expenditures,

6.5. Results Using the Four Methods to Quantify Relative Bias
Interview Survey Variables Analyzed
As has been discussed, four methods to estimate relative nonresponse bias were used in the analysis. The
main variable used in the report is the summary variable, ZTOTALX4, that contains all CE Interview
expenditures. This variable was analyzed by year to find out if relative bias has changed over time, and by

14

See the August 2008 study “Assessing Nonresponse Bias in the CE Interview Survey: A Summary of Four
Studies,” by Boriana Chopova, Jennifer Edgar, Jeffrey Gonzalez, Susan King, Dave McGrath, and Lucilla Tan.

19

wave to find out if different interview waves contain more or less bias than others. As described above in
the report, relative nonresponse bias point estimates are a percentage calculated by dividing the
nonresponse bias by the adjusted base-weighted mean expenditures of all CUs.
Interview Survey Findings
Figures 4 and 5. Relative Bias by Year and Wave
Figure 4

Figure 5

ZTOTALX4 by Year

The graphs for Methods 1-4 in Figure 4 show negative relative bias for all three methods for years 20102014 while there are varying degrees of negative relative bias for the earlier years and in later years of the
research period. In fact, starting in 2015, Method 2 and 3 for actually show a small positive bias. In
general, the four methods have relative bias ranging from -1.8 percent to 0.8 percent. Over the ten-year
period, relative bias shows a negative trend for Method 1, a bit of an upward trend for Method 2 and
Method 3 and flat over the 2010-2019 period for Method 4.
The data points in Figure 4 also show the relative bias for all four methods by year do not differ that
dramatically, especially in the early years 2010-2014. They are within one percentage point of each other
for these early years of the research period but Methods 2 and 3 increase slightly starting in 2015. A slight
negative relative bias implies that our responders spend a little less than our nonresponders and vice versa
for positive relative bias. Method 4, which separates the responders into pseudo responders and pseudo
nonresponders (described above), shows similar results.
Overall, Figure 4 shows that there is not total agreement regarding a recent relative bias trend where
Method 2 has trended slightly positive where Method 3 has been flat while Method 1 has trended
negative, but Method 4 has begun to trend higher. In addition, through 2014, Method 1 and Method 2
were similar but split beginning after 2014 with Method 1 now showing close to -1.5 percent while
Method 2 trending very close to 0 percent.

20

ZTOTALX4 by Wave
The chart in Figure 5 clearly shows negative relative bias between -0.2 percent and -2.0 percent. There is
some evidence that ZTOTALX4 expenditures for Wave 4 display slightly less negative relative bias than
the other waves for most of the methods. Perhaps, this is due to an extra effort by the field reps to get the
CUs to participate in the survey.
Interview Survey Summary
In summary, the four methods for the Interview Survey show the presence of slight negative relative bias
over time and by wave. The level of negative relative bias varies by method and is generally in the range
of -0.5 percent to -2.0 percent apart from 2015-2019 for Method 2 and Method 3. However, the relative
bias does not appear to be strongly correlated to the decreasing response rates over the ten-year period.
Diary Survey Variables Analyzed
Similar to the Interview Survey, four methods to estimate relative bias were used in the Diary Survey
analysis using the variable ZTOTAL (total expenditures). ZTOTAL was analyzed by year to find out if
bias has changed over time.
The relative bias estimates for the Diary Survey using Methods 1-3 were calculated in the same manners
as were their Interview Survey counterparts, with one difference: For the Diary Survey, a noncontact
percentage greater than 40 percent was used as the cut-off to separate pseudo responders versus pseudo
nonresponders. This cut-off was selected to yield a response rate between 52.8 percent and 71.5 percent,
which corresponds to the Diary Survey’s actual response rate during the research period.
Diary Survey Findings
Figure 6. Relative Bias by Year
Figure 6

21

ZTOTAL
In general, the four methods for ZTOTAL, the Diary Survey summary variable that contains all
expenditures, show a non-negative relative bias (with one data point exception) in the range of 0.0 percent
to 3.6 percent over the ten-year period. However, in 2019, all four Methods have slightly higher relative
bias in the 1.7 percent to 3.6 percent range as shown in Figure 6 above. As a reminder, a slight positive
relative bias implies that CE responders are spending a little more than the estimates for nonresponders,
which is opposite to the results for most summary variables in the Interview Survey.
Diary Survey Summary
In summary, there is a slight level of positive relative bias for most of the summary variables in the Diary
Survey using the all expenditures variable, ZTOTAL. When looking at the ZTOTAL graph, the four
methods hint at a slight trend towards increasing positive bias but not as dramatically as the drop in Diary
Survey response rates over the ten-year period. A strong correlation that would show increasing
nonresponse relative bias, either positive or negative, related to declining response rates could be cause
for concern because survey data may become inaccurate in representing expenditures and other items that
CE publishes. A reminder that positive relative nonresponse bias is not a measure of respondents
underreporting expenditures but instead compares the responders’ actual reported expenditures to the four
estimates of the nonresponders’ reported expenditures.
7. Conclusion
In 2006, OMB issued a directive requiring any federal household survey with a response rate below 80
percent to perform a nonresponse analysis. Both the Interview and Diary Surveys have a response rate
below 80 percent, so they are required to perform the nonresponse analysis. Each of the four studies in
this report was designed to analyze nonresponse in the Interview and Diary Surveys by answering one or
more of the following questions: (1) Are the data in the Interview and Diary Surveys MCAR? (2) What
are the demographic characteristics of the nonrespondents and respondents? and (3) What additional
information does the linear trend analysis provide regarding socio-demographic movement over the ten
collection years.
The studies undertaken to find out whether missing data in the CE Surveys are MCAR were described in
Section 3. Statistically significant differences were found by region of the country, PSU size class,
urbanicity, and housing tenure for the Interview Survey and for all subgroups except Housing value for
the Diary Survey. Likewise, the study comparing respondent demographic characteristics to the
American Community Survey’s population found statistically significant differences for most of the
variables examined. Because statistically significant differences were found in each of these studies, we
conclude that the data are not MCAR. No individual study was intended to provide a definitive answer to
the questions raised in this research. However, all the studies conclude that the Interview and Diary
Survey respondents and nonrespondents have different characteristics for many variables and the data are
not MCAR.
The studies undertaken to estimate nonresponse bias in the CE Surveys were described in Section 5. The
total expenditure summary variable for the Interview Survey, ZTOTALX4, was analyzed in detail to
determine if there was a presence of relative nonresponse bias. Analysis of the Interview Survey
presented robust graphic detail and tables of bias for ZTOTALX4 by year and wave. The results showed

22

a slight negative relative bias in a general -0.5 percent to -2.0 percent range over the ten-year period. This
implies that the responders spent a little less than the nonresponders over the period and there was
statistical evidence supporting this.
The Diary Survey total expenditures summary variable, ZTOTAL, was also analyzed in detail to
determine if there was a presence of relative nonresponse bias. As opposed to the total expenditures
variable in the Interview Survey, this variable showed a slight positive relative bias in a general 0.0
percent to 2 percent range over the ten-year period. This implies that the responders spent a little more
than the nonresponders over the period.
None of the four methods was designed to exclusively find the exact level of relative bias but rather
provide a range of estimates. Each method had its strengths and weaknesses and they differ enough to
provide a realistic range of estimates for the analysis. Under the MAR 15 assumption, the conclusion is
that the relative bias seems to be minor and not essentially important.

15

Missing at Random means the propensity for a data point to be missing is not related to the missing data, but it is
instead related to some of the observed data.

23

Appendix A
Interview Survey 2019 – Comparison of selected characteristics of Calibration-weighted CE respondents to
the ACS
ACS
Gender (%) 1
Male
Female
Age (%)
Under age 25
25-34
35-44
45-54
55-64
65-74
75 and over
Race (%) 1
White
Black
Other
Education 2 (%) 1
Less than high school
High school graduate
Some college/Assoc degree
College graduate
CU size (%) 1
1 person
2 persons
3 persons
4+ persons
Housing Tenure (%)
Owner
Renter

CE

49.2
50.8

48.9
51.1

31.5
13.9
12.8
12.4
12.9
9.6
6.9

31.7
13.8
12.6
12.5
13.0
9.7
6.7

72.0
12.8
15.2

78.4
13.3
8.4

11.4
26.9
28.6
33.1

11.0
25.3
27.9
35.8

28.3
34.3
15.3
22.1

30.1
33.2
14.3
22.4

64.1
35.9

63.6
36.4

No. of rooms in housing unit (%) 1
1
2
3-4
5-6
7-8
9+
Owner-occupied housing value (%) 1
Less than $50,000
$50,000 to $99,999
$100,000 to $149,999
$150,000 to $199,999
$200,000 to $299,999
$300,000 to $499,999
$500,000 to $999,999
$1,000,000 +
Monthly rent (%) 1
Less than $500
$500 to $749
$750 to $999
$1,000 to $1,499
$1,500 to $1,999
$2000 +
No cash rent
CU income (%) 1
Less than $15,000
$15,000 to $24,999
$25,000 to $34,999
$35,000 to $49,999
$50,000 to $74,999
$75,000 to $99,999
$100,000 to $149,999
$150,000 to $199,999
$200,000 +

1

ACS

CE

2.4
2.9
25.5
36.9
20.7
11.6

1.1
2.7
22.9
38.3
23.8
11.2

6.2
10.2
11.4
13.2
20.4
21.4
13.1
3.9

6.2
9.7
11.9
13.8
20.6
21.6
13.2
3.0

14.1
18.8
18.8
23.4
11.4
8.7
4.8

15.3
19.7
19.7
23.7
10.5
8.7
2.4

9.8
8.3
8.4
11.9
17.4
12.8
15.7
7.2
8.5

12.3
10.7
9.6
13.1
16.0
11.5
13.7
6.2
6.9

Indicates a statistically significant difference (p < 0.05) between the Interview Survey and the ACS, using calibration-weighted CE
respondents. For these comparisons, the Rao-Scott Chi-square test with the BRR variance method is used to reflect CE’s sample
design. The distributions for age and housing tenure are shaded in this table because their differences were not compared. The reason
for excluding comparisons for these two variables is that they are used in calibration, meaning their replicate weights and final weight
in the BRR procedure create design correction factors that are zero or very close to zero. This causes the resulting test statistics to
become extremely large and their associated p-values to become extremely small. Therefore, the comparison of CE’s distribution to
ACS’s distribution for these two variables is not practical.
2
Comparison for persons age 25 and older

24

Appendix B
Comparison of CE’s and ACS’s demographic distributions over the 10-year period 2010–2019:
The number of years the Rao-Scott chi-square statistic showed a statistically significant difference
between CE and ACS (p<0.05) for both the Interview and Diary Surveys
Interview Survey:
Demographic characteristic
Gender
Age
Race
Education
CU size
Tenure
# Rooms in housing unit
Owner-occupied housing value
Monthly rent
CU income

Calibration-weighted
CE respondents vs. ACS
8
n.a.
10
8
10
n.a.
10
7
10
10

Diary Survey:
Calibration-weighted
CE respondents vs. ACS
4
n.a.
10
10
4
n.a.
10

Demographic characteristic
Gender
Age
Race
Education
CU size
Tenure
CU Income

25

Appendix C
Interview Survey: Linear Regression of time (by data collection year) on CE/ACS ratio
CE subgroup percentage / ACS subgroup percentage
Calibration-weighted CE Respondents
Subgroup*
Gender
Male
Female
Age
Under age 25
25-34
35-44
45-54
55-64
65-74
75 and over
Race
White
Black
Other
Education
Less than high school
High school graduate
Some college/Assoc degree
College graduate
CU size
1 person
2 persons
3 persons
4+ persons
Housing tenure
Owner
Renter
Number of Rooms
1
2
3-4
5-6
7-8
9+

P-value

Slope

0.698
0.705

Positive
Negative

0.024
0.143
0.543
0.571
0.052
0.027
0.001

Negative
Negative
Positive
Positive
Positive
Positive
Positive

0.020
0.795
0.871

Positive
Positive
Positive

0.002
0.033
0.014
0.003

Negative
Negative
Positive
Positive

0.168
0.011
0.106
0.120

Negative
Positive
Negative
Negative

0.003
0.002

Negative
Positive

0.934
0.818
0.402
0.556
0.378
0.082

Negative
Negative
Positive
Positive
Positive
Negative

* Shaded data in this table show the subgroups where the β1 coefficient is significant, as well as the
direction of the slope for the ten-year regression line.

26

Interview Survey: Linear Regression of time (by data collection year) on CE/ACS relativity-- Continued
CE subgroup percentage / ACS subgroup percentage
Calibration-weighted CE Respondents
Subgroup*
Owner-occupied housing value
Less than $50,000
$50,000 to $99,999
$100,000 to $149,999
$150,000 to $199,999
$200,000 to $299,999
$300,000 to $499,999
$500,000 to $999,999
$1,000,000 +
Monthly rent
Less than $500
$500 to $749
$750 to $999
$1,000 to $1,499
$1,500 to $1,999
$2000 +
No cash rent
CU income
Less than $15,000
$15,000 to $24,999
$25,000 to $34,999
$35,000 to $49,999
$50,000 to $74,999
$75,000 to $99,999
$100,000 to $149,999
$150,000 to $199,999
$ 200,000 +

P-value

Slope

0.041
0.598
0.232
0.102
0.218
0.311
0.012
0.697

Positive
Negative
Negative
Negative
Negative
Positive
Positive
Negative

0.007
0.226
0.055
0.065
0.003
0.019
0.002

Negative
Positive
Positive
Positive
Positive
Positive
Negative

0.007
0.000
0.008
0.323
0.011
0.151
0.161
0.095
0.116

Positive
Positive
Positive
Positive
Negative
Negative
Negative
Positive
Positive

* Shaded data in this table show the subgroups where the β1 coefficient is significant, as well as the
direction of the slope for the ten-year regression line.

27

Appendix D
Diary Survey 2019 – Comparison of selected characteristics of Calibration-weighted CE respondents to
the ACS

Gender (%)
Male
Female
Age (%)
Under age 25
25-34
35-44
45-54
55-64
65-74
75 and over
Race (%) 1
White
Black
Other
Education 2 (%) 1
Less than high school
High school graduate
Some college/Assoc degree
College graduate
CU size (%)
1 person
2 persons
3 persons
4+ persons
Housing tenure (%)
Owner
Renter
CU income (%) 1
Less than $15,000
$15,000 to $24,999
$25,000 to $34,999
$35,000 to $49,999
$50,000 to $74,999
$75,000 to $99,999
$100,000 to $149,999
$150,000 to $199,999
$200,000 +

ACS

CE

49.2
50.8

49.2
50.8

31.5
13.9
12.8
12.4
12.9
9.6
6.9

31.7
13.8
12.6
12.5
13.0
9.7
6.7

72.0
12.8
15.2

78.1
13.3
8.6

11.4
26.9
28.6
33.1

10.7
25.1
28.3
35.9

28.3
34.3
15.3
22.1

29.9
33.0
14.7
22.4

64.1
35.9

63.6
36.4

9.8
8.3
8.4
11.9
17.4
12.8
15.7
7.2
8.5

10.5
10.2
9.8
13.1
16.8
11.8
14.5
6.0
7.2

1

Indicates a statistically significant difference (p < 0.05) between the Diary Survey and the ACS, using calibration-weighted CE
respondents. For these comparisons, the Rao-Scott Chi-square test with the BRR variance method is used to reflect CE’s sample
design. The distributions for age and housing tenure are shaded in this table because their differences were not compared. The
reason for excluding comparisons for these two variables is that they are used in calibration, meaning their replicate weights and
final weight in the BRR procedure create design correction factors that are zero or very close to zero. This causes the resulting
test statistics to become extremely large and their associated p-values to become extremely small. Therefore, the comparison of
CE’s distribution to ACS’s distribution for these two variables is not practical.
2 Comparison for persons age 25 and older

28

Appendix E
Diary Survey – Linear Regression of time (by data collection year) on CE/ACS relativity
CE subgroup percentage / ACS subgroup percentage
Calibration-weighted CE Respondents
Subgroup*
Gender
Male
Female
Age
Under age 25
25-34
35-44
45-54
55-64
65-74
75 and over
Race
White
Black
Other
Education
Less than high school
High school graduate
Some college/Assoc degree
College graduate
CU size
1 person
2 persons
3 persons
4+ persons
Housing tenure
Owner
Renter
CU income
Less than $15,000
$15,000 to $24,999
$25,000 to $34,999
$35,000 to $49,999
$50,000 to $74,999
$75,000 to $99,999
$100,000 to $149,999
$150,000 to $199,999
$200,000 +

P-value

Slope

0.794
0.791

Negative
Positive

0.020
0.145
0.518
0.400
0.049
0.023
0.001

Negative
Negative
Positive
Positive
Positive
Positive
Positive

0.075
0.104
0.000

Negative
Positive
Positive

0.260
0.000
0.020
0.253

Negative
Negative
Positive
Positive

0.683
0.913
0.254
0.392

Negative
Negative
Positive
Negative

0.003
0.002

Negative
Positive

0.021
0.299
0.044
0.726
0.159
0.584
0.758
0.531
0.044

Positive
Positive
Positive
Negative
Negative
Negative
Positive
Positive
Positive

* Shaded data in this table show the subgroups where the β1 coefficient is significant, as well as the
direction of the slope for the ten-year regression line.

29

Appendix F
Interview Survey 2019 – Subgroup response rates by wave
Wave 1
Subgroup
Overall
Region1,2,3 4
Northeast
Midwest
South
West
PSU size class1, 2, 3, 4
Self-representing
Non-self-representing
Rural
Housing value - Owners
Quartile 1-2
Quartile 3-4
Housing value - Renters3
Quartile 1-2
Quartile 3-4
Urbanicity1, 2, 3, 4
Urban
Rural
Housing tenure1, 2, 3, 4
Owner
Renter
Other

n
10,115

Wave 2

Weighted
Response
n
Rate %
56.02 10,055

Wave 3

Weighted
Response
n
Rate %
53.60 10,128

Wave 4

Weighted
Response
n
Rate %
52.84 10,091

Weighted
Response
Rate %
53.93

1,954
2,155
3,382
2,624

50.26
58.22
57.00
56.86

1,920
2,160
3,397
2,578

48.22
53.91
54.85
55.55

1,905
2,185
3,448
2,590

48.75
51.61
54.68
54.23

1,893
2,208
3,440
2,550

50.10
52.77
55.09
56.24

4,270
5,267
578

50.93
58.00
70.62

4,284
5,210
561

48.87
55.48
67.49

4,272
5,276
580

48.60
54.85
61.37

4,254
5,262
575

49.26
56.04
64.59

3,112
2,845

58.84
58.02

3,061
2,860

55.15
54.18

3,085
2,879

54.08
53.19

3,074
2,906

55.04
54.50

1,588
1,615

52.77
53.02

1,565
1,603

52.72
51.72

1,586
1,610

52.97
50.36

1,541
1,616

52.89
52.11

8,391
1,724

54.61
62.59

8,334
1,721

52.19
60.17

8,367
1,761

51.89
57.17

8,358
1,733

52.99
58.28

6,474
3,595
46

56.66
54.70
61.88

6,520
3,481
54

52.71
54.95
64.44

6,612
3,446
70

52.13
53.74
64.18

6,582
3,443
66

52.88
55.73
59.04

1, 2, 3, 4

Indicates a statistically significant difference (p < 0.05) was found for at least one comparison using
the computed Rao-Scott chi-square statistic for the test of no association between survey participation and
subgroup in waves 1, 2, 3 and 4 respectively.

30

Appendix G
Interview Survey Wave 4 comparison of subgroup response rates by year (2010-2019):
Number of occurrences using Rao-Scott chi-square test (significance where p < 0.05)
Region

Higher
Lower
Not Significant
SCORE
PSU size class

Higher
Lower
Not Significant
SCORE
Housing value Owners
Higher
Lower
Not Significant
SCORE
Urbanicity
Higher
Lower
Not Significant
SCORE
Tenure
Higher
Lower
Not Significant
SCORE

Northeast
v.
Midwest
0
8
2
-8

Northeast
v. South

Northeast
v. West

Midwest
v. South

Midwest
v. West

South
v. West

0
10
0
-10

1
8
1
-7

2
6
2
-4

3
4
3
-1

3
0
7
3

Self-representing
v. Non-Selfrepresenting
0
9
1
-9

Self-representing
v. Rural
0
9
1
-9

1st and 2nd Quartiles
v. 3rd and 4th
Quartiles
6
0
4
6

Housing value Renters
Higher
Lower
Not Significant
SCORE

Urban
v. Rural
0
8
2
-8
Owners
v. Renters
0
10
0
-10

Non-Selfrepresenting
v. Rural
0
5
5
-5

Owners
v. Other
0
9
1
-9

Renters
v. Others
0
4
6
-4

31

1st and 2nd Quartiles
v. 3rd and 4th
Quartiles
6
0
4
6

Appendix H
Interview Survey: Relativity regression results for response rate comparison of subgroups
Wave 1
Subgroup*
Region
Northeast
Midwest
South
West
PSU size class
Self-representing
Non-self-representing
Rural
Housing – Owners
Quartiles 1-2
Quartiles 3-4
Housing – Renters
Quartiles 1-2
Quartiles 3-4
Urbanicity
Urban
Rural
Housing Tenure
Owner
Renter
Other

P-value

Wave 2

Wave 3

Wave 4

Slope

P-value

Slope

P-value

Slope

P-value

Slope

0.88873
0.37342
0.28505
0.52744

Positive
Positive
Negative
Positive

0.61112
0.41514
0.36411
0.01883

Positive
Negative
Negative
Positive

0.78111
0.22274
0.98336
0.05997

Negative
Negative
Positive
Positive

0.51139
0.04188
0.87270
0.05477

Negative
Negative
Positive
Positive

0.03539
0.60718
0.00004

Negative
Negative
Positive

0.14395
0.64737
0.00035

Negative
Negative
Positive

0.16954
0.65847
0.00183

Negative
Negative
Positive

0.07388 Negative
0.99626 Negative
0.00545 Positive

0.10719
0.00421

Positive
Positive

0.40687
0.00640

Positive
Positive

0.40220
0.02356

Positive
Positive

0.33878 Positive
0.00118 Positive

0.00014
0.00382

Negative
Negative

0.00857
0.08759

Negative
Negative

0.06381
0.09115

Negative
Negative

0.03252 Negative
0.02610 Negative

0.00095
0.00027

Negative
Positive

0.10006
0.05031

Negative
Positive

0.06758
0.02326

Negative
Positive

0.10468 Negative
0.07469 Positive

0.00001
0.00001
0.04018

Positive
Negative
Negative

0.00212
0.00168
0.48356

Positive
Negative
Negative

0.06485
0.02363
0.83441

Positive
Negative
Negative

0.01560 Positive
0.00778 Negative
0.67836 Negative

*Shaded data in this table show the subgroups where the β1 coefficient is significant, as well as the
direction of the slope for the ten-year regression line.

32

Appendix I
Table I.1. Diary Survey: subgroup response rates for 2010-2014
2010
Subgroup
Overall
Region 1
Northeast
Midwest
South
West
PSU size class 1
Self-representing
Non-self-representing
Rural
Housing Value - Owners
Quartile 1-2
Quartile 3-4
Housing Value - Renters
Quartile 1-2
Quartile 3-4
Urbanicity 1
Urban
Rural
Tenure 1
Owner
Renter
Other

2011
Response
n
n
Rate %
19,988
71.92 19,823
4,146
4,452
6,933
4,457
10,752
8,208
1,028

68.23
76.73
71.37
71.00

4,042
4,396
6,880
4,505

2012
Response
n
Rate %
70.29 20,298
68.14
75.92
68.96
68.55

4,079
4,489
7,162
4,568

2013
Response
n
Rate %
67.74 20,296
66.35
71.66
66.09
67.59

4,056
4,421
7,276
4,543

2014
Response
n
Rate %
60.65 20,476
58.35
65.94
60.88
56.96

Response
Rate %
64.80

4,084
4,521
7,216
4,655

64.87
66.53
64.83
63.03

70.80 10,767
72.29 8,109
76.04
947

70.09 10,902
70.74 8,417
68.73
979

66.56 10,848
68.67 8,423
69.05 1,025

58.89 11,041
61.41 8,429
66.19 1,006

63.51
65.72
66.94

6,526
5,296

73.78
71.75

6,354
5,208

70.16
71.96

6,385
5,361

69.19
69.70

6,455
5,263

62.97
61.03

6,415
5,316

66.15
66.90

2,877
2,852

70.36
70.29

2,834
2,788

68.49
69.18

2,903
2,896

64.83
66.18

2,921
2,912

58.69
57.65

2,999
2,919

61.56
64.37

16,521
3,467

71.58 16,508
73.28 3,315

69.68 16,844
72.88 3,454

66.91 16,757
71.24 3,539

59.69
64.55

17,050
3,426

63.82
69.02

12,984
6,797
207

72.76 12,797
70.23 6,901
73.22
125

71.93 12,864
67.21 7,285
68.43
149

69.45 12,794
64.59 7,384
71.79
118

62.93 12,739
56.58 7,569
60.97
168

66.51
61.70
74.05

1

Indicates a significant difference (p < 0.05) was found for the computed Rao-Scott chi-square statistic
for the test of no association between at least two subgroups for at least five of the ten years in the study.

33

Table I.2. Diary Survey: subgroup response rates for 2015–2019
2015
Subgroup
Overall
Region 1
Northeast
Midwest
South
West
PSU size class 1
Self-representing
Non-self-representing
Rural
Housing Value - Owners
Quartile 1-2
Quartile 3-4
Housing Value - Renters
Quartile 1-2
Quartile 3-4
Urbanicity 1
Urban
Rural
Tenure 1
Owner
Renter
Other

2016
Response
n
n
Rate %
20,517
57.73 20,391
3,817
4,338
7,063
5,299
8,519
10,493
1,505

58.50
57.66
56.55
59.14

3,855
4,080
7,323
5,133

2017
Response
n
Rate %
56.75 20,100
59.48
55.89
54.84
58.58

3,808
4,182
7,064
5,046

2018
Response
n
Rate %
58.36 20,124
55.93
61.49
59.17
55.75

2019
Response
n
Rate %
55.42 20,238

Response
Rate %
53.27

3,802
4,108
7,110
5,104

51.92
56.23
55.20
57.80

3,688
4,178
6,937
5,435

47.01
53.88
53.66
57.10

57.82 8,515
57.38 10,733
60.63 1,143

56.18 8,434
56.04 10,463
67.67 1,203

56.13 8,418
58.81 10,518
68.34 1,188

52.26
56.41
66.44

8,673
10,347
1,218

47.56
56.38
60.56

7,731
4,741

58.25
59.88

6,554
5,836

58.59
60.40

6,353
5,843

60.44
61.74

6,206
5,775

56.96
60.94

6,223
5,743

56.76
55.98

3,320
3,447

55.64
55.83

3,210
3,402

53.88
52.70

3,164
3,243

52.11
56.54

3,131
3,231

50.23
49.46

3,102
3,173

48.60
48.69

16,851
3,666

57.26 17,006
60.01 3,385

55.46 16,596
63.07 3,504

57.03 16,657
64.46 3,467

54.44
60.03

16,743
3,495

51.79
60.03

12,649
7,692
176

59.26 12,352
54.79 7,902
73.97
137

59.85 12,567
51.48 7,414
72.43
119

60.82 12,487
53.54 7,517
81.52
120

58.66
49.40
75.62

12,668
7,466
104

56.49
47.45
66.63

1

Indicates a significant difference (p < 0.05) was found for the computed Rao-Scott chi-square statistic
for the test of no association between at least two subgroups for at least five of the ten years in the study.

34

Appendix J
Diary comparison of subgroup response rates by year (2010-2019):
Number of occurrences using Rao-Scott chi-square test (significance where p < 0.05)
Region

Higher
Lower
Not Significant
SCORE
PSU size class

Higher
Lower
Not Significant
SCORE
Housing value Owners
Higher
Lower
Not Significant
SCORE

Urbanicity
Higher
Lower
Not Significant
SCORE
Tenure
Higher
Lower
Not Significant
SCORE

Northeast
v.
Midwest
1
8
1
-7

Northeast
v. South

Northeast
v. West

Midwest
v. South

Midwest
v. West

South
v. West

2
5
3
-3

1
3
6
-2

6
0
4
6

6
4
0
2

3
4
3
-1

Self-representing
v. Non-Selfrepresenting
0
7
3
-7

Self-representing
v. Rural
0
8
2
-8

1st and 2nd Quartiles
v. 3rd and 4th
Quartiles
2
5
3
-3

Housing value Renters
Higher
Lower
Not Significant
SCORE

Urban
v. Rural
0
10
0
-10
Owners
v. Renters
10
0
0
10

Non-Selfrepresenting
v. Rural
0
7
3
-7

Owners
v. Other
0
6
4
-6

Renters
v. Others
0
7
3
-7

35

1st and 2nd Quartiles
v. 3rd and 4th
Quartiles
0
2
8
-2

Appendix K
Diary Survey: Relativity regression results for response rate comparison of subgroups
Subgroup*
Region
Northeast
Midwest
South
West
PSU size class
Self-Representing
Non-Self-Representing
Rural
Housing – Owners
Quartiles 1-2
Quartiles 3-4
Housing – Renters
Quartiles 1-2
Quartiles 3-4
Urbanicity
Urban
Rural
Housing Tenure
Owner
Renter
Other

P-value

Slope

0.455
0.032
0.317
0.072

Negative
Negative
Positive
Positive

0.024
0.225
0.007

Negative
Positive
Positive

0.098
0.006

Positive
Positive

0.001
0.009

Negative
Negative

0.002
0.001

Negative
Positive

0.000
0.000
0.001

Positive
Negative
Positive

*Shaded data in this table show the subgroups where the β1 coefficient is significant, as well as the
direction of the slope for the ten-year regression line.

36