The purpose of this workshop is to explore some issues in the analysis of
survey data using SAS 9.44 and SAS/Stat 14.2. Most of code shown in this
seminar will work in earlier versions of SAS and SAS/Stat. To find out
what version of SAS and SAS/Stat you are running, open SAS and look at the
information in the log file. ** **

NOTE: SAS (r) Proprietary Software 9.4 (TS1M4) NOTE: Updated analytical products: SAS/STAT 14.2 SAS/ETS 14.2 SAS/OR 14.2 SAS/IML 14.2 SAS/QC 14.2

There are seven survey procedures.

**proc surveyselect**: This procedure can be used to select a sample
from a dataset.

**proc surveyimpute**: This procedure can be used to do single imputations on a survey dataset.

**proc surveymeans**: This procedure can be used to obtain weighted
descriptive statistics for continuous variables. This procedure can produce graphs.

**proc surveyfreq**: This procedure can be used to run weighted one-way and
multi-way crosstabulations. This procedure can produce graphs.

**proc surveyregress**: This procedure can be used to run weighted
OLS regressions.

**proc surveylogistic**: This procedure can be used to run weighted
logistic, ordinal, multinomial and probit regressions.

**proc surveyphreg**: This procedure can be used to run weighted proportional
hazards regression.

We will also briefly discuss **proc glimmix**.

**proc glimmix**: This procedure will allow for sampling weights, so
it can be used to run weighted multilevel models. This procedure does not
have a **strata**, **cluster** or a **domain** statement, and it does not
allow for replicate weights. It requires that a sampling weight be specified at each level of the model.

## Why do we need survey data analysis software?

Regular statistical software (that is not designed for survey data) analyzes data as if the data were collected using simple random sampling. For experimental and quasi-experimental designs, this is exactly what we want. However, very few surveys use a simple random sample to collect data. Not only is it nearly impossible to do so, but it is not as efficient (either financially and statistically) as other sampling methods. When any sampling method other than simple random sampling is used, we usually need to use survey data analysis software to take into account the differences between the design that was used to collect the data and simple random sampling. This is because the sampling design affects both the calculation of the point estimates and the standard errors of those estimates. If you ignore the sampling design, e.g., if you assume simple random sampling when another type of sampling design was used, both the point estimates and their standard errors will likely be calculated incorrectly. The sampling weight will affect the calculation of the point estimate, and the stratification and/or clustering will affect the calculation of the standard errors. Ignoring the clustering will likely lead to standard errors that are underestimated, possibly leading to results that seem to be statistically significant, when in fact, they are not. The difference in point estimates and standard errors obtained using non-survey software and survey software with the design properly specified will vary from data set to data set, and even between analyses using the same data set. While it may be possible to get reasonably accurate results using non-survey software, there is no practical way to know beforehand how far off the results from non-survey software will be.

## Sampling designs

Most people do not conduct their own surveys. Rather, they use survey data that some agency or company collected and made available to the public. The documentation must be read carefully to find out what kind of sampling design was used to collect the data. This is very important because many of the estimates and standard errors are calculated differently for the different sampling designs. Hence, if you mis-specify the sampling design, the point estimates and standard errors will likely be wrong.

Below are some common features of many sampling designs.

__Sampling weights__: There are several types of weights that can be
associated with a survey. Perhaps the most common is the sampling weight. A
sampling weight is a probability weight that has had one or more adjustments
made to it. Both a sampling weight and a probability weight are used to weight
the sample back to the population from which the sample was drawn. By
definition, a probability weight is the inverse of the probability of being
included in the sample due to the sampling design (except for a certainty PSU,
see below). The probability weight, called a *pweight* in Stata, is
calculated as N/n, where N = the number of elements in the population and n =
the number of elements in the sample. For example, if a population has 10
elements and 3 are sampled at random with replacement, then the probability
weight would be 10/3 = 3.33. In a two-stage design, the probability weight is
calculated as f_{1}f_{2}, which means that the inverse of the
sampling fraction for the first stage is multiplied by the inverse of the
sampling fraction for the second stage. Under many sampling plans, the sum of
the probability weights will equal the population total.

While many textbooks will end their discussion of probability weights here, this definition does not fully describe the sampling weights that are included with actual survey data sets. Rather, the sampling weight, which is sometimes called a “final weight,” starts with the inverse of the sampling fraction, but then incorporates several other values, such as corrections for unit non-response, errors in the sampling frame (sometimes called non-coverage), and poststratification. Because these other values are included in the probability weight that is included with the data set, it is often inadvisable to modify the sampling weights, such as trying to standardize them for a particular variable, e.g., age.

__PSU__: This is the **p**rimary **s**ampling **u**nit. This is
the first unit that is sampled in the design. For example, school districts
from California may be sampled and then schools within districts may be
sampled. The school district would be the PSU. If states from the US were
sampled, and then school districts from within each state, and then schools from
within each district, then states would be the PSU. One does not need to use
the same sampling method at all levels of sampling. For example,
probability-proportional-to-size sampling may be used at level 1 (to select
states), while cluster sampling is used at level 2 (to select school
districts). In the case of a simple random sample, the PSUs and the elementary
units are the same. In general, accounting for the clustering in the data
(i.e., using the PSUs), will increase the standard errors of the point
estimates. Conversely, ignoring the PSUs will tend to yield standard errors
that are too small, leading to false positives when doing significance tests.

__Strata__: Stratification is a method of breaking up the population into
different groups, often by demographic variables such as gender, race or SES.
Each element in the population must belong to one, and only one, strata. Once
the strata have been defined, samples are taken from each stratum as if it were
independent of all of the other strata. For example, if a sample is to be
stratified on gender, men and women would be sampled independently of one
another. This means that the probability weights for men will likely be
different from the probability weights for the women. In most cases, you need
to have two or more PSUs in each stratum. The purpose of stratification is to
reduce the standard error of the estimates, and stratification works most
effectively when the variance of the dependent variable is smaller within the
strata than in the sample as a whole.

__FPC__: This is the **f**inite **p**opulation **c**orrection.
This is used when the sampling fraction (the number of elements or respondents
sampled relative to the population) becomes large. The FPC is used in the
calculation of the standard error of the estimate. If the value of the FPC is
close to 1, it will have little impact and can be safely ignored. In some
survey data analysis programs, such as SUDAAN, this information will be needed
if you specify that the data were collected without replacement (see below for
a definition of “without replacement”). The formula for calculating the FPC is
((N-n)/(N-1))^{1/2}, where N is the number of elements in the population
and n is the number of elements in the sample. To see the impact of the FPC for
samples of various proportions, suppose that you had a population of 10,000
elements.

Sample size (n) FPC 1 1.0000 10 .9995 100 .9950 500 .9747 1000 .9487 5000 .7071 9000 .3162

__Replicate weights__: Replicate weights are a series of weight variables
that are used to correct the standard errors for the sampling plan. They serve
the same function as the PSU and strata variables (which are used a Taylor
series linearization) to correct the standard errors of the estimates for the
sampling design. Many public use data sets are now being released with
replicate weights instead of PSUs and strata in an effort to more securely
protect the identity of the respondents. In theory, the same standard errors
will be obtained using either the PSU and strata or the replicate weights.
There are different ways of creating replicate weights; the method used is
determined by the sampling plan. The most common are balanced repeated and
jackknife replicate weights. You will need to read the documentation for the
survey data set carefully to learn what type of replicate weight is included in
the data set; specifying the wrong type of replicate weight will likely lead to
incorrect standard errors. For more information on replicate weights, please
see
Stata Library: Replicate Weights and Appendix D of the
WesVar
Manual by Westat, Inc. Several statistical packages, including Stata, SAS,
SUDAAN, WesVar and R, allow the use of replicate weights.

## Consequences of not using the design elements

Sampling design elements include the sampling weights, post-stratification weights (if provided), PSUs, strata, and replicate weights. Rarely are all of these elements included in a single public-use data set. However, ignoring the design elements that are included can often lead to inaccurate point estimates and/or inaccurate standard errors.

## Sampling with and without replacement

Most samples collected in the real world are collected “without replacement”. This means that once a respondent has been selected to be in the sample and has participated in the survey, that particular respondent cannot be selected again to be in the sample. Many of the calculations change depending on if a sample is collected with or without replacement. Hence, programs like SUDAAN request that you specify if a survey sampling design was implemented with our without replacement, and an FPC is used if sampling without replacement is used, even if the value of the FPC is very close to one.

## Examples

For the examples in this workshop, we will use the data set from NHANES 2011-2012. The data set and documentation can be downloaded from the NHANES web site. The data files can be downloaded as SAS.xpt files.

## Reading the documentation

The first step in analyzing any survey data set is to read the documentation. With many of the public use data sets, the documentation can be quite extensive and sometimes even intimidating. Instead of trying to read the documentation “cover to cover”, there are some parts you will want to focus on. First, read the Introduction. This is usually an “easy read” and will orient you to the survey. There is usually a section or chapter called something like “Sample Design and Analysis Guidelines”, “Variance Estimation”, etc. This is the part that tells you about the design elements included with the survey and how to use them. Some even give example code. If multiple sampling weights have been included in the data set, there will be some instruction about when to use which one. If there is a section or chapter on missing data or imputation, please read that. This will tell you how missing data were handled. You should also read any documentation regarding the specific variables that you intend to use. As we will see little later on, we will need to look at the documentation to get the value labels for the variables. This is especially important because some of the values are actually missing data codes, and you need to do something so that SAS doesn’t treat those as valid values (or you will get some very “interesting” means, totals, etc.).

## The variables

We will use about a dozen different variables in the examples in this workshop. Below is a brief summary of them. Some of the variables have been recoded to be binary variables (values of 2 recoded to a value of 0). The count of missing observations includes values truly missing as well as refused and don’t know.

**ridageyr** – Age in years at exam – recoded; range of values: 0 – 79
are actual values, 80 = 80+ years of age

**pad630** – How much time do you spend doing moderate-intensity
activities on a type work day?; range of values: 10-960 (minutes), 7053 missing
observations

**hsq496** – During the past 30 days, for about how many days have you
felt worried, tense or anxious?; range of values: 0-30; 3073 missing
observations

**female** – Recode of the variable riagendr; 0 = male, 1 = female; no
missing observations

**dmdborn4** – Country of birth; 1 = born in the United States, 0 =
otherwise; 5 missing observations

**dmdmartl** – Marital status; 1 = married, 2 = widowed, 3 = divorced, 4 =
separated, 5 = never married, 6 = living with partner; 4203 missing observations

**dmdeduc2** – Education level of adults aged 20+ years; 1 = less than 9th
grade, 2 = 9-11th grade, 3 = high school graduate, GED or equivalent, 4 = some
college or AA degree, 5 = college graduate or above; 4201 missing observations

**pad675** – How much time do you spend doing moderate-intensity sports,
fitness, or recreation activities on a typical day?; range of values: 10-600 (minutes);
6220 missing observations

**hsq571** – During the past 12 months, have you donated blood?; 0 = no, 1
= yes; 3673 missing observations

**pad680** – How much time do you usually spend sitting on a typical day?;
range of values: 0-1380 (minutes); 2365 missing observations

**paq665** – Do you do any moderate-intensity sports, fitness or
recreational activities that cause a small increase in breathing or heart rate
at least 10 minutes continually?; 0 = no, 1 = yes; 2329 missing observations

**hsd010** – Would you say that your general health is…; 1 = excellent,
2 = very good, 3 = good, 4 = fair, 5 = poor; 3064 missing observations

**hsq470** – number of days in the last 30 days that physical health is not good;
range of values: 0 – 30 (days), 3075 missing observations

**hsq480** – number of days in the last 30 days that mental health is not good;
range of values: 0 – 30 (days), 3073 missing observations

There are three other variables that we should identify. One is the sampling weight
variable. It is **wtint2yr**. The cluster variable is **sdmvpsu** and the
stratification variable is **sdmvstra**. There are 14 strata and 31 clusters in this
dataset. Let’s briefly look at each of these variables.

proc means data = nhanes2012 n min mean max sum; var wtint2yr; run;The MEANS Procedure Analysis Variable : WTINT2YR N Minimum Mean Maximum Sum -------------------------------------------------------------------- 9756 3320.89 31425.86 220233.32 306590681 --------------------------------------------------------------------

We see that there are 9756 observations in the dataset. The average weight is 31425.86, with a minimum of 3320.89 and a maximum of 220233.32. What does this mean? Each row of data in this dataset has a value for the sampling weight. The person who contributed that row of data represents that many people in the population. What is “the population?” Quoting from the NHANES documentation ( NHANES 2011-2012 Overview ). The NHANES target population is the noninstitutionalized civilian resident population of the United States. The sum of the weights, 306,590,681, is the estimated number of people in the population. However, if you look at other sources for the population of the United States in 2012, you will see something like 314.1 million.

Now let’s look at the cluster and strata variables.

proc freq data = nhanes2012; tables sdmvpsu sdmvstra; run;The FREQ Procedure Cumulative Cumulative SDMVPSU Frequency Percent Frequency Percent ------------------------------------------------------------ 1 4374 44.83 4374 44.83 2 4490 46.02 8864 90.86 3 892 9.14 9756 100.00 Cumulative Cumulative SDMVSTRA Frequency Percent Frequency Percent ------------------------------------------------------------- 90 862 8.84 862 8.84 91 998 10.23 1860 19.07 92 875 8.97 2735 28.03 93 602 6.17 3337 34.20 94 688 7.05 4025 41.26 95 722 7.40 4747 48.66 96 676 6.93 5423 55.59 97 608 6.23 6031 61.82 98 708 7.26 6739 69.08 99 682 6.99 7421 76.07 100 700 7.18 8121 83.24 101 715 7.33 8836 90.57 102 624 6.40 9460 96.97 103 296 3.03 9756 100.00proc freq data = nhanes2012; tables sdmvpsu*sdmvstra; run;The FREQ Procedure Table of SDMVPSU by SDMVSTRA SDMVPSU SDMVSTRA Frequency| Percent | Row Pct | Col Pct | 90| 91| 92| 93| 94| 95| 96| Total ---------+--------+--------+--------+--------+--------+--------+--------+ 1 | 278 | 309 | 328 | 276 | 322 | 348 | 336 | 4374 | 2.85 | 3.17 | 3.36 | 2.83 | 3.30 | 3.57 | 3.44 | 44.83 | 6.36 | 7.06 | 7.50 | 6.31 | 7.36 | 7.96 | 7.68 | | 32.25 | 30.96 | 37.49 | 45.85 | 46.80 | 48.20 | 49.70 | ---------+--------+--------+--------+--------+--------+--------+--------+ 2 | 351 | 333 | 244 | 326 | 366 | 374 | 340 | 4490 | 3.60 | 3.41 | 2.50 | 3.34 | 3.75 | 3.83 | 3.49 | 46.02 | 7.82 | 7.42 | 5.43 | 7.26 | 8.15 | 8.33 | 7.57 | | 40.72 | 33.37 | 27.89 | 54.15 | 53.20 | 51.80 | 50.30 | ---------+--------+--------+--------+--------+--------+--------+--------+ 3 | 233 | 356 | 303 | 0 | 0 | 0 | 0 | 892 | 2.39 | 3.65 | 3.11 | 0.00 | 0.00 | 0.00 | 0.00 | 9.14 | 26.12 | 39.91 | 33.97 | 0.00 | 0.00 | 0.00 | 0.00 | | 27.03 | 35.67 | 34.63 | 0.00 | 0.00 | 0.00 | 0.00 | ---------+--------+--------+--------+--------+--------+--------+--------+ Total 862 998 875 602 688 722 676 9756 8.84 10.23 8.97 6.17 7.05 7.40 6.93 100.00 (Continued) Frequency| Percent | Row Pct | Col Pct | 97| 98| 99| 100| 101| 102| 103| Total ---------+--------+--------+--------+--------+--------+--------+--------+ 1 | 316 | 388 | 362 | 343 | 358 | 270 | 140 | 4374 | 3.24 | 3.98 | 3.71 | 3.52 | 3.67 | 2.77 | 1.44 | 44.83 | 7.22 | 8.87 | 8.28 | 7.84 | 8.18 | 6.17 | 3.20 | | 51.97 | 54.80 | 53.08 | 49.00 | 50.07 | 43.27 | 47.30 | ---------+--------+--------+--------+--------+--------+--------+--------+ 2 | 292 | 320 | 320 | 357 | 357 | 354 | 156 | 4490 | 2.99 | 3.28 | 3.28 | 3.66 | 3.66 | 3.63 | 1.60 | 46.02 | 6.50 | 7.13 | 7.13 | 7.95 | 7.95 | 7.88 | 3.47 | | 48.03 | 45.20 | 46.92 | 51.00 | 49.93 | 56.73 | 52.70 | ---------+--------+--------+--------+--------+--------+--------+--------+ 3 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 892 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 9.14 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | ---------+--------+--------+--------+--------+--------+--------+--------+ Total 608 708 682 700 715 624 296 9756 6.23 7.26 6.99 7.18 7.33 6.40 3.03 100.00

This tells us is that there are two clusters (AKA PSUs) per strata. This is pretty typical for a survey dataset. The numbering of the clusters and strata does not matter in most statistical software packages.

## Descriptive statistics

We will start by calculating some descriptive statistics of some of the
continuous variables. We will use **proc surveymeans** to get some basic
information regarding the continuous variable **ridageyr**.

* descriptives with a continuous variable;proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var ridageyr; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- RIDAGEYR 9756 37.185195 0.696477 35.7157572 38.6546320 ---------------------------------------------------------------------------------

We see some familiar numbers in this output. We see the 14 strata, 31 clusters, 9756 observations, and the estimated population total of 306,590,681.

There are many options that you can use. The options are usually included
on the **proc** statement. The **
range** option gives the range, which is the maximum minus the minimum.

* with some options;proc surveymeans data = nhanes2012 min mean max range; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var ridageyr; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable Minimum Maximum Range Mean of Mean ---------------------------------------------------------------------------------------- RIDAGEYR 0 80.000000 80.000000 37.185195 0.696477 ----------------------------------------------------------------------------------------

Notice that the output includes only the statistics requested on the **proc
surveymeans** statement.

proc surveymeans data = nhanes2012 quartiles; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var ridageyr; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Quantiles Variable Percentile Estimate Std Error 95% Confidence Limits ---------------------------------------------------------------------------------- RIDAGEYR 25% Q1 17.514078 0.580720 16.2888667 18.7392897 50% Median 36.205625 1.394588 33.2633021 39.1479485 75% Q3 54.651947 0.925135 52.7000816 56.6038114 ----------------------------------------------------------------------------------

* other options include deciles, quartiles, median, q1, q3, and specific values;proc surveymeans data = nhanes2012 percentile = (10 25 50 75 90); weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var ridageyr; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Quantiles Variable Percentile Estimate Std Error 95% Confidence Limits ---------------------------------------------------------------------------------- RIDAGEYR 10% D1 6.557412 0.318603 5.8852178 7.2296057 25% Q1 17.514078 0.580720 16.2888667 18.7392897 50% Median 36.205625 1.394588 33.2633021 39.1479485 75% Q3 54.651947 0.925135 52.7000816 56.6038114 90% D9 67.552258 1.029785 65.3796014 69.7249153 ----------------------------------------------------------------------------------

In the example below, five options are specified. The **nmiss** option
shows the number of missing values for the variable **pad630** (How much time do you
spend doing moderate-intensity
activities on a type work day?). The **
df** option shows the degrees of freedom used. The degrees of freedom
are equal to the number of clusters (PSUs) minus the number of strata. In
this example, 31 – 14 = 17. The **cv** option gives the coefficient of variation, which is the
standard deviation divided by the mean. The **geomean** option gives
the geometric mean, which is the *n*th root of n numbers. It is
sometimes used when combining items that have different ranges. The **
gmstderr** option gives the standard error of the geometric mean.

* using some options;proc surveymeans data = nhanes2012 nmiss df cv geomean gmstderr; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var pad630; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Coeff of Variable N Miss DF Variation -------------------------------------------------- PAD630 7702 17 0.039883 --------------------------------------------------

Geometric Means Geometric Variable Mean Std Error ---------------------------------------- PAD630 90.048920 3.648271 ----------------------------------------

Notice that SAS does not do a listwise deletion of missing values across all of
the variables listed on the **var** statement. (Notice that the N is
different for each of the three variables listed in the output.)

* does not do a listwise deletion across multiple variables;proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var ridageyr pad630 hsq496; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- RIDAGEYR 9756 37.185195 0.696477 35.715757 38.654632 PAD630 2054 139.887377 5.579060 128.116590 151.658164 HSQ496 5883 5.383908 0.189951 4.983147 5.784669 ---------------------------------------------------------------------------------

The ODS graphics must be turned on for SAS to produce the graphs. If
you do not submit the **ods graphics on;** statement, SAS will give you all
of the output from **proc surveymeans** except for the graphs. There
will be a warning in the log file indicating that ODS graphics must be turned on
in order to get the graphs.

* getting some graphs;ods graphics on; proc surveymeans data = nhanes2012 plots = all; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var ridageyr; run; ods graphics off;

<output omitted>

The diamond is the mean (37.19), and the line is the median (36.21).

* getting one graph at a time;ods graphics on; proc surveymeans data = nhanes2012 plots = boxplot; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var ridageyr; run; ods graphics off;

* getting just the histogram;ods graphics on; proc surveymeans data = nhanes2012 plots = histogram; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var ridageyr; run; ods graphics off;

There are a few different ways to get descriptive statistics with categorical
variables. You can use **proc surveymeans** if your variable is binary
(i.e., coded 0/1).

* descriptives with a binary variable; * this is actually a proportion;proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var female; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- female 9756 0.511952 0.006440 0.49836568 0.52553917 ---------------------------------------------------------------------------------

Probably the most common procedure for getting descriptive statistics for
categorical variables is **proc surveyfreq**. The **tables**
statement in **proc surveyfreq** works the same way that the **tables**
statement in **proc freq** works.

* this might be more common;proc surveyfreq data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; tables female; run;

The SURVEYFREQ Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Table of female Weighted Std Dev of Std Err of female Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------- 0 4856 149630839 8783128 48.8048 0.6440 1 4900 156959842 11234711 51.1952 0.6440 Total 9756 306590681 19723273 100.000 -------------------------------------------------------------------------

You may want to use formats to help label the output.

* using formats;proc surveyfreq data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; tables female*dmdborn4; format female fm. dmdborn4 cb.; run;

The SURVEYFREQ Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Table of female by DMDBORN4 Weighted Std Dev of Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------------------------- male born elsewhere 1027 22449131 2368069 7.3247 0.8655 born in US 3825 127102676 8587374 41.4710 0.6134 Total 4852 149551807 8773197 48.7957 0.6428 ------------------------------------------------------------------------------------------- female born elsewhere 1056 23543299 1926175 7.6817 0.7451 born in US 3843 133390830 11273589 43.5227 1.2458 Total 4899 156934129 11235137 51.2043 0.6428 ------------------------------------------------------------------------------------------- Total born elsewhere 2083 45992430 4177655 15.0064 1.5756 born in US 7668 260493506 19670647 84.9936 1.5756 Total 9751 306485936 19715992 100.000 ------------------------------------------------------------------------------------------- Frequency Missing = 5

In the next example, several options were used. The **expected** option gives the expected frequencies for each cell in the
table. The **row** option gives the row percentages. The **col** option gives the column percentages. The **
chisq** option gives the Rao-Scott chi-square test; **lrchisq** option gives the likelihood ratio chi-square test; the **wchisq**
option gives the Wald chi-square test; the **wllchisq** option gives the Wald log-linear chi-square test.

proc surveyfreq data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; tables female*dmdborn4 / expected row col chisq lrchisq wchisq wllchisq; format female fm. dmdborn4 cb.; run;

The SURVEYFREQ Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Table of female by DMDBORN4 Weighted Std Dev of Expected Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Wgt Freq Percent Percent -------------------------------------------------------------------------------------------------- male born elsewhere 1027 22449131 2368069 22442305 7.3247 0.8655 born in US 3825 127102676 8587374 127109501 41.4710 0.6134 Total 4852 149551807 8773197 48.7957 0.6428 -------------------------------------------------------------------------------------------------- female born elsewhere 1056 23543299 1926175 23550124 7.6817 0.7451 born in US 3843 133390830 11273589 133384005 43.5227 1.2458 Total 4899 156934129 11235137 51.2043 0.6428 -------------------------------------------------------------------------------------------------- Total born elsewhere 2083 45992430 4177655 15.0064 1.5756 born in US 7668 260493506 19670647 84.9936 1.5756 Total 9751 306485936 19715992 100.000 -------------------------------------------------------------------------------------------------- Frequency Missing = 5 Table of female by DMDBORN4 Row Std Err of Column Std Err of female DMDBORN4 Percent Row Percent Percent Col Percent -------------------------------------------------------------------------- male born elsewhere 15.0109 1.6401 48.8105 1.2315 born in US 84.9891 1.6401 48.7930 0.6756 Total 100.000 -------------------------------------------------------------------------- female born elsewhere 15.0020 1.5769 51.1895 1.2315 born in US 84.9980 1.5769 51.2070 0.6756 Total 100.000 -------------------------------------------------------------------------- Total born elsewhere 100.000 born in US 100.000 Total -------------------------------------------------------------------------- Frequency Missing = 5

Table of female by DMDBORN4 Rao-Scott Chi-Square Test Pearson Chi-Square 0.0002 Design Correction 0.7893 Rao-Scott Chi-Square 0.0002 DF 1 Pr > ChiSq 0.9889 F Value 0.0002 Num DF 1 Den DF 17 Pr > F 0.9891 Sample Size = 9751 Rao-Scott Likelihood Ratio Test Likelihood Ratio Chi-Square 0.0002 Design Correction 0.7893 Rao-Scott Chi-Square 0.0002 DF 1 Pr > ChiSq 0.9889 F Value 0.0002 Num DF 1 Den DF 17 Pr > F 0.9891 Sample Size = 9751 Wald Chi-Square Test Chi-Square 0.0002 F Value 0.0002 Num DF 1 Den DF 17 Pr > F 0.9891 Sample Size = 9751

Table of female by DMDBORN4 Wald Log-Linear Chi-Square Test Chi-Square 0.0002 F Value 0.0002 Num DF 1 Den DF 17 Pr > F 0.9891 Sample Size = 9751

In the next example, we will use three options. The **cv** option displays coefficients of
variation for percentages. The definition of “coefficient of variation” is that it is the standard deviation / mean, or, in our case, the standard error
divided by the point estimate. For example, for males born elsewhere for the percentage, .8655/7.3247 =
.1182. The **cvwt** option displays coefficients of
variation for weighted frequencies. For example, for males born elsewhere:
2368069/22449131 = .1055. The **deff** option displays design effects for percentages. This attempts to quantify the extent to which
the observed sampling error differs from what would be expected if SRS had been used. It is defined as variance(observed) / variance(SRS). It can be thought of as a measure of efficiency. If the design effect is 1, then the current analysis
with the current sampling plan is as efficient as the same analysis using a SRS. If the design effect
is less than 1, then the current analysis with the current sample is more efficient than the same analysis
with SRS. If the design effect is greater than 1, then the current analysis with the current sample
is less efficient than the same analysis with a SRS. In general, clustering increases the design effect.

This is related to the idea of an “effective sample size”. For example, males born elsewhere: 1027/10.7602 = 95.44 total born elsewhere: 2083/18.9775 = 109.76.

proc surveyfreq data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; tables female*dmdborn4 / cv cvwt deff; format female fm. dmdborn4 cb.; run;

The SURVEYFREQ Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Table of female by DMDBORN4 Weighted Std Dev of CV for Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Wgt Freq Percent Percent ------------------------------------------------------------------------------------------------- male born elsewhere 1027 22449131 2368069 0.1055 7.3247 0.8655 born in US 3825 127102676 8587374 0.0676 41.4710 0.6134 Total 4852 149551807 8773197 0.0587 48.7957 0.6428 ------------------------------------------------------------------------------------------------- female born elsewhere 1056 23543299 1926175 0.0818 7.6817 0.7451 born in US 3843 133390830 11273589 0.0845 43.5227 1.2458 Total 4899 156934129 11235137 0.0716 51.2043 0.6428 ------------------------------------------------------------------------------------------------- Total born elsewhere 2083 45992430 4177655 0.0908 15.0064 1.5756 born in US 7668 260493506 19670647 0.0755 84.9936 1.5756 Total 9751 306485936 19715992 0.0643 100.000 ------------------------------------------------------------------------------------------------- Frequency Missing = 5 Table of female by DMDBORN4 CV for Design female DMDBORN4 Percent Effect ----------------------------------------------- male born elsewhere 0.1182 10.7602 born in US 0.0148 1.5114 Total 0.0132 1.6126 ----------------------------------------------- female born elsewhere 0.0970 7.6319 born in US 0.0286 6.1566 Total 0.0126 1.6126 ----------------------------------------------- Total born elsewhere 0.1050 18.9775 born in US 0.0185 18.9775 Total ----------------------------------------------- Frequency Missing = 5

Let’s look at some graphs. Using the format will put the labels on the x-axis on the graph.

ods graphics on; proc surveyfreq data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; tables dmdmartl / plots = wtfreqplot; format dmdmartl matsat.; run; ods graphics off;The SURVEYFREQ Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Table of DMDMARTL Weighted Std Dev of Std Err of DMDMARTL Frequency Frequency Wgt Freq Percent Percent -------------------------------------------------------------------------------------- married 2683 118822198 10556102 53.0792 2.0495 widowed 467 12586462 1087437 5.6225 0.3200 divorced 571 23926362 2606988 10.6882 0.7248 separated 204 5366932 614868 2.3975 0.3161 never married 1188 44479637 4687152 19.8695 2.3629 living with partner 440 18676762 1874572 8.3431 0.6473 Total 5553 223858353 14237911 100.000 -------------------------------------------------------------------------------------- Frequency Missing = 4203

* choose more interesting variables;ods graphics on; proc surveyfreq data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; tables female*dmdborn4 / plots = mosaicplot; format female fm. dmdborn4 cb.; run; ods graphics off;The SURVEYFREQ Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Table of female by DMDBORN4 Weighted Std Dev of Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------------------------- male born elsewhere 1027 22449131 2368069 7.3247 0.8655 born in US 3825 127102676 8587374 41.4710 0.6134 Total 4852 149551807 8773197 48.7957 0.6428 ------------------------------------------------------------------------------------------- female born elsewhere 1056 23543299 1926175 7.6817 0.7451 born in US 3843 133390830 11273589 43.5227 1.2458 Total 4899 156934129 11235137 51.2043 0.6428 ------------------------------------------------------------------------------------------- Total born elsewhere 2083 45992430 4177655 15.0064 1.5756 born in US 7668 260493506 19670647 84.9936 1.5756 Total 9751 306485936 19715992 100.000 ------------------------------------------------------------------------------------------- Frequency Missing = 5

If you are requesting more than one plot, you need to enclose the plots in
parentheses. The **or** option will give the odds ratios, and the **
risk** option will give risks.

ods graphics on; proc surveyfreq data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; tables dmdmartl*female*dmdborn4 / risk or plots =(oddsratioplot relriskplot); format dmdmartl matsat. female fm. dmdborn4 cb.; run; ods graphics off;

The SURVEYFREQ Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Table of female by DMDBORN4 Controlling for DMDMARTL=married Weighted Std Dev of Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------------------------- male born elsewhere 554 11803069 1179456 9.9367 1.1615 born in US 874 46849089 4983912 39.4410 1.0838 Total 1428 58652159 5189428 49.3777 0.5675 ------------------------------------------------------------------------------------------- female born elsewhere 476 11167772 1125718 9.4019 1.0815 born in US 777 48962647 5297262 41.2204 1.3449 Total 1253 60130420 5451479 50.6223 0.5675 ------------------------------------------------------------------------------------------- Total born elsewhere 1030 22970842 2253478 19.3386 2.2056 born in US 1651 95811737 10207366 80.6614 2.2056 Total 2681 118782579 10555944 100.000 ------------------------------------------------------------------------------------------- Column 1 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.2012 0.0228 0.1532 0.2492 Row 2 0.1857 0.0220 0.1393 0.2321 Total 0.1934 0.0221 0.1469 0.2399 Difference 0.0155 0.0078 -0.0010 0.0320 Difference is (Row 1 - Row 2) Sample Size = 5549

Column 2 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.7988 0.0228 0.7508 0.8468 Row 2 0.8143 0.0220 0.7679 0.8607 Total 0.8066 0.0221 0.7601 0.8531 Difference -0.0155 0.0078 -0.0320 0.0010 Difference is (Row 1 - Row 2) Sample Size = 5549 Odds Ratio and Relative Risks (Row1/Row2) Estimate 95% Confidence Limits Odds Ratio 1.1046 0.9937 1.2278 Column 1 Relative Risk 1.0835 0.9944 1.1806 Column 2 Relative Risk 0.9809 0.9609 1.0014 Sample Size = 5549 Table of female by DMDBORN4 Controlling for DMDMARTL=widowed Weighted Std Dev of Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------------------------- male born elsewhere 23 299145 63828 2.3767 0.5554 born in US 99 2433302 326571 19.3327 2.1606 Total 122 2732447 337748 21.7094 2.3135 ------------------------------------------------------------------------------------------- female born elsewhere 82 1350041 202386 10.7261 1.8146 born in US 263 8503975 963871 67.5645 3.0838 Total 345 9854015 951308 78.2906 2.3135 ------------------------------------------------------------------------------------------- Total born elsewhere 105 1649186 210849 13.1029 1.9883 born in US 362 10937276 1100321 86.8971 1.9883 Total 467 12586462 1087437 100.000 -------------------------------------------------------------------------------------------

Column 1 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.1095 0.0237 0.0595 0.1594 Row 2 0.1370 0.0239 0.0865 0.1875 Total 0.1310 0.0199 0.0891 0.1730 Difference -0.0275 0.0316 -0.0941 0.0391 Difference is (Row 1 - Row 2) Sample Size = 5549 Column 2 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.8905 0.0237 0.8406 0.9405 Row 2 0.8630 0.0239 0.8125 0.9135 Total 0.8690 0.0199 0.8270 0.9109 Difference 0.0275 0.0316 -0.0391 0.0941 Difference is (Row 1 - Row 2) Sample Size = 5549 Odds Ratio and Relative Risks (Row1/Row2) Estimate 95% Confidence Limits Odds Ratio 0.7744 0.4141 1.4482 Column 1 Relative Risk 0.7991 0.4607 1.3860 Column 2 Relative Risk 1.0319 0.9564 1.1134 Sample Size = 5549

Table of female by DMDBORN4 Controlling for DMDMARTL=divorced Weighted Std Dev of Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------------------------- male born elsewhere 32 646692 190158 2.7028 0.8131 born in US 205 8640920 1381509 36.1146 3.6127 Total 237 9287612 1406845 38.8175 3.6318 ------------------------------------------------------------------------------------------- female born elsewhere 70 1676180 267604 7.0056 1.2917 born in US 264 12962570 1692897 54.1769 3.5153 Total 334 14638749 1727388 61.1825 3.6318 ------------------------------------------------------------------------------------------- Total born elsewhere 102 2322871 384346 9.7084 1.8069 born in US 469 21603490 2586103 90.2916 1.8069 Total 571 23926362 2606988 100.000 ------------------------------------------------------------------------------------------- Column 1 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.0696 0.0211 0.0252 0.1141 Row 2 0.1145 0.0204 0.0715 0.1575 Total 0.0971 0.0181 0.0590 0.1352 Difference -0.0449 0.0210 -0.0893 -0.0005 Difference is (Row 1 - Row 2) Sample Size = 5549 Column 2 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.9304 0.0211 0.8859 0.9748 Row 2 0.8855 0.0204 0.8425 0.9285 Total 0.9029 0.0181 0.8648 0.9410 Difference is (Row 1 - Row 2) Sample Size = 5549

Column 2 Risk Estimates Standard Risk Error 95% Confidence Limits Difference 0.0449 0.0210 0.0005 0.0893 Difference is (Row 1 - Row 2) Sample Size = 5549 Odds Ratio and Relative Risks (Row1/Row2) Estimate 95% Confidence Limits Odds Ratio 0.5788 0.3154 1.0619 Column 1 Relative Risk 0.6081 0.3466 1.0669 Column 2 Relative Risk 1.0507 1.0006 1.1033 Sample Size = 5549 Table of female by DMDBORN4 Controlling for DMDMARTL=separated Weighted Std Dev of Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------------------------- male born elsewhere 36 798720 216266 14.8822 3.5300 born in US 43 1220641 289387 22.7437 4.3090 Total 79 2019361 376397 37.6260 4.7175 ------------------------------------------------------------------------------------------- female born elsewhere 54 1387134 213988 25.8459 3.9489 born in US 71 1960437 364269 36.5281 4.9696 Total 125 3347571 413911 62.3740 4.7175 ------------------------------------------------------------------------------------------- Total born elsewhere 90 2185854 249474 40.7282 3.2853 born in US 114 3181078 458084 59.2718 3.2853 Total 204 5366932 614868 100.000 -------------------------------------------------------------------------------------------

Column 1 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.3955 0.0822 0.2222 0.5689 Row 2 0.4144 0.0599 0.2880 0.5408 Total 0.4073 0.0329 0.3380 0.4766 Difference -0.0188 0.1254 -0.2835 0.2458 Difference is (Row 1 - Row 2) Sample Size = 5549 Column 2 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.6045 0.0822 0.4311 0.7778 Row 2 0.5856 0.0599 0.4592 0.7120 Total 0.5927 0.0329 0.5234 0.6620 Difference 0.0188 0.1254 -0.2458 0.2835 Difference is (Row 1 - Row 2) Sample Size = 5549 Odds Ratio and Relative Risks (Row1/Row2) Estimate 95% Confidence Limits Odds Ratio 0.9248 0.3077 2.7793 Column 1 Relative Risk 0.9545 0.4948 1.8413 Column 2 Relative Risk 1.0322 0.6625 1.6082 Sample Size = 5549

Table of female by DMDBORN4 Controlling for DMDMARTL=never married Weighted Std Dev of Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------------------------- male born elsewhere 150 3945129 570145 8.8807 1.1797 born in US 482 21151252 2485409 47.6125 1.9035 Total 632 25096380 2750788 56.4931 1.9690 ------------------------------------------------------------------------------------------- female born elsewhere 133 3316186 623580 7.4649 1.1880 born in US 421 16011195 2027247 36.0420 2.3406 Total 554 19327382 2250319 43.5069 1.9690 ------------------------------------------------------------------------------------------- Total born elsewhere 283 7261315 1072947 16.3456 2.0345 born in US 903 37162447 4176512 83.6544 2.0345 Total 1186 44423762 4681954 100.000 ------------------------------------------------------------------------------------------- Column 1 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.1572 0.0196 0.1158 0.1986 Row 2 0.1716 0.0287 0.1110 0.2321 Total 0.1635 0.0203 0.1205 0.2064 Difference -0.0144 0.0254 -0.0680 0.0393 Difference is (Row 1 - Row 2) Sample Size = 5549 Column 2 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.8428 0.0196 0.8014 0.8842 Row 2 0.8284 0.0287 0.7679 0.8890 Total 0.8365 0.0203 0.7936 0.8795 Difference is (Row 1 - Row 2) Sample Size = 5549

Column 2 Risk Estimates Standard Risk Error 95% Confidence Limits Difference 0.0144 0.0254 -0.0393 0.0680 Difference is (Row 1 - Row 2) Sample Size = 5549 Odds Ratio and Relative Risks (Row1/Row2) Estimate 95% Confidence Limits Odds Ratio 0.9006 0.6143 1.3202 Column 1 Relative Risk 0.9162 0.6665 1.2593 Column 2 Relative Risk 1.0174 0.9537 1.0853 Sample Size = 5549 Table of female by DMDBORN4 Controlling for DMDMARTL=living with partner Weighted Std Dev of Std Err of female DMDBORN4 Frequency Frequency Wgt Freq Percent Percent ------------------------------------------------------------------------------------------- male born elsewhere 69 2257394 449540 12.0866 1.9362 born in US 168 7272128 876424 38.9368 2.4468 Total 237 9529522 1065259 51.0234 1.7000 ------------------------------------------------------------------------------------------- female born elsewhere 64 2000636 413700 10.7119 2.0043 born in US 139 7146604 832299 38.2647 2.5917 Total 203 9147240 910699 48.9766 1.7000 ------------------------------------------------------------------------------------------- Total born elsewhere 133 4258030 799318 22.7985 3.5450 born in US 307 14418732 1572309 77.2015 3.5450 Total 440 18676762 1874572 100.000 -------------------------------------------------------------------------------------------

Column 1 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.2369 0.0380 0.1567 0.3170 Row 2 0.2187 0.0414 0.1313 0.3061 Total 0.2280 0.0355 0.1532 0.3028 Difference 0.0182 0.0358 -0.0574 0.0937 Difference is (Row 1 - Row 2) Sample Size = 5549 Column 2 Risk Estimates Standard Risk Error 95% Confidence Limits Row 1 0.7631 0.0380 0.6830 0.8433 Row 2 0.7813 0.0414 0.6939 0.8687 Total 0.7720 0.0355 0.6972 0.8468 Difference -0.0182 0.0358 -0.0937 0.0574 Difference is (Row 1 - Row 2) Sample Size = 5549 Odds Ratio and Relative Risks (Row1/Row2) Estimate 95% Confidence Limits Odds Ratio 1.1089 0.7191 1.7100 Column 1 Relative Risk 1.0831 0.7741 1.5155 Column 2 Relative Risk 0.9767 0.8859 1.0769 Sample Size = 5549

## Analysis of subpopulations

Before we continue, we should pause to discuss the analysis of
subpopulations. The analysis of subpopulations is one place where survey
data and experimental data are quite different. If you have data from an
experiment (or quasi-experiment), and you want to analyze the responses from,
say, just the women, or just people over age 50, you can just delete the
unwanted cases from the data set or use a **by** statement.
Survey data are different. With survey data, you (almost) never get to delete
any cases from the data set, even if you will never use them in any of your
analyses. Because of the way the **by** statement works, you usually don’t use
it with survey data either. Instead, SAS has provided a **domain**
statement in most survey procedures that allows you to correctly analyze
subpopulations of your survey data. A domain and a subpopulation are the
same thing. The **domain** statement is very similar to using a **by**
statement in that you will get output for each level of the variable (or
variables) listed on the statement. This means that you will often times
get more output that you want; you simply ignore the output for domains that are
not of interest to you. Please note that there is no **domain**
statement in **proc surveyfreq**; you are expected to include the variables
that you would have put on the domain statement on the **tables** statement.

First, however, let’s take a second to see why deleting cases from a survey data set can be so problematic. If the data set is subset (meaning that observations not to be included in the subpopulation are deleted from the data set), two problems arise. First, the estimated number of elements in the population cannot be correctly calculated because some numbers are missing as you sum down the column of sampling weights. Secondly, the standard errors of the estimates cannot be calculated correctly. When the subpopulation option(s) is used, only the cases defined by the subpopulation are used in the calculation of the estimate, but all cases are used in the calculation of the standard errors. For more information on this issue, please see Sampling Techniques, Third Edition by William G. Cochran (1977) and Small Area Estimation by J. N. K. Rao (2003).

We will begin with an analysis that we have seen before.

* subpops;proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; var pad630; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- PAD630 2054 139.887377 5.579060 128.116590 151.658164 ---------------------------------------------------------------------------------

Now let’s add the **domain** statement. The **format** statement
is not technically needed, but it is a nice way to more clearly label the
output. If you were interested only in the mean for females, you would
ignore the output for males.

proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; domain female; var pad630; format female fm.; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- PAD630 2054 139.887377 5.579060 128.116590 151.658164 --------------------------------------------------------------------------------- Domain Analysis: female Std Error female Variable N Mean of Mean 95% CL for Mean ------------------------------------------------------------------------------------------- male PAD630 1136 155.627196 7.008380 140.840807 170.413584 female PAD630 918 121.684284 5.352345 110.391824 132.976744 -------------------------------------------------------------------------------------------

In this example, we include two variables on the **domain** statement.
Notice that this is the same as running **proc surveymeans** twice with each
of the variables on the **domain** statement in turn.

proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; domain female dmdmartl; var pad630; format dmdmartl matsat. female fm.; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- PAD630 2054 139.887377 5.579060 128.116590 151.658164 --------------------------------------------------------------------------------- Domain Analysis: female Std Error female Variable N Mean of Mean 95% CL for Mean ------------------------------------------------------------------------------------------- male PAD630 1136 155.627196 7.008380 140.840807 170.413584 female PAD630 918 121.684284 5.352345 110.391824 132.976744 ------------------------------------------------------------------------------------------- Domain Analysis: DMDMARTL Std Error DMDMARTL Variable N Mean of Mean 95% CL for Mean ---------------------------------------------------------------------------------------------- married PAD630 841 139.439779 6.869524 124.946351 153.933208 widowed PAD630 96 122.878708 9.530837 102.770399 142.987017 divorced PAD630 166 164.023980 12.070142 138.558206 189.489754 separated PAD630 70 195.067692 37.432563 116.091889 274.043496 never married PAD630 363 140.786819 10.691710 118.229282 163.344355 living with partner PAD630 169 165.483679 10.304480 143.743126 187.224232 ----------------------------------------------------------------------------------------------

In this example, we cross the domain variables, giving us each combination of the two variables.

proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; domain female*dmdmartl; var pad630; format dmdmartl matsat. female fm.; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- PAD630 2054 139.887377 5.579060 128.116590 151.658164 --------------------------------------------------------------------------------- Domain Analysis: female*DMDMARTL Std Error female DMDMARTL Variable N Mean of Mean ----------------------------------------------------------------------------------------- male married PAD630 494 156.694056 8.765612 widowed PAD630 23 132.611146 20.775755 divorced PAD630 77 209.422973 27.286194 separated PAD630 32 187.968526 38.861059 never married PAD630 214 146.423066 12.353287 living with partner PAD630 102 201.422030 13.418949 female married PAD630 347 118.625504 9.590405 widowed PAD630 73 120.956913 11.104393 divorced PAD630 89 124.634331 15.505908 separated PAD630 38 200.933304 52.499861 ----------------------------------------------------------------------------------------- Domain Analysis: female*DMDMARTL female DMDMARTL Variable 95% CL for Mean ------------------------------------------------------------------ male married PAD630 138.200232 175.187881 widowed PAD630 88.778134 176.444159 divorced PAD630 151.854136 266.991811 separated PAD630 105.978858 269.958193 never married PAD630 120.359908 172.486223 living with partner PAD630 173.110522 229.733538 female married PAD630 98.391518 138.859490 widowed PAD630 97.528692 144.385134 divorced PAD630 91.919726 157.348937 separated PAD630 90.168280 311.698328 ------------------------------------------------------------------

Domain Analysis: female*DMDMARTL Std Error female DMDMARTL Variable N Mean of Mean ----------------------------------------------------------------------------------------- female never married PAD630 149 131.709083 13.305583 living with partner PAD630 67 122.573635 14.885114 ----------------------------------------------------------------------------------------- Domain Analysis: female*DMDMARTL female DMDMARTL Variable 95% CL for Mean ------------------------------------------------------------------ female never married PAD630 103.636758 159.781409 living with partner PAD630 91.168789 153.978481 ------------------------------------------------------------------

In this example, we cross three variables on the **domain** statement.

proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; domain female*dmdmartl*dmdeduc2; var pad630; format dmdmartl matsat. female fm. dmdeduc2 edu.; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- PAD630 2054 139.887377 5.579060 128.116590 151.658164 --------------------------------------------------------------------------------- Domain Analysis: female*DMDMARTL*DMDEDUC2 female DMDMARTL DMDEDUC2 Variable N Mean ------------------------------------------------------------------------------------------------- male married less than 9th grade PAD630 44 175.262504 no hs diploma PAD630 68 191.892326 hs grad or GED PAD630 111 165.884895 some college or AA degree PAD630 166 155.183990 ------------------------------------------------------------------------------------------------- Domain Analysis: female*DMDMARTL*DMDEDUC2 Std Error female DMDMARTL DMDEDUC2 Variable of Mean ---------------------------------------------------------------------------------- male married less than 9th grade PAD630 28.123585 no hs diploma PAD630 18.189105 hs grad or GED PAD630 9.758340 some college or AA degree PAD630 13.216380 ---------------------------------------------------------------------------------- Domain Analysis: female*DMDMARTL*DMDEDUC2 female DMDMARTL DMDEDUC2 Variable 95% CL for Mean ------------------------------------------------------------------------------------------- male married less than 9th grade PAD630 115.926926 234.598081 no hs diploma PAD630 153.516670 230.267982 hs grad or GED PAD630 145.296598 186.473193 some college or AA degree PAD630 127.299865 183.068115 -------------------------------------------------------------------------------------------

The SURVEYMEANS Procedure Domain Analysis: female*DMDMARTL*DMDEDUC2 female DMDMARTL DMDEDUC2 Variable N Mean ------------------------------------------------------------------------------------------------- male married college grad or above PAD630 105 133.266995 widowed less than 9th grade PAD630 4 187.343598 no hs diploma PAD630 4 167.204010 hs grad or GED PAD630 2 103.256927 some college or AA degree PAD630 9 125.939470 college grad or above PAD630 4 123.887738 divorced less than 9th grade PAD630 0 . no hs diploma PAD630 13 238.105548 hs grad or GED PAD630 28 159.620092 some college or AA degree PAD630 28 271.147197 college grad or above PAD630 8 181.383414 separated less than 9th grade PAD630 6 205.133253 no hs diploma PAD630 7 199.085099 hs grad or GED PAD630 9 279.838117 some college or AA degree PAD630 8 81.121846 college grad or above PAD630 2 237.326057 never married less than 9th grade PAD630 8 221.332123 no hs diploma PAD630 24 260.453605 hs grad or GED PAD630 53 169.780030 some college or AA degree PAD630 93 125.941216 college grad or above PAD630 36 104.576598 living with partner less than 9th grade PAD630 9 188.915139 no hs diploma PAD630 21 257.398122 hs grad or GED PAD630 28 215.157719 some college or AA degree PAD630 36 198.181294 college grad or above PAD630 8 105.547477 female married less than 9th grade PAD630 14 123.187262 no hs diploma PAD630 36 143.361616 hs grad or GED PAD630 60 111.808026 some college or AA degree PAD630 121 146.288791 college grad or above PAD630 116 88.919333 widowed less than 9th grade PAD630 5 176.095932 no hs diploma PAD630 17 90.605348 hs grad or GED PAD630 15 110.480512 some college or AA degree PAD630 27 101.838525 college grad or above PAD630 9 260.996206 divorced less than 9th grade PAD630 3 54.288869 no hs diploma PAD630 10 163.202217 hs grad or GED PAD630 23 145.507378 some college or AA degree PAD630 39 129.588332 college grad or above PAD630 14 76.006626 separated less than 9th grade PAD630 4 169.359877 no hs diploma PAD630 10 165.848237 hs grad or GED PAD630 10 302.022494 some college or AA degree PAD630 10 142.532187 -------------------------------------------------------------------------------------------------

The SURVEYMEANS Procedure Domain Analysis: female*DMDMARTL*DMDEDUC2 Std Error female DMDMARTL DMDEDUC2 Variable of Mean ---------------------------------------------------------------------------------- male married college grad or above PAD630 10.848793 widowed less than 9th grade PAD630 62.966878 no hs diploma PAD630 14.100541 hs grad or GED PAD630 20.074215 some college or AA degree PAD630 35.754504 college grad or above PAD630 52.934045 divorced less than 9th grade PAD630 . no hs diploma PAD630 29.710731 hs grad or GED PAD630 17.529990 some college or AA degree PAD630 56.919768 college grad or above PAD630 33.002598 separated less than 9th grade PAD630 35.534816 no hs diploma PAD630 38.033471 hs grad or GED PAD630 48.201023 some college or AA degree PAD630 29.502335 college grad or above PAD630 84.810682 never married less than 9th grade PAD630 60.764206 no hs diploma PAD630 41.069041 hs grad or GED PAD630 18.531657 some college or AA degree PAD630 11.381655 college grad or above PAD630 26.159027 living with partner less than 9th grade PAD630 71.240615 no hs diploma PAD630 43.612166 hs grad or GED PAD630 24.033974 some college or AA degree PAD630 25.916937 college grad or above PAD630 7.580480 female married less than 9th grade PAD630 33.994125 no hs diploma PAD630 14.005356 hs grad or GED PAD630 12.927725 some college or AA degree PAD630 22.892464 college grad or above PAD630 8.306940 widowed less than 9th grade PAD630 72.509645 no hs diploma PAD630 17.212933 hs grad or GED PAD630 37.211889 some college or AA degree PAD630 11.742558 college grad or above PAD630 63.187041 divorced less than 9th grade PAD630 15.497090 no hs diploma PAD630 47.287308 hs grad or GED PAD630 25.434714 some college or AA degree PAD630 28.490532 college grad or above PAD630 11.322661 separated less than 9th grade PAD630 80.576093 no hs diploma PAD630 46.573934 hs grad or GED PAD630 117.298227 some college or AA degree PAD630 26.011047 ----------------------------------------------------------------------------------

The SURVEYMEANS Procedure Domain Analysis: female*DMDMARTL*DMDEDUC2 female DMDMARTL DMDEDUC2 Variable 95% CL for Mean ------------------------------------------------------------------------------------------- male married college grad or above PAD630 110.378042 156.155948 widowed less than 9th grade PAD630 54.495098 320.192099 no hs diploma PAD630 137.454469 196.953551 hs grad or GED PAD630 60.904035 145.609819 some college or AA degree PAD630 50.504061 201.374879 college grad or above PAD630 12.206665 235.568810 divorced less than 9th grade PAD630 . . no hs diploma PAD630 175.421385 300.789710 hs grad or GED PAD630 122.635045 196.605139 some college or AA degree PAD630 151.056984 391.237409 college grad or above PAD630 111.754017 251.012810 separated less than 9th grade PAD630 130.161344 280.105162 no hs diploma PAD630 118.841490 279.328709 hs grad or GED PAD630 178.142847 381.533387 some college or AA degree PAD630 18.877360 143.366332 college grad or above PAD630 58.391158 416.260955 never married less than 9th grade PAD630 93.130856 349.533391 no hs diploma PAD630 173.805502 347.101708 hs grad or GED PAD630 130.681652 208.878407 some college or AA degree PAD630 101.928024 149.954409 college grad or above PAD630 49.385875 159.767320 living with partner less than 9th grade PAD630 38.610579 339.219699 no hs diploma PAD630 165.384495 349.411749 hs grad or GED PAD630 164.450467 265.864972 some college or AA degree PAD630 143.501336 252.861252 college grad or above PAD630 89.554062 121.540892 female married less than 9th grade PAD630 51.465926 194.908597 no hs diploma PAD630 113.812897 172.910335 hs grad or GED PAD630 84.532910 139.083141 some college or AA degree PAD630 97.989913 194.587668 college grad or above PAD630 71.393222 106.445445 widowed less than 9th grade PAD630 23.113955 329.077910 no hs diploma PAD630 54.289234 126.921462 hs grad or GED PAD630 31.970289 188.990735 some college or AA degree PAD630 77.063892 126.613157 college grad or above PAD630 127.683203 394.309208 divorced less than 9th grade PAD630 21.592867 86.984872 no hs diploma PAD630 63.434717 262.969717 hs grad or GED PAD630 91.844821 199.169934 some college or AA degree PAD630 69.478564 189.698101 college grad or above PAD630 52.117900 99.895353 separated less than 9th grade PAD630 -0.640820 339.360573 no hs diploma PAD630 67.585825 264.110649 hs grad or GED PAD630 54.544868 549.500120 some college or AA degree PAD630 87.653676 197.410699 -------------------------------------------------------------------------------------------

The SURVEYMEANS Procedure Domain Analysis: female*DMDMARTL*DMDEDUC2 female DMDMARTL DMDEDUC2 Variable N Mean ------------------------------------------------------------------------------------------------- female separated college grad or above PAD630 4 117.921631 never married less than 9th grade PAD630 4 309.991244 no hs diploma PAD630 10 166.333455 hs grad or GED PAD630 19 190.285276 some college or AA degree PAD630 79 109.549232 college grad or above PAD630 37 126.519184 living with partner less than 9th grade PAD630 2 120.000000 no hs diploma PAD630 9 144.995045 hs grad or GED PAD630 17 98.815434 some college or AA degree PAD630 26 152.592251 college grad or above PAD630 13 89.011298 ------------------------------------------------------------------------------------------------- Domain Analysis: female*DMDMARTL*DMDEDUC2 Std Error female DMDMARTL DMDEDUC2 Variable of Mean ---------------------------------------------------------------------------------- female separated college grad or above PAD630 34.795950 never married less than 9th grade PAD630 93.152302 no hs diploma PAD630 46.458980 hs grad or GED PAD630 55.647515 some college or AA degree PAD630 15.629741 college grad or above PAD630 19.292689 living with partner less than 9th grade PAD630 0 no hs diploma PAD630 24.397178 hs grad or GED PAD630 21.160766 some college or AA degree PAD630 23.746801 college grad or above PAD630 23.175916 ---------------------------------------------------------------------------------- Domain Analysis: female*DMDMARTL*DMDEDUC2 female DMDMARTL DMDEDUC2 Variable 95% CL for Mean ------------------------------------------------------------------------------------------- female separated college grad or above PAD630 44.508594 191.334667 never married less than 9th grade PAD630 113.457066 506.525422 no hs diploma PAD630 68.313575 264.353336 hs grad or GED PAD630 72.879282 307.691269 some college or AA degree PAD630 76.573361 142.525104 college grad or above PAD630 85.815170 167.223199 living with partner less than 9th grade PAD630 120.000000 120.000000 no hs diploma PAD630 93.521499 196.468590 hs grad or GED PAD630 54.170121 143.460748 -------------------------------------------------------------------------------------------

The SURVEYMEANS Procedure Domain Analysis: female*DMDMARTL*DMDEDUC2 female DMDMARTL DMDEDUC2 Variable 95% CL for Mean ------------------------------------------------------------------------------------------- female living with partner some college or AA degree PAD630 102.490879 202.693622 college grad or above PAD630 40.114391 137.908206 -------------------------------------------------------------------------------------------

By using **proc print**, we can see that there are only two cases that
have a valid value for **pad630** in subpopulation females who are living
with a partner and have less than nine years of education, and both of those
values are 120. This is why no standard error can be estimated.

proc print data = nhanes2012; var pad630; where female = 1 and dmdmartl = 6 and dmdeduc2 = 1; run;

Obs PAD630 344 120 479 . 1339 . 1962 . 1987 120 2075 . 2148 . 2178 . 2631 . 2972 . 3148 . 4118 . 4595 . 6610 . 7064 . 7112 . 7214 . 7709 . 7829 . 8095 . 8479 .

Now let’s say that you want to compare the means from two domains. In
this example, we get the mean of **pad630** for females and males.

proc surveymeans data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; domain female; var pad630; format female fm.; run;

The SURVEYMEANS Procedure Data Summary Number of Strata 14 Number of Clusters 31 Number of Observations 9756 Sum of Weights 306590681 Statistics Std Error Variable N Mean of Mean 95% CL for Mean --------------------------------------------------------------------------------- PAD630 2054 139.887377 5.579060 128.116590 151.658164 --------------------------------------------------------------------------------- Domain Analysis: female Std Error female Variable N Mean of Mean 95% CL for Mean ------------------------------------------------------------------------------------------- male PAD630 1136 155.627196 7.008380 140.840807 170.413584 female PAD630 918 121.684284 5.352345 110.391824 132.976744 -------------------------------------------------------------------------------------------

There are a few different ways that you could compare 155.63 and 121.68.
In this example, we will use **proc surveyreg** and the **contrast**
statement. Notice that the output in the section titled Estimated
Regression Coefficients is almost identical to the output of the **proc
surveymeans** above.

proc surveyreg data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; class female; model pad630 = female / noint solution vadjust = none; contrast 'comparing males and females' female 1 -1; format female fm.; run;

The SURVEYREG Procedure Regression Analysis for Dependent Variable PAD630 Data Summary Number of Observations 2054 Sum of Weights 88768571 Weighted Mean of PAD630 139.88738 Weighted Sum of PAD630 1.24176E10 Design Summary Number of Strata 14 Number of Clusters 31 Fit Statistics R-square 0.5545 Root MSE 126.37 Denominator DF 17 Class Level Information CLASS Variable Levels Values female 2 female male Tests of Model Effects Effect Num DF F Value Pr > F Model 2 325.56 <.0001 female 2 325.56 <.0001 NOTE: The denominator degrees of freedom for the F tests is 17. Estimated Regression Coefficients Standard Parameter Estimate Error t Value Pr > |t| female female 121.684284 5.35234462 22.73 <.0001 female male 155.627196 7.00837974 22.21 <.0001 NOTE: The denominator degrees of freedom for the t tests is 17.

Regression Analysis for Dependent Variable PAD630 Analysis of Contrasts Contrast Num DF F Value Pr > F comparing males and females 1 31.67 <.0001 NOTE: The denominator degrees of freedom for the F tests is 17.

In this example, we do the same analysis using **proc surveymeans** and
the **lsmeans** statement. This example is adapted from code on the SAS
website here.

proc surveyreg data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; class female; model pad630 = female / noint solution vadjust = none; lsmeans female / diff; format female fm.; run;

The SURVEYREG Procedure Regression Analysis for Dependent Variable PAD630 Data Summary Number of Observations 2054 Sum of Weights 88768571 Weighted Mean of PAD630 139.88738 Weighted Sum of PAD630 1.24176E10 Design Summary Number of Strata 14 Number of Clusters 31 Fit Statistics R-square 0.5545 Root MSE 126.37 Denominator DF 17 Class Level Information CLASS Variable Levels Values female 2 female male Tests of Model Effects Effect Num DF F Value Pr > F Model 2 325.56 <.0001 female 2 325.56 <.0001 NOTE: The denominator degrees of freedom for the F tests is 17. Estimated Regression Coefficients Standard Parameter Estimate Error t Value Pr > |t| female female 121.684284 5.35234462 22.73 <.0001 female male 155.627196 7.00837974 22.21 <.0001 NOTE: The denominator degrees of freedom for the t tests is 17.

Regression Analysis for Dependent Variable PAD630 female Least Squares Means Standard female Estimate Error DF t Value Pr > |t| female 121.68 5.3523 17 22.73 <.0001 male 155.63 7.0084 17 22.21 <.0001 Differences of female Least Squares Means Standard female _female Estimate Error DF t Value Pr > |t| female male -33.9429 6.0314 17 -5.63 <.0001

If you square the t-value from this analysis, you will get the F-value given
in the previous **proc surveyreg** analysis. The estimate of -33.94 is
simply the difference of the means, 121.68 – 155.63 (with a little rounding
error).

## Regression

Now we will look at a few examples of regression analyses. We will use
**proc surveyreg** and **proc surveylogistic**. The variables in
these examples were chosen because they were either continuous or categorical,
not because of data that they contain. In other words, the models shown
here were not constructed to make substantive sense; rather, they were
constructed to illustrate how certain things can be done. The variable **pad630** is the
number of minutes spent doing moderate-intensity activities on a typical work day.

proc surveyreg data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; class female; model pad630 = female ridageyr / solution; format female fm.; run;

The SURVEYREG Procedure Regression Analysis for Dependent Variable PAD630 Data Summary Number of Observations 2054 Sum of Weights 88768571 Weighted Mean of PAD630 139.88738 Weighted Sum of PAD630 1.24176E10 Design Summary Number of Strata 14 Number of Clusters 31 Fit Statistics R-Square 0.01933 Root MSE 126.29 Denominator DF 17 Class Level Information CLASS Variable Levels Values female 2 female male Tests of Model Effects Effect Num DF F Value Pr > F Model 2 18.23 <.0001 Intercept 1 327.92 <.0001 female 1 30.26 <.0001 RIDAGEYR 1 4.97 0.0396 NOTE: The denominator degrees of freedom for the F tests is 17. Estimated Regression Coefficients Standard Parameter Estimate Error t Value Pr > |t| Intercept 167.289537 9.31899525 17.95 <.0001 female female -33.125134 6.02167950 -5.50 <.0001 female male 0.000000 0.00000000 . . RIDAGEYR -0.287604 0.12906252 -2.23 0.0396 NOTE: The degrees of freedom for the t tests is 17. Matrix X'WX is singular and a generalized inverse was used to solve the normal equations. Estimates are not unique.

There is a **class**
statement in **proc surveyreg** (there isn’t one in **proc reg**), and, depending on the version of SAS/Stat that you are running, it does have many of the options
that are found on the **class** statements in most other SAS procedures. The
default in SAS is to use the highest-numbered category as the reference group.
Hence, in previous example, the reference group is 1 (females), not 0 (males), for the variable **female.**
In the example below, the category coded 0 is used as the reference group for both predictor variables,
**female** and **hsq571** (have you donated blood in the last year?).
Besides using the options on the **class** statement, you can
change the reference group by using a format such that
the group that you want to be the reference group has the value label that comes first alphabetically.
Notice on the **model** statement that the “|” symbol was used. This tells SAS to include both
the main effects and the interaction in the model.

proc surveyreg data = nhanes2012; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; class female (ref = first) hsq571 (ref = '0'); * class female hsq571 / ref = first; model pad630 = female|hsq571 ridageyr / solution; run;

The SURVEYREG Procedure Regression Analysis for Dependent Variable PAD630 Data Summary Number of Observations 1673 Sum of Weights 76183526 Weighted Mean of PAD630 145.83021 Weighted Sum of PAD630 1.11099E10 Design Summary Number of Strata 14 Number of Clusters 31 Fit Statistics R-Square 0.04574 Root MSE 126.20 Denominator DF 17 Class Level Information CLASS Variable Levels Values female 2 1 0 HSQ571 2 1 0 Tests of Model Effects Effect Num DF F Value Pr > F Model 4 27.13 |t| Intercept 209.155683 11.9883632 17.45

Below are a few examples of binary logistic regression. The variable **paq665** asks if you
do any moderate-intensity sports. A little data management is needed before we can run the logistic regression.
Notice the options on the **class** statement and the **model** statement.

* logistic regression;data nhanes2012b; set nhanes2012; age1 = 0; if ridageyr > 20 then age1 = 1; paq665 = paq665-1; run;

* how you specify the reference group depends on whether or not you have a format; * notice where the desc option goes;proc surveylogistic data = nhanes2012b; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; class hsd010 (reference = '3') female (reference = 'male') / param = ref; model paq665 (desc) = hsd010|female ridageyr; format female fm.; run;

The SURVEYLOGISTIC Procedure Model Information Data Set WORK.NHANES2012B Response Variable PAQ665 Number of Response Levels 2 Stratum Variable SDMVSTRA Number of Strata 14 Cluster Variable SDMVPSU Number of Clusters 31 Weight Variable WTINT2YR Model Binary Logit Optimization Technique Fisher's Scoring Variance Adjustment Degrees of Freedom (DF) Variance Estimation Method Taylor Series Variance Adjustment Degrees of Freedom (DF) Number of Observations Read 9756 Number of Observations Used 5890 Sum of Weights Read 3.0659E8 Sum of Weights Used 2.2591E8 Response Profile Ordered Total Total Value PAQ665 Frequency Weight 1 1 3347 117045323 2 0 2543 108863614 Probability modeled is PAQ665=1. NOTE: 3866 observations were deleted due to missing values for the response or explanatory variables. Class Level Information Class Value Design Variables HSD010 1 1 0 0 0 2 0 1 0 0 3 0 0 0 0 4 0 0 1 0 5 0 0 0 1

Class Level Information Class Value Design Variables female female 1 male 0 Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied. Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 312879907 301730876 SC 312879914 301730950 -2 Log L 312879905 301730854 Testing Global Null Hypothesis: BETA=0 Test F Value Num DF Den DF Pr > F Likelihood Ratio 1114905 10 Infty <.0001 Score 66.25 10 17 <.0001 Wald 54.07 10 17 <.0001 Joint Tests Wald Effect DF Chi-Square Pr > ChiSq HSD010 4 107.3724 <.0001 female 1 0.2340 0.6286 HSD010*female 4 7.8696 0.0965 RIDAGEYR 1 19.3881 <.0001 NOTE: Under full-rank parameterizations, Type 3 effect tests are replaced by joint tests. The joint test for an effect is a test that all the parameters associated with that effect are zero. Such joint tests might not be equivalent to Type 3 effect tests under GLM parameterization. Analysis of Maximum Likelihood Estimates Standard Parameter Estimate Error t Value Pr > |t| Intercept -0.2185 0.1105 -1.98 0.0645 HSD010 1 -0.3381 0.1390 -2.43 0.0263 HSD010 2 -0.4097 0.1646 -2.49 0.0234 HSD010 4 0.5232 0.1553 3.37 0.0036 HSD010 5 1.4377 0.4666 3.08 0.0068 female female 0.0682 0.1410 0.48 0.6348 HSD010*female 1 female -0.4494 0.1744 -2.58 0.0196 HSD010*female 2 female -0.1535 0.2124 -0.72 0.4796 HSD010*female 4 female -0.1603 0.2996 -0.54 0.5996 HSD010*female 5 female -0.1676 0.5184 -0.32 0.7503 RIDAGEYR 0.00963 0.00219 4.40 0.0004 NOTE: The degrees of freedom for the t tests is 17. Odds Ratio Estimates Point 95% Confidence Effect Estimate Limits RIDAGEYR 1.010 1.005 1.014 NOTE: The degrees of freedom in computing the confidence limits is 17. Association of Predicted Probabilities and Observed Responses Percent Concordant 61.3 Somers' D 0.232 Percent Discordant 38.1 Gamma 0.234 Percent Tied 0.6 Tau-a 0.114 Pairs 8511421 c 0.616

We can use the **expb** option on the **model** statement to get the
odds ratios. We can use the **clodds** option to get the confidence
limits around the odds ratios. SAS will provide a generalized R-square,
but not all statisticians agree that this is appropriate. The variable **hsq470**
is the number of days in the last 30 days that physical health was not good,
and **hsq480** is the number of days in the past 30 days that mental health was not good.

proc surveylogistic data = nhanes2012b; weight wtint2yr; cluster sdmvpsu; strata sdmvstra; model paq665 (desc) = ridageyr hsq470 hsq480 / expb clodds rsquare; run;

The SURVEYLOGISTIC Procedure Model Information Data Set WORK.NHANES2012B Response Variable PAQ665 Number of Response Levels 2 Stratum Variable SDMVSTRA Number of Strata 14 Cluster Variable SDMVPSU Number of Clusters 31 Weight Variable WTINT2YR Model Binary Logit Optimization Technique Fisher's Scoring Variance Adjustment Degrees of Freedom (DF) Variance Estimation Method Taylor Series Variance Adjustment Degrees of Freedom (DF) Number of Observations Read 9756 Number of Observations Used 5873 Sum of Weights Read 3.0659E8 Sum of Weights Used 2.2552E8 Response Profile Ordered Total Total Value PAQ665 Frequency Weight 1 1 3334 116723574 2 0 2539 108793841 Probability modeled is PAQ665=1. NOTE: 3883 observations were deleted due to missing values for the response or explanatory variables. Model Convergence Status Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics Intercept Intercept and Criterion Only Covariates AIC 312354637 306355580 SC 312354644 306355607 -2 Log L 312354635 306355572 R-Square 1.0000 Max-rescaled R-Square 1.0000 Testing Global Null Hypothesis: BETA=0 Test F Value Num DF Den DF Pr > F Likelihood Ratio 1999688 3 Infty <.0001 Score 12.07 3 17 0.0002 Wald 13.15 3 17 0.0001 Analysis of Maximum Likelihood Estimates Standard Parameter Estimate Error t Value Pr > |t| Exp(Est) Intercept -0.5190 0.1022 -5.08 <.0001 0.595 RIDAGEYR 0.0106 0.00222 4.77 0.0002 1.011 HSQ470 0.0296 0.00755 3.92 0.0011 1.030 HSQ480 0.0124 0.00289 4.30 0.0005 1.013 NOTE: The degrees of freedom for the t tests is 17. Association of Predicted Probabilities and Observed Responses Percent Concordant 57.5 Somers' D 0.159 Percent Discordant 41.6 Gamma 0.161 Percent Tied 0.9 Tau-a 0.078 Pairs 8465026 c 0.580 Odds Ratio Estimates and t Confidence Intervals Effect Unit Estimate 95% Confidence Limits RIDAGEYR 1.0000 1.011 1.006 1.015 NOTE: The degrees of freedom in computing Odds Ratio Estimates and t Confidence Intervals Effect Unit Estimate 95% Confidence Limits HSQ470 1.0000 1.030 1.014 1.047 HSQ480 1.0000 1.013 1.006 1.019 NOTE: The degrees of freedom in computing the confidence limits is 17.

## Using proc glimmix

The following example is copied directly from the SAS website because I don’t have any good data
to use for an example. Please see this
page
for this example and more information. Besides the comments that SAS makes below, there are a few things
that I would like to point out. First, notice that you MUST supply two weight variables: a weight for level 1
and a weight for level 2. This is not an inconvenience of using SAS; rather, this is true of running
any type of multilevel model in any statistical package. You need to do this because the level 1 sampling weights
and the level 2 sampling weights enter into the multilevel model equation in different places. Having the
two sampling weights is often a problem with public-use survey data sets, because the data are often not
released with level 1 and level 2 weights. The other issue that you need to know about is the scaling of the
level 1 sampling weights. This is not an issue in single-level models, but it is an issue in multilevel models.
At this time, SAS does not have an option to scale the weights for you; rather, you need to do it yourself in
a data step before you run **proc glimmix**. Please see Pfeffermann, et. al. (1998) and Rabe-Hesketh and
Skrondal (2006) for more information.

proc glimmix data=dws method=quadrature empirical=classical; class id; model y = x1 x2 / dist=binomial link=probit obsweight=sw1 solution; random int / subject=id weight=w2; run;

To fit a weighted multilevel model, you should use **METHOD=QUAD**.
The **EMPIRICAL=CLASSICAL** option in the **PROC GLIMMIX** statement instructs
**PROC GLIMMIX** to compute the empirical (sandwich) variance estimators
for the fixed effect and the variance. The empirical variance estimators
are recommended for the inference about fixed effects and variance estimated by pseudo-likelihood.

## A few words about proc surveyimpute

The following is quoted from the SAS documentation: http://support.sas.com/documentation/cdl/en/statug/68162/HTML/default/viewer.htm#statug_surveyimpute_overview.htm

The SURVEYIMPUTE procedure imputes missing values of an item in a data set by replacing them with observed values from the same item. The principles by which the imputation is performed are particularly useful for survey data. PROC SURVEYIMPUTE also computes replicate weights (such as jackknife weights) that account for the imputation and that can be used for replication-based variance estimation for complex surveys. The procedure implements a fractional hot-deck imputation technique (Kim and Fuller 2004; Fuller 2009; Kim and Shao 2014) in addition to some traditional hot-deck imputation techniques (Andridge and Little 2010).

Nonresponse is a common problem in almost all surveys of human populations. Estimators that are based on survey data that include nonresponse can suffer from nonresponse bias if the nonrespondents are different from the respondents. Estimators that use complete cases (only the observed units) might also be less precise. Imputation techniques are important tools for reducing nonresponse bias and producing efficient estimators.

The main objectives of any imputation technique are to eliminate the nonresponse bias and to provide an imputed data set that results in consistent analyses conducted with the imputed data. In addition, a variance estimator must be available that accounts for both the sampling variance and the imputation variance. Imputation techniques use implicit or explicit models. Some model-based imputation techniques include multiple imputation, mean imputation, and regression imputation. For more information about multiple imputation in SAS/STAT, see Chapter 75: The MI Procedure, and Chapter 76: The MIANALYZE Procedure.

Imputation techniques that do not use explicit models include hot-deck imputation, cold-deck imputation, and fractional imputation. PROC SURVEYIMPUTE implements imputation techniques that do not use explicit models. It also produces replicate weights that can be used with any survey analysis procedure in SAS/STAT to estimate both the sampling variability and the imputation variability.

Hot-deck imputation is the most commonly used imputation technique for survey data. A donor is selected for a recipient unit, and the observed values of the donor are imputed for the missing items of the recipient. Although the imputation method is straightforward, the variance estimator that accounts for imputation variance might not be simple and is often ignored in practice. PROC SURVEYIMPUTE does not create imputation-adjusted replicate weights for hot-deck imputation.

Fractional hot-deck imputation (Kalton and Kish 1984; Fay 1996; Kim and Fuller 2004; Fuller and Kim 2005), also known as fractional imputation (FI), is a variation of hot-deck imputation in which one missing item for a recipient is imputed from multiple donors. Each donor donates a fraction of the original weight of the recipient such that the sum of the fractional weights from all the donors is equal to the original weight of the recipient. For fully efficient fractional imputation (FEFI), all observed values in an imputation cell are used as donors for a recipient unit in that cell (Kim and Fuller 2004).

The SURVEYIMPUTE procedure implements single and multiple hot-deck imputation and FEFI. Available donor selection techniques include simple random selection with or without replacement, probability proportional to weights selection (Rao and Shao 1992), and approximate Bayesian bootstrap selection (Rubin and Schenker 1986).

## For more information on using the NHANES data sets

There are helpful resources for learning how to analyze the NHANES data sets correctly. One is a listserv at http://www.cdc.gov/nchs/nhanes/nhanes_listserv.htm . There are also online tutorials at http://www.cdc.gov/nchs/tutorials/index.htm .

## References

Applied Survey Data Analysis by Steven G. Heeringa, Brady T. West, and Patricia A. Berglund

Analysis of Health Surveys by Edward L. Korn and Barry I. Graubard

Sampling of Populations: Methods and Applications, Fourth Edition by Paul Levy and Stanley Lemeshow

Analysis of Survey Data Edited by R. L. Chambers and C. J. Skinner

Sampling Techniques, Third Edition by William G. Cochran

Pfeffermann, D., Skinner, C. J., Holmes, D. J., Goldstein, H., and Rasbash, J. (1998), Weighting for Unequal Selection Probabilities in Multilevel Models, Journal of the Royal Statistical Society, Series B, 60, 23-40.

Rabe-Hesketh, S. and Skrondal, A. (2006), Multilevel Modelling of Complex Survey Data, Journal of the Royal Statistical Society, Series A, 169, 805-827.