The purpose of this seminar is to introduce multilevel modeling using Stata 12. Before we begin, you will want to be sure that your copy of Stata is up-to-date. To do this, please type

update all

in the Stata command window and follow any instructions given. These updates include not only fixes to known bugs, but also add some new features that may be useful. I am using Stata 12.1.

Before we begin looking at examples in Stata, we will review some basic issues and concepts in multilevel data analysis. Please note that in this seminar we will only be considering outcomes that are continuous.

## Why do we need multilevel analysis and how is it different from ordinary least squares regression?

## 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, sometimes called a probability weight,
which is used to weight the sample back to the population from which the sample
was drawn. By definition, this 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 probability weights that are included with actual survey data sets. Rather, the "final weight" usually 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 probability 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 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, one samples 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
independent 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 (which use 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, 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 particular 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 seminar, we will use the Adult data set from NHANES
III. The data set, set up file and documentation can be downloaded from
the NHANES web site. An
executable file is available that contains the data, SAS code to set up the
data, and the documentation: (** ADULT.exe
**(16 MB):

**(65 MB),**

__Data__**(128 KB),**

__SAS code__**(1 MB)) . The NHANES III data sets were released with both pseudo-PSUs/pseudo-strata and replicate weights. We will show examples using both of these methods of variance estimation. For more information on the setup for NHANES III using other packages, and setups using other commonly used public-use survey data sets, please see our page on sample setups for commonly used survey data sets .**

__Documentation__## 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 "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 (although usually for SUDAAN). 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 Stata doesn’t treat those as valid values (or you will get some very "interesting" means, totals, etc.). Despite the length of the SAS code that comes with the data set, the value labels are not included.

## Getting the data into Stata

The first, and most obvious, thing that you need to do after downloading the data, is to get the data into Stata. The data file itself is actually an ASCII file, and ASCII files can easily be read into Stata. However, the SAS code contains a lot (but not all) of the information that is needed to make the numbers in the ASCII file meaningful. For example, the SAS code contains the column numbers for each variable, the variable name, and the variable label. It does not, however, contain the value labels; you need to get those from the documentation. If you really had to, you could open the SAS code in any text editor and "copy and paste" the information into a Stata do-file, modify it as needed to make a program that could read the ASCII file. Even if you are not a SAS user, this is probably much more work than making the few necessary modifications to the SAS code provided by NHANES. Let’s look at some of the SAS code to see what we need to modify to get it to run. The first few lines of the SAS code look like this:

FILENAME ADULT "D:QuestionnaireDATADULT.DAT" LRECL=

3348;

*** LRECL includes 2 positions for CRLF, assuming use of PC SAS;

DATAWORK;

INFILE ADULT MISSOVER;

LENGTH

SEQN7

DMPFSEQ5

and the last few lines look like this:

HAZMNK5R = "Average K5 BP from household and MEC"

HAZNOK5R = "Number of BP’s used for average K5";

There are two things that you will need to change. The first is the path specification in the first line. Leave the quotes and the file name (ADULT.DAT). The second thing that needs to be changed is at the very end of the file. Replace the box with

run;

Once you have made these changes, you can click on the running person at the top of the SAS screen (assuming that nothing is highlighted), and the whole program will run. You should glance through the log file looking for anything in red print that indicates an error (such as the .dat file isn’t in the location that you specified, which is a common mistake). To make sure that everything worked as planned, you can run the following command:

proc contents data = work; run;

This should give you some output telling you about the data set. Once
you know that the data set is in SAS correctly, we can now move it over into
Stata. First, we need to save the SAS data set to our hard drive. On
the **set** statement, specify the path where you want the SAS data set saved.

data "D:dataworkingnhanes_adult1"; set work; run;

Now that the SAS data set is saved to our hard drive, we can use a program like Stat/Transfer to transfer the data into Stata format.

## The svyset command

Before you do anything else, please make sure that your Stata is up-to-date. You can type

update all

and follow the instructions given. Stata has made many nice upgrades to
the **svy:** commands since Stata 11 was released, so updating is a really
good idea.

When you first try to open the NHANES data set in Stata, you will likely get an error message about being out of memory. Unlike SAS and SPSS, Stata holds a data set in memory, so if an insufficient amount of RAM is allocated to Stata, Stata won’t be able to read in the data set. You get around this by increasing the memory:

set memory 50m

Now you should be able to open the data set. (If 50m doesn’t do it on
your computer, try 70m, 90m, etc.) Now that the data are in Stata, we need
to do one more thing before starting our analyses: we need to issue the **
svyset** command. The **svyset** command tells Stata about the design
elements in the survey. Once this command has been issued, all you need to
do for your analyses is use the **svy:** prefix before each command.
Because the NHANES III data were released with both PSUs/strata and replicate
weights, we have a choice of how to specify the **svyset** command. We
will illustrate both ways, starting the use of the PSU/strata variables.
Now if you read the NHANES documentation on variance estimation, you would know that these
aren’t really the PSUs and strata used in the data collection. Rather,
they are pseudo-PSUs and pseudo-strata. Noise was added to the original
PSU and strata variables to help protect the identity of the survey respondents,
which is why they are called pseudo-PSUs and pseudo-strata. Stata doesn’t
care about these variables being "pseudo", and they are used in the **svyset**
command as regular PSU and strata variables. The **svyset** command looks like this:

use "D:dataworkingnhanes_adult1", clear svyset sdppsu6 [pweight = wtpfqx6], strata(sdpstra6) singleunit(centered)pweight: wtpfqx6 VCE: linearized Single unit: centered Strata 1: sdpstra6 SU 1: sdppsu6 FPC 1: <zero>

The singleunit option was added in Stata 10. This option allows for
different ways of handling a single PSU in a stratum. If you use the
default option, **missing**, then you will get no standard errors when Stata
encounters a single PSU in a stratum. This can happen as a result of
missing data or subsetting the data. There are three other options.
One is **certainty**, meaning that the singleton PSUs be treated as certainty
PSUs; certainty PSUs are PSUs that were selected into the sample with a
probability of 1 (in other words, these PSUs were certain to be in the sample)
and do not contribute to the standard error. The **scaled** option
gives a scaled version of the **certainty** option. The scaling factor comes
from using the average of the variances from the strata with multiple sampling
units for each stratum with one PSU. The **centered** option centers
strata with one sampling unit at the grand mean instead of the stratum mean.

svydescribeSurvey: Describing stage 1 sampling units pweight: wtpfqx6 VCE: linearized Single unit: centered Strata 1: sdpstra6 SU 1: sdppsu6 FPC 1: <zero> #Obs per Unit ---------------------------- Stratum #Units #Obs min mean max -------- -------- -------- -------- -------- -------- 1 2 418 194 209.0 224 2 2 478 222 239.0 256 3 2 476 216 238.0 260 4 2 381 180 190.5 201 5 2 388 182 194.0 206 6 2 404 194 202.0 210 7 2 444 210 222.0 234 8 2 430 210 215.0 220 9 2 419 198 209.5 221 10 2 471 229 235.5 242 11 2 439 201 219.5 238 12 2 379 179 189.5 200 13 2 414 203 207.0 211 14 2 482 228 241.0 254 15 2 461 227 230.5 234 16 2 555 273 277.5 282 17 2 509 249 254.5 260 18 2 474 236 237.0 238 19 2 517 231 258.5 286 20 2 480 233 240.0 247 21 2 410 193 205.0 217 22 2 499 227 249.5 272 23 2 433 186 216.5 247 24 2 467 224 233.5 243 25 2 423 203 211.5 220 26 2 438 179 219.0 259 27 2 478 203 239.0 275 28 2 472 233 236.0 239 29 2 505 252 252.5 253 30 2 475 224 237.5 251 31 2 525 246 262.5 279 32 2 427 207 213.5 220 33 2 539 262 269.5 277 34 2 492 222 246.0 270 35 2 264 130 132.0 134 36 2 219 108 109.5 111 37 2 167 77 83.5 90 38 2 185 86 92.5 99 39 2 303 135 151.5 168 40 2 218 98 109.0 120 41 2 236 86 118.0 150 42 2 197 91 98.5 106 43 2 423 190 211.5 233 44 2 497 220 248.5 277 45 2 345 166 172.5 179 46 2 217 107 108.5 110 47 2 226 97 113.0 129 48 2 594 274 297.0 320 49 2 357 172 178.5 185 -------- -------- -------- -------- -------- -------- 49 98 20050 77 204.6 320svy: tab hssex(running tabulate on estimation sample) Number of strata = 49 Number of obs = 20050 Number of PSUs = 98 Population size = 187647206 Design df = 49 ----------------------- sex | proportions ----------+------------ 1 | .4777 2 | .5223 | Total | 1 ----------------------- Key: proportions = cell proportionssvy: tab hssex, count missing(running tabulate on estimation sample) Number of strata = 49 Number of obs = 20050 Number of PSUs = 98 Population size = 187647206 Design df = 49 ---------------------- sex | count ----------+----------- 1 | 9.0e+07 2 | 9.8e+07 | Total | 1.9e+08 ---------------------- Key: count = weighted countssvy: tab hssex, count cellwidth(10) format(%15.2g)(running tabulate on estimation sample) Number of strata = 49 Number of obs = 20050 Number of PSUs = 98 Population size = 187647206 Design df = 49 ---------------------- sex | count ----------+----------- 1 | 89637541 2 | 98009665 | Total | 1.9e+08 ---------------------- Key: count = weighted countslabel define sex 1 male 2 female label values hssex sex label define race 1 white 2 black 3 other 8 MAUR * MAUR = "Mexican-American of Unknown Race" label values dmaracer race label define mar 1 "married house" 2 "married not in house" /// 3 "living as married" 4 widowed 5 divorced 6 separated /// 7 "never married" 8 blank 9 DK label values hfa12 mar label define food 1 enough 2 sometimes 3 "often not enough" 8 blank label values hff4 food label define yn 1 yes 2 no 8 blank 9 DK foreach var of varlist hfa13 hfe7 hfe8a hfe8b hfe8c hfe8d hfe8e hff6a /// hff6b hff6c hff6d hff7 hff8 hff9 hff10 hff11 hah13-hah17 hav5 { label values `var' yn } label define hah 1 "no difficulty" 2 "some difficulty" 3 "much difficulty" /// 4 "unable to do" 8 blank 9 DK foreach var of varlist hah1-hah12 { label values `var' hah }svy: tab hah1, count cellwidth(15) format(%15.2f) missing(running tabulate on estimation sample) Number of strata = 49 Number of obs = 20050 Number of PSUs = 98 Population size = 187647206 Design df = 49 --------------------------- difficult | y walking | a quarter | of a mile | count ----------+---------------- no diffi | 97132055.68 some dif | 8379187.23 much dif | 3032776.77 unable t | 4769359.13 blank | 130435.68 DK | 1236016.62 . | 72967375.21 | Total | 187647206.32 --------------------------- Key: count = weighted countssvy: tab dmaracer, count cellwidth(15) format(%15.2f) missing(running tabulate on estimation sample) Number of strata = 49 Number of obs = 20050 Number of PSUs = 98 Population size = 187647206 Design df = 49 --------------------------- race | count ----------+---------------- white | 158131126.11 black | 21728087.51 other | 7773929.35 MAUR | 14063.35 | Total | 187647206.32 --------------------------- Key: count = weighted countssvy: tab hfa12, count cellwidth(15) format(%15.2f) missing(running tabulate on estimation sample) Number of strata = 49 Number of obs = 20050 Number of PSUs = 98 Population size = 187647206 Design df = 49 --------------------------- marital | status | count ----------+---------------- married | 106397053.60 married | 2367517.23 living a | 7442555.25 widowed | 13310800.60 divorced | 14540696.43 separate | 4570546.85 never ma | 38181973.78 88 | 826108.26 99 | 9954.32 | Total | 187647206.32 --------------------------- Key: count = weighted counts* "Highest grade or yr of school completed" svy: mean hfa8r(running mean on estimation sample) Survey: Mean estimation Number of strata = 49 Number of obs = 20050 Number of PSUs = 98 Population size = 187647206 Design df = 49 -------------------------------------------------------------- | Linearized | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 12.90589 .1268616 12.65095 13.16082 --------------------------------------------------------------

As of Stata 10, you can request the standard deviation of a variable after
running the **svy: mean** command.

estat sd------------------------------------- | Mean Std. Dev. -------------+----------------------- hfa8r | 12.90589 7.880968 -------------------------------------## Using the replicate weights

Let’s reissue the **svyset** command, this time using the replicate
weights. First, we will clear the current settings.

svyset, clear

Next, we need to do a little math to turn the value of Fay’s adjustment into
the Fay’s value desired by Stata. Here is the formula: Fay=1-1/sqrt(adjfay)
. We will use the **vce(brr)** and **mse** options to obtain the standard errors given by SUDAAN.

display 1-(1/sqrt(1.7)).23303501svyset [pweight = wtpfqx6], brrweight(wtpqrp1 - wtpqrp52) fay(.23303501) vce(brr) msepweight: wtpfqx6 VCE: brr MSE: on brrweight: wtpqrp1 wtpqrp2 wtpqrp3 wtpqrp4 wtpqrp5 wtpqrp6 wtpqrp7 wtpqrp8 wtpqrp9 wtpqrp10 wtpqrp11 wtpqrp12 wtpqrp13 wtpqrp14 wtpqrp15 wtpqrp16 wtpqrp17 wtpqrp18 wtpqrp19 wtpqrp20 wtpqrp21 wtpqrp22 wtpqrp23 wtpqrp24 wtpqrp25 wtpqrp26 wtpqrp27 wtpqrp28 wtpqrp29 wtpqrp30 wtpqrp31 wtpqrp32 wtpqrp33 wtpqrp34 wtpqrp35 wtpqrp36 wtpqrp37 wtpqrp38 wtpqrp39 wtpqrp40 wtpqrp41 wtpqrp42 wtpqrp43 wtpqrp44 wtpqrp45 wtpqrp46 wtpqrp47 wtpqrp48 wtpqrp49 wtpqrp50 wtpqrp51 wtpqrp52 fay: .23303501 Strata 1: <one> SU 1: <observations> FPC 1: <zero>svy: mean hff5(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 1333 Population size = 7092623 Replications = 52 Design df = 51 -------------------------------------------------------------- | BRR * | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hff5 | 15.65079 1.789433 12.05836 19.24323 --------------------------------------------------------------

As you can see, the mean for the variable **hff5** is the same whether we
used the PSU/strata or the replicate weights, which it must be, since these
things only adjust the standard errors.

Let’s briefly consider an issue that arises when data are missing. We will run the **nmissing** command to confirm that only **hff5**
has missing data, and then we will run two **svy: mean** commands, the first with only the variable
**hfa8r**, and
the second with both variables. As you can see, the mean for **hfa8r**
is different when run with **hff5**, because Stata is doing a listwise
deletion of incomplete cases before calculating the means. In other words,
even though there are no missing data from **hfa8r**, only 1333 of the 20050
data points are used in the calculation of the mean of **hfa8r** when you use both variables
together.

* search nmissing nmissing hfa8r hff5hff5 18717svy: mean hfa8r(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 20050 Population size = 187647206 Replications = 52 Design df = 51 -------------------------------------------------------------- | BRR * | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 12.90589 .1109928 12.68306 13.12871 --------------------------------------------------------------svy: mean hfa8r hff5(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 1333 Population size = 7092623 Replications = 52 Design df = 51 -------------------------------------------------------------- | BRR * | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 17.9756 1.739453 14.48351 21.4677 hff5 | 15.65079 1.789433 12.05836 19.24323 --------------------------------------------------------------## Comparing variance estimation techniques

Now that we have seen the use of both the PSU/strata and the replicate
weights to adjust the standard errors, let’s compare the two side-by-side.
We will start by reissuing the **svyset** command using the PSU/strata.

svyset, clearsvyset sdppsu6 [pweight = wtpfqx6], strata(sdpstra6) singleunit(centered)pweight: wtpfqx6 VCE: linearized Single unit: centered Strata 1: sdpstra6 SU 1: sdppsu6 FPC 1: <zero>svy: mean hfa8r(running mean on estimation sample) Survey: Mean estimation Number of strata = 49 Number of obs = 20050 Number of PSUs = 98 Population size = 187647206 Design df = 49 -------------------------------------------------------------- | Linearized | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 12.90589 .1268616 12.65095 13.16082 --------------------------------------------------------------

We can also issue the **estat** command. The Deff and the Deft are types of design
effects, which tell you about the efficiency of your sample. The Deff is a
ratio of two variances. In the numerator we have the variance estimate
from the current sample (including all of its design elements), and in the
denominator we have the variance from a hypothetical sample of the same size
drawn as an SRS. In other words, the Deff tells you how efficient your
sample is compared to an SRS of equal size. If the Deff is less than 1,
your sample is more efficient than SRS; usually the Deff is greater than 1.
The Deft is the ratio of two standard error estimates. Again, the
numerator is the standard error estimate from the current sample. The
denominator is a hypothetical SRS (with replacement) standard error from a
sample of the same size as the current sample. You can also use the **meff** and the
**meft** option to get the misspecification effects.
Misspecification effects are a ratio of the variance estimate from the current
analysis to a hypothetical variance estimated from a misspecified model.
Please see the Stata documentation for more details on how these are calculated.

estat effects---------------------------------------------------------- | Linearized | Mean Std. Err. Deff Deft -------------+-------------------------------------------- hfa8r | 12.90589 .1268616 5.19536 2.27933 ----------------------------------------------------------

Now let’s use the replicate weights and run the same analyses.

svyset, clearsvyset [pweight = wtpfqx6], brrweight(wtpqrp1 - wtpqrp52) fay(.23303501) vce(brr) msepweight: wtpfqx6 VCE: brr MSE: on brrweight: wtpqrp1 wtpqrp2 wtpqrp3 wtpqrp4 wtpqrp5 wtpqrp6 wtpqrp7 wtpqrp8 wtpqrp9 wtpqrp10 wtpqrp11 wtpqrp12 wtpqrp13 wtpqrp14 wtpqrp15 wtpqrp16 wtpqrp17 wtpqrp18 wtpqrp19 wtpqrp20 wtpqrp21 wtpqrp22 wtpqrp23 wtpqrp24 wtpqrp25 wtpqrp26 wtpqrp27 wtpqrp28 wtpqrp29 wtpqrp30 wtpqrp31 wtpqrp32 wtpqrp33 wtpqrp34 wtpqrp35 wtpqrp36 wtpqrp37 wtpqrp38 wtpqrp39 wtpqrp40 wtpqrp41 wtpqrp42 wtpqrp43 wtpqrp44 wtpqrp45 wtpqrp46 wtpqrp47 wtpqrp48 wtpqrp49 wtpqrp50 wtpqrp51 wtpqrp52 fay: .23303501 Strata 1: <one> SU 1: <observations> FPC 1: <zero>svy: mean hfa8r(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 20050 Population size = 187647206 Replications = 52 Design df = 51 -------------------------------------------------------------- | BRR * | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 12.90589 .1109928 12.68306 13.12871 --------------------------------------------------------------estat effects---------------------------------------------------------- | BRR * | Mean Std. Err. Deff Deft -------------+-------------------------------------------- hfa8r | 12.90589 .1109928 3.9769 1.99422 ----------------------------------------------------------

As you can see, every part of the output is exactly the same except the
denominator df, the design df and the standard errors. Notice that the
standard errors are always larger for the analyses with the PSU/strata set than
with the replicate weights. That is not because the replicate weight
method of variance correction is more efficient than the linearization method.
Rather, these are pseudo-PSUs and pseudo-strata, and the noise added to the PSUs
and strata to make them pseudo is causing the inflation in the standard errors.
If we had access to the real PSUs and strata and used those in the analyses, I
suspect that the standard errors would be extremely close to those obtained with
the replicate weights.

## Analyses 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 the **by:** prefix. 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:** prefix works, you usually don’t use it with survey data
either. Instead, Stata has provided two options that allow you to
correctly analyze subpopulations of your survey data. These options are **
subpop** and **over**. The **subpop** option is sort of like
deleting unwanted cases (without really deleting them, of course), and the **
over** option is very similar to **by:** processing. We will start
with some examples of the **subpop** option.

But first, 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), 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). Also, if you look in the
Stata 9 Survey manual, you will find an entire section (pages 38-43) dedicated
to the analysis of subpopulations. The formulas for using both **if**
and **subpop** are given, along with an explanation of how they are
different. If you look at the help for any **svy:** command, you will
see the same warning:

Warning: Use of if or in restrictions will not produce correct variance estimates for subpopulations in many cases. To compute estimates for subpopulations, use the subpop() option. The full specification for subpop() is subpop([varname] [if])

So now we know what not to do, so let’s see how to do this right. We will
start with a simple mean and then use **hssex **as our subpopulation
variable.

svy: mean hfa8r(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 20050 Population size = 187647206 Replications = 52 Design df = 51 -------------------------------------------------------------- | BRR * | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 12.90589 .1109928 12.68306 13.12871 --------------------------------------------------------------svy, subpop(hssex): mean hfa8rNote: subpop() takes on values other than 0 and 1 subpop() != 0 indicates subpopulation (running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 20050 Population size = 187647206 Subpop. no. obs = 20050 Subpop. size = 187647206 Replications = 52 Design df = 51 -------------------------------------------------------------- | BRR * | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 12.90589 .1109928 12.68306 13.12871 --------------------------------------------------------------

Clearly, something went wrong here. The note at the top of the output
tells us what happened: Stata wants the subpopulation variable to be coded 0/1.
Let’s look at the coding of **hssex**.

codebook hssex--------------------------------------------------------------------------------------------------------------------------------------------- hssex sex --------------------------------------------------------------------------------------------------------------------------------------------- type: numeric (byte) label: sex range: [1,2] units: 1 unique values: 2 missing .: 0/20050 tabulation: Freq. Numeric Label 9401 1 male 10649 2 female

Let’s recode **hssex** into a new variable, which we will call **hssex1**,
and rerun the analysis.

generate hssex1 = hssexrecode hssex1 (2 = 0)(hssex1: 10649 changes made)svy, subpop(hssex1): mean hfa8r(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 20050 Population size = 187647206 Subpop. no. obs = 9401 Subpop. size = 89637541.1 Replications = 52 Design df = 51 -------------------------------------------------------------- | BRR * | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 13.0614 .1534762 12.75328 13.36951 --------------------------------------------------------------

We can also use the **over** option to get estimates for all categories of the
variable. In this case, we get the mean of the highest year of school
completed for men and women (1 = male and 2 = female). The **over**
option allows for variables coded 1/2 and for multicategory variables.

svy: mean hfa8r, over(hssex)(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 20050 Population size = 187647206 Replications = 52 Design df = 51 1: hssex = 1 2: hssex = 2 -------------------------------------------------------------- | BRR * Over | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 1 | 13.0614 .1534762 12.75328 13.36951 2 | 12.76366 .1046096 12.55365 12.97367 --------------------------------------------------------------svy: mean hfa8r, over(hfa12)(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 20050 Population size = 187647206 Replications = 52 Design df = 51 1: hfa12 = 1 2: hfa12 = 2 3: hfa12 = 3 4: hfa12 = 4 5: hfa12 = 5 6: hfa12 = 6 7: hfa12 = 7 88: hfa12 = 88 99: hfa12 = 99 -------------------------------------------------------------- | BRR * Over | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 1 | 12.81528 .1065852 12.6013 13.02926 2 | 11.49089 .3356867 10.81697 12.16481 3 | 12.41727 .244054 11.92731 12.90723 4 | 10.84711 .1758893 10.494 11.20022 5 | 12.79547 .1453802 12.50361 13.08733 6 | 11.27132 .2968793 10.67531 11.86733 7 | 12.79864 .1511575 12.49518 13.1021 88 | 81.54784 2.655634 76.21643 86.87925 99 | 62.79067 24.52562 13.55343 112.0279 --------------------------------------------------------------

The **over** option is available only for **svy: mean**, **svy: proportion**,
**svy: ratio** and **svy: total**. Unfortunately, there are no nice display options for
**svy: total** like there are for **svy: tab** to show the actual values of
the totals. We can use the **matrix list** command to list out the
values stored in the matrix, although sometimes those are in scientific notation
as well. We can use the **estat size** command to get the unweighted
and weighted size (i.e., count) of each subpopulation. This is a good
thing to do, because you need to know how many observations are in each
subpopulation. If "99" was a subpopulation of interest to us, we would be
in trouble because there are only three observations in that subpopulation.

svy: total hssex, over(hfa12)(running total on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 ..Survey: Total estimation Number of obs = 20050 Population size = 187647206 Replications = 52 Design df = 51 1: hfa12 = 1 2: hfa12 = 2 3: hfa12 = 3 4: hfa12 = 4 5: hfa12 = 5 6: hfa12 = 6 7: hfa12 = 7 88: hfa12 = 88 99: hfa12 = 99 -------------------------------------------------------------- | BRR * Over | Total Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hssex | 1 | 1.59e+08 2200084 1.54e+08 1.63e+08 2 | 3573113 284678.1 3001597 4144628 3 | 1.11e+07 651988.5 9826916 1.24e+07 4 | 2.45e+07 506533.4 2.35e+07 2.55e+07 5 | 2.36e+07 962190.5 2.17e+07 2.56e+07 6 | 7756844 456243 6840898 8672790 7 | 5.53e+07 1789277 5.17e+07 5.89e+07 88 | 1203385 243289.5 714960.5 1691809 99 | 15765.66 10722.36 -5760.372 37291.69 --------------------------------------------------------------mat list e(b)e(b)[1,9] hssex: hssex: hssex: hssex: hssex: hssex: hssex: hssex: hssex: _subpop_1 _subpop_2 _subpop_3 widowed divorced separated _subpop_7 88 99 y1 1.585e+08 3573112.5 11135838 24474595 23634198 7756844.2 55314851 1203384.5 15765.66estat size1: hfa12 = 1 2: hfa12 = 2 3: hfa12 = 3 4: hfa12 = 4 5: hfa12 = 5 6: hfa12 = 6 7: hfa12 = 7 88: hfa12 = 88 99: hfa12 = 99 ---------------------------------------------------------------------- | BRR * Over | Total Std. Err. Obs Size -------------+-------------------------------------------------------- hssex | 1 | 1.59e+08 2200084 10241 106397053.6 2 | 3573113 284678.1 364 2367517.23 3 | 1.11e+07 651988.5 781 7442555.25 4 | 2.45e+07 506533.4 2352 13310800.6 5 | 2.36e+07 962190.5 1388 14540696.43 6 | 7756844 456243 686 4570546.85 7 | 5.53e+07 1789277 4135 38181973.78 88 | 1203385 243289.5 100 826108.26 99 | 15765.66 10722.36 3 9954.32 ----------------------------------------------------------------------

The **subpop** option can be combined with the **over** option. This
is handy because **if** cannot be used with the **over** option. By
combining the options, you can have "the best of both worlds." In the
example below, our subpopulation includes only white males, and the mean of
education is given for each marital status. Notice that for category "88",
the mean is really high (83.44). This is because Stata considers 88 to be
a valid value, not the missing data code that it is (according to the
documentation).

svy, subpop(hssex1 if dmaracer==1): mean hfa8r, over(hfa12)(running mean on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Mean estimation Number of obs = 20050 Population size = 187647206 Replications = 52 Design df = 51 1: hfa12 = 1 2: hfa12 = 2 3: hfa12 = 3 4: hfa12 = 4 5: hfa12 = 5 6: hfa12 = 6 7: hfa12 = 7 88: hfa12 = 88 -------------------------------------------------------------- | BRR * Over | Mean Std. Err. [95% Conf. Interval] -------------+------------------------------------------------ hfa8r | 1 | 12.85045 .1013903 12.64691 13.054 2 | 11.15848 .6515755 9.850389 12.46657 3 | 11.90575 .2359017 11.43216 12.37934 4 | 10.8672 .3819635 10.10037 11.63402 5 | 12.8703 .1584319 12.55224 13.18837 6 | 12.6802 1.564755 9.53882 15.82157 7 | 12.72527 .2070723 12.30955 13.14098 88 | 83.43886 3.637654 76.13596 90.74175 --------------------------------------------------------------

For more information on analyzing subpopulations in Stata, please see our Stata FAQ: How can I analyze a subpopulation of my survey data in Stata 9?

## Regression analyses

Let’s look at some regression analyses. Stata 9 has a very nice suite
of regression commands that can be used with the **svy:** prefix. Type
**help survey** for a list of commands that can be used with the **svy:**
prefix.

svy: reg hav6s hav2s hav3s hff4 hfa13 hfe7 hfa8r(running regress on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Linear regression Number of obs = 5866 Population size = 69288876 Replications = 52 Design df = 51 F( 6, 46) = 83.92 Prob > F = 0.0000 R-squared = 0.4285 ------------------------------------------------------------------------------ | BRR * hav6s | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hav2s | .0335188 .0164996 2.03 0.047 .0003945 .0666432 hav3s | .0458665 .016843 2.72 0.009 .0120528 .0796802 hff4 | 78.15901 47.06818 1.66 0.103 -16.33432 172.6523 hfa13 | 14.97253 6.777161 2.21 0.032 1.366808 28.57825 hfe7 | -9.015854 11.81718 -0.76 0.449 -32.73983 14.70812 hfa8r | .6153294 .6913622 0.89 0.378 -.7726382 2.003297 _cons | -59.27143 62.78533 -0.94 0.350 -185.3182 66.77539 ------------------------------------------------------------------------------

As we see in the example below, we can put **i.** before categorical
predictor variables to have Stata automatically create dummy variables for us.
(As of Stata 11, the **xi:** prefix is no longer needed. If you are
using an earlier version of Stata, you should put the **xi:** prefix before
the **svy:** prefix.)

svy: reg hav2s hfe7 hfa13 hssex i.dmpcregn hah15(running regress on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Linear regression Number of obs = 13398 Population size = 114679831 Replications = 52 Design df = 51 F( 7, 45) = 4.33 Prob > F = 0.0010 R-squared = 0.1045 ------------------------------------------------------------------------------ | BRR * hav2s | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hfe7 | 1078.949 215.3567 5.01 0.000 646.602 1511.295 hfa13 | 1212.34 267.1979 4.54 0.000 675.9174 1748.762 hssex | -403.5371 128.8811 -3.13 0.003 -662.2767 -144.7975 | dmpcregn | 2 | 33.12827 72.97049 0.45 0.652 -113.3661 179.6226 3 | -19.01354 68.06759 -0.28 0.781 -155.6649 117.6378 4 | 249.894 122.4217 2.04 0.046 4.122106 495.6659 | hah15 | 935.0711 512.2536 1.83 0.074 -93.32097 1963.463 _cons | -5005.517 1185.052 -4.22 0.000 -7384.609 -2626.425 ------------------------------------------------------------------------------

No
**svy:** prefix is needed before the **test** command.

test 2.dmpcregn 3.dmpcregn 4.dmpcregnAdjusted Wald test ( 1) 2.dmpcregn = 0 ( 2) 3.dmpcregn = 0 ( 3) 4.dmpcregn = 0 F( 3, 49) = 1.99 Prob > F = 0.1277

Let’s create a 0/1 variable and run a logistic regression.

generate clubs = hav5recode clubs (2 = 0)(clubs: 14184 changes made)svy: logit clubs hfe7 hfa13 hssex i.dmpcregn hah15(running logit on estimation sample) BRR replications (52) ----+--- 1 ---+--- 2 ---+--- 3 ---+--- 4 ---+--- 5 .................................................. 50 .. Survey: Logistic regression Number of obs = 13398 Population size = 114679831 Replications = 52 Design df = 51 F( 7, 45) = 7.13 Prob > F = 0.0000 ------------------------------------------------------------------------------ | BRR * clubs | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- hfe7 | .1212481 .0502015 2.42 0.019 .0204643 .2220319 hfa13 | -.392244 .0611189 -6.42 0.000 -.5149452 -.2695427 hssex | -.0568606 .0474936 -1.20 0.237 -.152208 .0384869 | dmpcregn | 2 | .0246446 .1229863 0.20 0.842 -.2222608 .2715499 3 | -.2444328 .1344003 -1.82 0.075 -.5142527 .0253871 4 | -.1163411 .1270524 -0.92 0.364 -.3714094 .1387272 | hah15 | .362997 .0947355 3.83 0.000 .1728077 .5531864 _cons | -.5054835 .212936 -2.37 0.021 -.9329703 -.0779967 ------------------------------------------------------------------------------test 2.dmpcregn 3.dmpcregn 4.dmpcregnAdjusted Wald test ( 1) [clubs]2.dmpcregn = 0 ( 2) [clubs]3.dmpcregn = 0 ( 3) [clubs]4.dmpcregn = 0 F( 3, 49) = 2.12 Prob > F = 0.1096

We don’t have much time to talk about regression diagnostics here, although
that is a common question among researchers who use survey data. Most of
the assumptions still apply when using survey data, but they can be more
difficult to check. As of Stata 11, most of the diagnostic commands that
you would use after **regress**, **logistic**, etc., don’t work after **
svy: regress**, **svy: logit**, etc. Some of the assumptions don’t
really apply, though, because of the extremely large sample size involved.
Checking assumptions when doing a subpopulation analysis can be even more tricky.

## Using multiply imputed data

Some of the NHANES III data sets were released as imputed data sets. This means that some of the variables contained in the data set were multiply imputed. For information on which variables were imputed, the imputation method, etc., please see http://www.cdc.gov/nchs/nhanes.htm and ftp://ftp.cdc.gov/pub/Health_Statistics/NCHS/Datasets/NHANES/NHANESIII/7A/doc/main.pdf .

If you are using Stata 11 or later, we suggest using the built-in Stata
prefix **mi**. If you are using Stata 10 or earlier, please see the
last paragraph in this section for suggestions on how to analyze the multiply
imputed datasets.

The commands below are used to change the current working directory (**cd**),
to set the memory (**set mem**), to use the nh3core data set (**use**),
and to create the single multiply imputed data set (called **mymi**) from the
five imputed data sets provided by NHANES (**mi import nhanes1**).

cd "D:datanhanes IIImiStata_data"D:Datanhanes IIImiStata_dataset mem 200m(204800k)use nh3coremi import nhanes1 mymi, using(nh3mi1.dta nh3mi2.dta nh3mi3.dta nh3mi4.dta nh3mi5.dta) id(seqn)(variables sdppsu6 sdpstra6 wtpfqx6 wtpqrp1 wtpqrp2 wtpqrp3 wtpqrp4 wtpqrp5 wtpqrp6 wtpqrp7 wtpqrp8 wtpqrp9 wtpqrp10 wtpqrp11 wtpqrp12 wtpqrp13 wtpqrp14 wtpqrp15 wtpqrp16 wtpqrp17 wtpqrp18 wtpqrp19 wtpqrp20 wtpqrp21 wtpqrp22 wtpqrp23 wtpqrp24 wtpqrp25 wtpqrp26 wtpqrp27 wtpqrp28 wtpqrp29 wtpqrp30 wtpqrp31 wtpqrp32 wtpqrp33 wtpqrp34 wtpqrp35 wtpqrp36 wtpqrp37 wtpqrp38 wtpqrp39 wtpqrp40 wtpqrp41 wtpqrp42 wtpqrp43 wtpqrp44 wtpqrp45 wtpqrp46 wtpqrp47 wtpqrp48 wtpqrp49 wtpqrp50 wtpqrp51 wtpqrp52 hfa7 hfa8 hfa12 hac1a hac1b hac1c hac1d hac1e hac1f hac1g hac1h hac1i hac1j hac1k hac1l hac1m hac1n hac1o had1 hae2 hae4a hae4b hae5a hae5b hae6 hae7 haf1 haf10 hag2 hag3 hag5a hag5b hag5c hag11 hag12 han6hs han6is han6js hap1 hap1a hap2 hap3 hap10 hap10a har1 har3 har14 har16 har23 har24 har26 har27 hye1g hye1h hye6a hye6b hye15 hyh2 hyh10 dmppirif hff1if hab1if ham5if ham6if han6srif haq1if har3rif hat28if hazak1if hazak5if hazbk1if hazbk5if hazck1if hazck5if hyd1if hyf2if bdpfndif bdpindif bdpkif bdptoaif bdptodif bdptrdif bdpwtdif bmpbutif bmpheaif bmphtif bmpkneif bmprecif bmpsthif bmpsb1if bmpsb2if bmpsp1if bmpsp2if bmptr1if bmptr2if bmpwstif bmpwtif fepif frpif hdpif hgpif htpif mcpsiif mhpif mvpsiif pbpif phpfstif pxpif rcpif rwpif sepif tcpif tgpif tipif fppsudif fppsumif fppsurif pep6g1if pep6g2if pep6g3if pep6h1if pep6h2if pep6h3if pep6i1if pep6i2if pep6i3if hff1mi hab1mi ham5mi ham6mi han6srmi haq1mi har3rmi hat28mi hazak1mi hazak5mi hazbk1mi hazbk5mi hazck1mi hazck5mi hyd1mi hyf2mi bmpsb1mi bmpsb2mi bmpsp1mi bmpsp2mi bmptr1mi bmptr2mi pep6g1mi pep6g2mi pep6g3mi pep6h1mi pep6h2mi pep6h3mi pep6i1mi pep6i2mi pep6i3mi dropped in m=1)<output omitted to save space> (variables sdppsu6 sdpstra6 wtpfqx6 wtpqrp1 wtpqrp2 wtpqrp3 wtpqrp4 wtpqrp5 wtpqrp6 wtpqrp7 wtpqrp8 wtpqrp9 wtpqrp10 wtpqrp11 wtpqrp12 wtpqrp13 wtpqrp14 wtpqrp15 wtpqrp16 wtpqrp17 wtpqrp18 wtpqrp19 wtpqrp20 wtpqrp21 wtpqrp22 wtpqrp23 wtpqrp24 wtpqrp25 wtpqrp26 wtpqrp27 wtpqrp28 wtpqrp29 wtpqrp30 wtpqrp31 wtpqrp32 wtpqrp33 wtpqrp34 wtpqrp35 wtpqrp36 wtpqrp37 wtpqrp38 wtpqrp39 wtpqrp40 wtpqrp41 wtpqrp42 wtpqrp43 wtpqrp44 wtpqrp45 wtpqrp46 wtpqrp47 wtpqrp48 wtpqrp49 wtpqrp50 wtpqrp51 wtpqrp52 hfa7 hfa8 hfa12 hac1a hac1b hac1c hac1d hac1e hac1f hac1g hac1h hac1i hac1j hac1k hac1l hac1m hac1n hac1o had1 hae2 hae4a hae4b hae5a hae5b hae6 hae7 haf1 haf10 hag2 hag3 hag5a hag5b hag5c hag11 hag12 han6hs han6is han6js hap1 hap1a hap2 hap3 hap10 hap10a har1 har3 har14 har16 har23 har24 har26 har27 hye1g hye1h hye6a hye6b hye15 hyh2 hyh10 dmppirif hff1if hab1if ham5if ham6if han6srif haq1if har3rif hat28if hazak1if hazak5if hazbk1if hazbk5if hazck1if hazck5if hyd1if hyf2if bdpfndif bdpindif bdpkif bdptoaif bdptodif bdptrdif bdpwtdif bmpbutif bmpheaif bmphtif bmpkneif bmprecif bmpsthif bmpsb1if bmpsb2if bmpsp1if bmpsp2if bmptr1if bmptr2if bmpwstif bmpwtif fepif frpif hdpif hgpif htpif mcpsiif mhpif mvpsiif pbpif phpfstif pxpif rcpif rwpif sepif tcpif tgpif tipif fppsudif fppsumif fppsurif pep6g1if pep6g2if pep6g3if pep6h1if pep6h2if pep6h3if pep6i1if pep6i2if pep6i3if hff1mi hab1mi ham5mi ham6mi han6srmi haq1mi har3rmi hat28mi hazak1mi hazak5mi hazbk1mi hazbk5mi hazck1mi hazck5mi hyd1mi hyf2mi bmpsb1mi bmpsb2mi bmpsp1mi bmpsp2mi bmptr1mi bmptr2mi pep6g1mi pep6g2mi pep6g3mi pep6h1mi pep6h2mi pep6h3mi pep6i1mi pep6i2mi pep6i3mi dropped in m=5)

The **mi describe** and **mi varying** commands provide useful
information about the data set. The **varcase** command is a
user-written command (**search varcase**) that changes the case of variable
names. It is used here to change some of the variable names from being in
all capital letters to being in all lower case letters.

mi describeStyle: flongsep mymi last mi update 27sep2010 15:21:48, 0 seconds ago Obs.: complete 20,870 incomplete 13,124 (M = 5 imputations) --------------------- total 33,994 Vars.: imputed: 36; dmppir(3410) bdpfnd(4179+15169) bdpind(4179+15169) bdpk(4179+15169) bdptoa(4179+15169) bdptod(4179+15169) bdptrd(4179+15169) bdpwtd(4179+15169) bmpbut(4258+3446) bmphea(799+24586) bmpht(2613+3446) bmpkne(1658+27398) bmprec(457+28012) bmpsth(3539+3446) bmpwst(4260+3446) bmpwt(2862) fep(5408+2107) frp(5494+2107) hdp(4603+5982) hgp(5515+2107) htp(5517+2107) mcpsi(5518+2107) mhp(5518+2107) mvpsi(5516+2107) pbp(5069+2107) phpfst(4187+2107) pxp(6117+2107) rcp(5517+2107) rwp(5515+2107) sep(3669+11728) tcp(4451+5982) tgp(4497+5982) tip(6085+2107) fppsud(2962+22546) fppsum(3240+22546) fppsur(3237+22546) passive: 0 regular: 0 system: 2; _mi_id _mi_miss (there are 163 unregistered variables)mi varyingPossible problem variable names -------------------------------------------------------------------------------------- imputed nonvarying: (none) passive nonvarying: (none) unregistered varying: (none) *unregistered super/varying: (none) unregistered super varying: (none) -------------------------------------------------------------------------------------- * super/varying means super varying but would be varying if registered as imputed; variables vary only where equal to soft missing in m=0.varcase(SDPPSU6- PEP6I3IF)

Now we are ready to use the **svyset** command. We include the **mi**
prefix.

mi svyset sdppsu6 [pweight = wtpfqx6], strata(sdpstra6) singleunit(centered)(variables SDPPSU6 SDPSTRA6 WTPFQX6 WTPQRP1 WTPQRP2 WTPQRP3 WTPQRP4 WTPQRP5 WTPQRP6 WTPQRP7 WTPQRP8 WTPQRP9 WTPQRP10 WTPQRP11 WTPQRP12 WTPQRP13 WTPQRP14 WTPQRP15 WTPQRP16 WTPQRP17 WTPQRP18 WTPQRP19 WTPQRP20 WTPQRP21 WTPQRP22 WTPQRP23 WTPQRP24 WTPQRP25 WTPQRP26 WTPQRP27 WTPQRP28 WTPQRP29 WTPQRP30 WTPQRP31 WTPQRP32 WTPQRP33 WTPQRP34 WTPQRP35 WTPQRP36 WTPQRP37 WTPQRP38 WTPQRP39 WTPQRP40 WTPQRP41 WTPQRP42 WTPQRP43 WTPQRP44 WTPQRP45 WTPQRP46 WTPQRP47 WTPQRP48 WTPQRP49 WTPQRP50 WTPQRP51 WTPQRP52 HFA7 HFA8 HFA12 HAC1A HAC1B HAC1C HAC1D HAC1E HAC1F HAC1G HAC1H HAC1I HAC1J HAC1K HAC1L HAC1M HAC1N HAC1O HAD1 HAE2 HAE4A HAE4B HAE5A HAE5B HAE6 HAE7 HAF1 HAF10 HAG2 HAG3 HAG5A HAG5B HAG5C HAG11 HAG12 HAN6HS HAN6IS HAN6JS HAP1 HAP1A HAP2 HAP3 HAP10 HAP10A HAR1 HAR3 HAR14 HAR16 HAR23 HAR24 HAR26 HAR27 HYE1G HYE1H HYE6A HYE6B HYE15 HYH2 HYH10 HFF1IF HAB1IF HAM5IF HAM6IF HAN6SRIF HAQ1IF HAR3RIF HAT28IF HAZAK1IF HAZAK5IF HAZBK1IF HAZBK5IF HAZCK1IF HAZCK5IF HYD1IF HYF2IF BMPSB1IF BMPSB2IF BMPSP1IF BMPSP2IF BMPTR1IF BMPTR2IF PEP6G1IF PEP6G2IF PEP6G3IF PEP6H1IF PEP6H2IF PEP6H3IF PEP6I1IF PEP6I2IF PEP6I3IF dropped in m=1) (variables sdppsu6 sdpstra6 wtpfqx6 wtpqrp1 wtpqrp2 wtpqrp3 wtpqrp4 wtpqrp5 wtpqrp6 wtpqrp7 wtpqrp8 wtpqrp9 wtpqrp10 wtpqrp11 wtpqrp12 wtpqrp13 wtpqrp14 wtpqrp15 wtpqrp16 wtpqrp17 wtpqrp18 wtpqrp19 wtpqrp20 wtpqrp21 wtpqrp22 wtpqrp23 wtpqrp24 wtpqrp25 wtpqrp26 wtpqrp27 wtpqrp28 wtpqrp29 wtpqrp30 wtpqrp31 wtpqrp32 wtpqrp33 wtpqrp34 wtpqrp35 wtpqrp36 wtpqrp37 wtpqrp38 wtpqrp39 wtpqrp40 wtpqrp41 wtpqrp42 wtpqrp43 wtpqrp44 wtpqrp45 wtpqrp46 wtpqrp47 wtpqrp48 wtpqrp49 wtpqrp50 wtpqrp51 wtpqrp52 hfa7 hfa8 hfa12 hac1a hac1b hac1c hac1d hac1e hac1f hac1g hac1h hac1i hac1j hac1k hac1l hac1m hac1n hac1o had1 hae2 hae4a hae4b hae5a hae5b hae6 hae7 haf1 haf10 hag2 hag3 hag5a hag5b hag5c hag11 hag12 han6hs han6is han6js hap1 hap1a hap2 hap3 hap10 hap10a har1 har3 har14 har16 har23 har24 har26 har27 hye1g hye1h hye6a hye6b hye15 hyh2 hyh10 hff1if hab1if ham5if ham6if han6srif haq1if har3rif hat28if hazak1if hazak5if hazbk1if hazbk5if hazck1if hazck5if hyd1if hyf2if bmpsb1if bmpsb2if bmpsp1if bmpsp2if bmptr1if bmptr2if pep6g1if pep6g2if pep6g3if pep6h1if pep6h2if pep6h3if pep6i1if pep6i2if pep6i3if added to m=1) <output omitted to save space> (variables SDPPSU6 SDPSTRA6 WTPFQX6 WTPQRP1 WTPQRP2 WTPQRP3 WTPQRP4 WTPQRP5 WTPQRP6 WTPQRP7 WTPQRP8 WTPQRP9 WTPQRP10 WTPQRP11 WTPQRP12 WTPQRP13 WTPQRP14 WTPQRP15 WTPQRP16 WTPQRP17 WTPQRP18 WTPQRP19 WTPQRP20 WTPQRP21 WTPQRP22 WTPQRP23 WTPQRP24 WTPQRP25 WTPQRP26 WTPQRP27 WTPQRP28 WTPQRP29 WTPQRP30 WTPQRP31 WTPQRP32 WTPQRP33 WTPQRP34 WTPQRP35 WTPQRP36 WTPQRP37 WTPQRP38 WTPQRP39 WTPQRP40 WTPQRP41 WTPQRP42 WTPQRP43 WTPQRP44 WTPQRP45 WTPQRP46 WTPQRP47 WTPQRP48 WTPQRP49 WTPQRP50 WTPQRP51 WTPQRP52 HFA7 HFA8 HFA12 HAC1A HAC1B HAC1C HAC1D HAC1E HAC1F HAC1G HAC1H HAC1I HAC1J HAC1K HAC1L HAC1M HAC1N HAC1O HAD1 HAE2 HAE4A HAE4B HAE5A HAE5B HAE6 HAE7 HAF1 HAF10 HAG2 HAG3 HAG5A HAG5B HAG5C HAG11 HAG12 HAN6HS HAN6IS HAN6JS HAP1 HAP1A HAP2 HAP3 HAP10 HAP10A HAR1 HAR3 HAR14 HAR16 HAR23 HAR24 HAR26 HAR27 HYE1G HYE1H HYE6A HYE6B HYE15 HYH2 HYH10 HFF1IF HAB1IF HAM5IF HAM6IF HAN6SRIF HAQ1IF HAR3RIF HAT28IF HAZAK1IF HAZAK5IF HAZBK1IF HAZBK5IF HAZCK1IF HAZCK5IF HYD1IF HYF2IF BMPSB1IF BMPSB2IF BMPSP1IF BMPSP2IF BMPTR1IF BMPTR2IF PEP6G1IF PEP6G2IF PEP6G3IF PEP6H1IF PEP6H2IF PEP6H3IF PEP6I1IF PEP6I2IF PEP6I3IF dropped in m=5) (variables sdppsu6 sdpstra6 wtpfqx6 wtpqrp1 wtpqrp2 wtpqrp3 wtpqrp4 wtpqrp5 wtpqrp6 wtpqrp7 wtpqrp8 wtpqrp9 wtpqrp10 wtpqrp11 wtpqrp12 wtpqrp13 wtpqrp14 wtpqrp15 wtpqrp16 wtpqrp17 wtpqrp18 wtpqrp19 wtpqrp20 wtpqrp21 wtpqrp22 wtpqrp23 wtpqrp24 wtpqrp25 wtpqrp26 wtpqrp27 wtpqrp28 wtpqrp29 wtpqrp30 wtpqrp31 wtpqrp32 wtpqrp33 wtpqrp34 wtpqrp35 wtpqrp36 wtpqrp37 wtpqrp38 wtpqrp39 wtpqrp40 wtpqrp41 wtpqrp42 wtpqrp43 wtpqrp44 wtpqrp45 wtpqrp46 wtpqrp47 wtpqrp48 wtpqrp49 wtpqrp50 wtpqrp51 wtpqrp52 hfa7 hfa8 hfa12 hac1a hac1b hac1c hac1d hac1e hac1f hac1g hac1h hac1i hac1j hac1k hac1l hac1m hac1n hac1o had1 hae2 hae4a hae4b hae5a hae5b hae6 hae7 haf1 haf10 hag2 hag3 hag5a hag5b hag5c hag11 hag12 han6hs han6is han6js hap1 hap1a hap2 hap3 hap10 hap10a har1 har3 har14 har16 har23 har24 har26 har27 hye1g hye1h hye6a hye6b hye15 hyh2 hyh10 hff1if hab1if ham5if ham6if han6srif haq1if har3rif hat28if hazak1if hazak5if hazbk1if hazbk5if hazck1if hazck5if hyd1if hyf2if bmpsb1if bmpsb2if bmpsp1if bmpsp2if bmptr1if bmptr2if pep6g1if pep6g2if pep6g3if pep6h1if pep6h2if pep6h3if pep6i1if pep6i2if pep6i3if added to m=5) pweight: wtpfqx6 VCE: linearized Single unit: centered Strata 1: sdpstra6 SU 1: sdppsu6 FPC 1: <zero>

At long last, we are ready to do our analysis. Please note that not all
of the commands that are available with the **svy:** prefix are available
with the **mi estimate: svy:** prefix. For the examples here, we
will get the mean of three variables (**bmpwst**, **bmpht** and **bmpbut**),
and then we will run a regression.

mi estimate: svy: mean bmpwst bmpht bmpbutMultiple-imputation estimates Imputations = 5 Survey: Mean estimation Number of obs = 30548 Number of strata = 49 Population size = 243785748 Number of PSUs = 98 Average RVI = 0.0242 Complete DF = 49 DF adjustment: Small sample DF: min = 46.64 avg = 46.67 Within VCE type: Linearized max = 46.72 ------------------------------------------------------------------------------ Mean | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- bmpwst | 84.72488 .2081347 407.07 0.000 84.30608 85.14368 bmpht | 160.6015 .1916889 837.82 0.000 160.2158 160.9871 bmpbut | 94.10488 .1790256 525.65 0.000 93.74465 94.4651 ------------------------------------------------------------------------------mi estimate: svy: regress bmpwst bmpht bmpbutMultiple-imputation estimates Imputations = 5 Survey: Linear regression Number of obs = 30548 Number of strata = 49 Population size = 243785748 Number of PSUs = 98 Average RVI = 0.3866 Complete DF = 49 DF adjustment: Small sample DF: min = 8.66 avg = 20.78 max = 43.77 Model F test: Equal FMI F( 2, 13.5) = 13019.57 Within VCE type: Linearized Prob > F = 0.0000 ------------------------------------------------------------------------------ bmpwst | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- bmpht | -.0063002 .0129422 -0.49 0.637 -.0351702 .0225698 bmpbut | .9663688 .0200984 48.08 0.000 .9206272 1.01211 _cons | -5.203297 .5062292 -10.28 0.000 -6.223686 -4.182908 ------------------------------------------------------------------------------

The preceding is intended only to give a cursory overview of the steps involved in analyzing multiply imputed survey data sets. By no means have we covered all (or even most) of the issues that can be involved. Rather, the point is that such data can be analyzed in Stata 11, and a few of the commands to do so have been illustrated. Reading over the relevant sections of the Stata 11 manuals will be very helpful and is strongly recommended.

If you are using Stata 10 or earlier, we suggest using the prefix **mim:** for analyzing multiply imputed
data sets, although there are some other prefixes available in Stata. The
prefix **mim:** is not part of Stata and needs to be downloaded (**search
mim**). The NHANES data were released with five imputed data sets.
Unlike SUDAAN, **mim** wants the data sets stacked into a single data set.
We can use the **mimstack** command to do this (**search mimstack**). We need to specify
unique case identifier in each data set (**seqn**) and the "stub" name (**nh3mi**)
of the imputed data sets. We strongly encourage everyone to read the help
file for **mim** before using the **mim:** prefix or the **mimstack**
command. Also, before you start using the multiply imputed data, you
should look at the help file for **mim** to see if the procedure
that you want to use is supported by **mim**. For example, **svy: tab**
is not supported by **mim**. You may also want to check periodically to
see if there are any updates to **mim** or similar procedures. We should also note the **mimstack**
can take some time to run, especially if you don’t have a lot of RAM on your
computer.

## A quick note on merging data sets

The NHANES documentation provides clear instructions on how to merge various
data sets from the NHANES III collection. You need to read that very
carefully. Depending on what data sets you merge, you may need to adjust
the sampling weights. Again, when and how to do this is spelled out in the
documentation, so please read that carefully. Also, be aware that you will likely have to modify your **
svyset** command to work with the merged data set. In fact, the **svyset**
command may need to be different for different models that you run from the
merged data set, depending on which variables are included in the model.

Another point to remember is that what you do to merge data sets or modify sampling weights with the NHANES data will likely NOT generalize to other survey data sets. You will need to read the documentation for each data set and will probably have to follow different procedures to accomplish the same tasks with other data sets. In other words, many ways of doing things are specific to that particular data set; be careful not to over generalize.

## For more information on using the NHANES data sets

There are several helpful resources for learning how to analyze the NHANES III 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

The Stata Journal, Vol. 7, No. 1, 1st Quarter 2007

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

Sampling of Populations: Methods and Applications, Third 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

Stata 9 Manual: Survey Data

Analyzing the NHANES III Multiply Imputed Data Set: Methods and Examples by Joseph L. Schafer (June, 2001)