Task 2c: How to Use Stata Code to Perform Linear Regression

In this example, you will assess the association between high density lipoprotein (HDL) cholesterol — the outcome variable — and body mass index (bmxbmi) — the exposure variable — after controlling for selected covariates in NHANES 1999-2002. These covariates include gender (riagendr), race/ethnicity (ridreth1), age (ridageyr), smoking (smoker, derived from SMQ020 and SMQ040; smoker =1 if non-smoker, 2 if past smoker and 3 if current smoker) and education (dmdeduc).

Step 1: Use svyset to define survey design variables

Remember that you need to define the SVYSET before using the SVY series of  commands. The general format of this command is below:

svyset [w=weightvar], psu(psuvar) strata(stratavar) vce(linearized)

To define the survey design variables for your high density lipoprotein cholesterol analysis, use the weight variable for four-years of MEC data (wtmec4yr), the PSU variable (sdmvpsu), and strata variable (sdmvstra) .The vce option specifies the method for calculating the variance and the default is "linearized" which is Taylor linearization.  Here is the svyset command for four years of MEC data:

svyset [w= wtmec4yr], psu(sdmvpsu) strata(sdmvstra) vce(linearized)

Step 2: Determine how to specify variables in the model

For continuous variables, you have a choice of using the variable in its original form (continuous) or changing it into a categorical variable (e.g. based on standard cutoffs, quartiles or common practice).  The categorical variables should reflect the underlying distribution of the continuous variable and not create categories where there are only a few observations. 

It is important to exam the data both ways, since the assumption that a dependent variable has a continuous relationship with the outcome may not be true.  Looking at the categorical version of the variable will help you to know whether this assumption is true. 

In this example, you could look at BMI as a continuous variable or convert it into a categorical variable based on standard BMI definitions of underweight, normal weight, overweight and obese.  Here is how categorical BMI variables are created:

Step 3: Determine the reference group for categorical variables

For all categorical variables, you need to decide which category to use as the reference group.  If you do not specify the reference group options, Stata will choose the lowest numbered group by default.  

Use the following general command to specify the reference group:

char var[omit]reference group value

For these analyses, use the following commands to specify the following reference groups.

Step 4: Create simple linear regression models to understand relationships

Before you perform a regression on the data, the data needs to meet  a requirement — the dependent variable must be a continuous variable and the independent variables may be either discrete, ordinal, or continuous.  The association between the dependent (or outcome) and independent (or exposure) variables is expressed using the svy:regress command. The general form of the command is:

svy:regress depvar indvar

Here is the command (and output) for the BMI-HDL example. This example uses the subpop (if eligible==1) statement to restrict the analysis to individuals with complete data for all the variables used in the final multiple regression model. The eligible variable is defined in the program available on the Sample Code and Datasets page.

svy, subpop(if eligible==1): regress lbdhdl bmxbmi

And, here is the output of the statement.

This analysis says that for each 1 unit increase of BMI, on average, HDL decreases by 0.69 mg/dl.  Or, you could do the simple regression using the BMI categories:

To perform the same analysis using the categorical BMI variable, bmicat, the statement would be:

svy, subpop(if eligible==1): regress lbdhdl bmicat

And, the output of that statement would be:

This model says that, on average, HDL levels decrease by 5.6 mg/dl between the underweight BMI category and the normal weight BMI category, or the normal weight  BMI category to the overweight BMI category.

Using the interaction expansion function (xi) to expand categorical variables into indicator variable sets

Delving deeper into this relationship, you will look at each comparison separately to see whether this continuous relationship really holds.  Stata has a  function (called xi or interaction expansion) which creates the "indicator variables" to allow you to see these relationships.   The xi function will expand terms containing categorical variables (denoted i.varname) into indicator (also called dummy) variable sets.  It has this general form:

xi:svy:regress depvar i.indvar

For this example, you will use the HDL variable as the dependent variable and the BMI categorical variable (bmicat) as the independent variable, denoted with the i. prefix. This example uses the subpop(if ridageyr >= 20 & ridageyr =.) statement to select participants who were age 20 years and older and did not have a missing value for the age variable.

xi:svy, subpop(if ridageyr >=20 & ridageyr =.): regress lbdhdl i.bmicat

Here are the results for this analysis which use "normal weight" - bmicat2 as the reference category:

This analysis using the BMI categorical variable (BMICAT) shows that the relationship is not linear and the difference in HDL is between underweight and normal is 3.2 compared to a 7.5 difference between normal weight and overweight.

It is also possible to generate indicator variables using the tab, generate command: 

tab var, gen(newvar);  for example:  tab bmicat, gen(ibmicat)

This command generates four variables: ibmicat1, ibmicat2, ibmicat3, and ibmicat4.

Step 5: Specify multiple linear regression models

Multiple linear regression uses the same command structure but now includes other independent variables.  And if you want to create indicator variables for categorical variables, you will want to use the xi option.   So, the general structure looks the same:

xi:  svy: regress depvar indvar i.var

This example will use the HDL variable (lbdhdl) as the dependent variable. The independent categorical variables (riagendr, ridreth1, smoker, educ, and bmicat) are specified with the i. prefix, while ridageyr remains an independent continuous variable.  Again, it uses the subpop(if ridageyr >= 20 & ridageyr =.) statement to select participants who were age 20 years and older and did not have a missing value for the age variable.

xi:  svy, subpop(if ridageyr >=20 & ridageyr <.): regress lbdhdl i.riagendr i.ridreth1 ridageyr i.smoker i.educ i.bmicat

In this example, the output is:

Later in this module, the results of this multiple regression will be presented in a summary table comparing it with the univariate regression.

Step 6: Calculate means "adjusted" for the covariates in the model

Sometimes you may want to calculate means which are adjusted for the covariates specified in the model to allow you to see the effect of a given predictor variable.  Stata has a built in command, adjust,  to do this. Adjust  is a post-estimation command

The adjust command uses only the sample mean, not the mean based on the survey design, when performing its computations. Therefore, if you want to use the survey mean, you would need to calculate it first and specify it explicitly in the adjust command. The following commands use summarize which is an rclass command and will not cause any trouble if run between the svy: regress and adjust commands; whereas svy:mean is an eclass command and cannot be used in between these commands. Here is the general form of the command:

sum _cat_1 [aw=weight] if conditions & e(sample)
local cat1 = r(mean)
...

adjust indvar1=cat1 indvar2=cat2.... if e(sample), by(indvar3)

The variables have to appear just as they are in the regression model.  Independent categorical variables are specified with the _I prefix, while the independent continuous variable, ridageyr, doesn't not require the prefix. The following command, will generate mean HDL levels for BMI categories (by (bmicat)), adjusting for every other variable in the model.

sum _Ibmicat_1 [aw=wtmec4yr] if ridageyr >=20 & ridageyr <. & e(sample)
local bmicat1 = r(mean)
sum _Ibmicat_3 [aw=wtmec4yr] if ridageyr >=20 & ridageyr <. & e(sample)
local bmicat3 = r(mean)
sum _Ibmicat_4 [aw=wtmec4yr] if ridageyr >=20 & ridageyr <. & e(sample)
local bmicat4 = r(mean)

adjust _Iriagendr_2=`riagendr2' _Iridreth1_1=`rid1' _Iridreth1_2=`rid2' ///
_Iridreth1_4=`rid4' _Iridreth1_5=`rid5' ridageyr=`ridage' ///
_Ieduc_1=`educ1' _Ieduc_2=`educ2' _Ismoker_1=`smoke1' ///
_Ismoker_2=`smoke2' if ridageyr >=20 & ridageyr <. & e(sample), by(bmicat) se

The output for this example is:

Later in this module, the results of this adjusted means calculation will be presented in a summary table comparing it with the crude mean.

Step 7: Compare results of crude analysis (simple linear regression) and adjusted analysis (multiple linear regression)

To understand how much adjustment matters, it is helpful to compare the regression coefficient from the simple and multiple regression models.  To help you review the results,  the following summary tables present the crude analysis (simple linear regression) and adjusted analysis (multiple linear regression).

Here are the summary tables of the results for the other covariates in the model.