## 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).

WARNING

There are several things you should be aware of while analyzing NHANES data with Stata. Please see the Stata Tips page to review them before continuing.

### 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:

Table of code to generate categorical BMI variable
Code to generate categorical BMI variables BMI Category

gen bmicat=1 if  bmxbmi>=0 &  bmxbmi<18.5

underweight

replace bmicat=2 if  bmxbmi>=18.5 & bmxbmi<25

normal weight

replace bmicat=3 if  bmxbmi>=25

overweight

replace bmicat=4 if  bmxbmi>=30 &  bmxbmi<.

obese

### 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.

Stata command Reference group

char ridreth1[omit]3

Non-Hispanic White

char smoker[omit]3

Current Smokers

char educ[omit]3

Greater than high school education

char bmicat[omit]2

Normal weight

### 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.

IMPORTANT NOTE

You can also just use the xi option to generate the indicator variables or interaction terms (rather than using it with the model command).  The advantage of creating the indicators prior to the model, is that you do not need to write a command to set the reference category (you will do this implicitly by selecting the indicators you include in the model) and the output is easier to read (the xi model command repeats the individual components in interaction terms).

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).

Table Comparing Differences between Crude Analysis (Simple Linear Regression) and Adjusted Analysis (Multiple Linear Regression) - BMI
BMI Crude Analysis
Mean HDL
Mean HDL
Crude Analysis
Coefficient*
(95% CI)
Coefficient*
(95% CI)
Crude Analysis
p value
p value

underweight

60.44

59.40

3.26
(.37 – 6.15

2.30
(-.44 – 5.04)

.028

.097

normal

57.18

57.10

Reference
Group

Reference
Group

Reference
Group

Reference
Group

overweight

49.69

50.55

-7.48
(-8.50 – -6.46)

-6.55
(-7.38 – -5.71)

<.001

<.001

obese

45.94

45.10

-11.24
(-12.17 – -10.31)

-12.00
(-12.79 – -11.22)

<.001

<.001

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

Table Comparing Differences between Crude Analysis (Simple Linear Regression) and Adjusted Analysis (Multiple Linear Regression) - Smoking
Smoking Crude Analysis
Mean HDL
Mean HDL
Crude Analysis
Coefficient*
(95% CI)
Coefficient*
(95% CI)
Crude Analysis
p value
p value
current 49.35 51.27 Reference Group Reference Group
past 51.64 52.38 2.76
(1.29 – 4.23)
2.33
(1.00 – 3.66)
.001 .001
never 52 50.05 2.32
(.85 – 3.79)
1.22
(-.22 – 2.66)
.003 .095

Table Comparing Differences between Crude Analysis (Simple Linear Regression) and Adjusted Analysis (Multiple Linear Regression) - Sex
Sex Crude Analysis
Mean HDL
Mean HDL
Crude Analysis
Coefficient*
(95% CI)
(95% CI)
Crude Analysis
p value
p value
men 45.91 46.08 Ref erence Group Ref erence Group
women 56.21 56.06 10.30

(9.54 – 11.06)

9.98

(9.3 – 10.64)

<.001 <.001

Table Comparing Differences between Crude Analysis (Simple Linear Regression) and Adjusted Analysis (Multiple Linear Regression) - Race/Ethnicity
Race/Ethnicity Crude Analysis
Mean HDL
Mean HDL
Crude Analysis
Coefficient*
(95% CI)
Coefficient*
(95% CI)
Crude Analysis
p value
p value
Non-Hispanic White 51.38 50.88 Ref erence Group Ref erence Group
Non-Hispanic Black 54.5 55.83 3.12
(1.54 – 4.70)
4.95
(3.61 – 6.29
<.001 <.001
Other Hispanic 47.71 48.64 -3.67
(-5.47 – -1.88)
-2.24
(-3.59 – -.89)
<.001 .002
Mexican-American 48.92 51.55 -2.46
(-3.59 – -1.33)
.67
(-.46 – 1.80)
<.001 .235
Other 50.91 50.32 -.47
(-3.28 – 2.33)
-.56
(-2.83 – 1.71)
.733 .619

Table Comparing Differences between Crude Analysis (Simple Linear Regression) and Adjusted Analysis (Multiple Linear Regression) - Education
Education Crude Analysis
Mean HDL
Mean HDL
Crude Analysis
Coefficient*
(95% CI)
Coefficient*
(95% CI)
Crude Analysis
p value
p value
< high school 49.37 49.34 -3.10
(-4.41 – -1.79)
-3.03
(-4.16 – -1.90)
<.001 <.001>
high school 50.30 50.52 -2.18
(-3.23 – -1.12)
-1.85
(-2.98 – -.73)
<.001 .002
> high school 52.47 52.37 Reference Group Reference Group

Table Comparing Differences between Crude Analysis (Simple Linear Regression) and Adjusted Analysis (Multiple Linear Regression) - Age
Age Crude Analysis
Mean HDL
Mean HDL
Crude Analysis
Coefficient*
(95% CI)
Coefficient*
(95% CI)
Crude Analysis
p value
p value
Age
(years)

-

-

.11
(.07 – .12)

-

<.001 <.001

### Step 8: Perform post-estimation test

Use the test post estimation command to produce the Wald F statistic and the corresponding p-value. Use the nosvyadjust option to produce the unadjusted Wald F. In the example, the command test is used to test all coefficients together; all coefficients separately; and to test the hypothesis that HDL cholesterol for non-smokers is the same as that for past smokers.

The general form of this statement is below.

test indvar 1 ind var 2 ..., [nosvyadjust]

This example tests all of the coefficients.

test

Here are the results of that statement:

The results of this test will be discussed in the next step.

This example tests the gender coefficient and, using the nosvyadjust option, produces the unadjusted Wald F. Tests for the additional variables are included in the program available on the Sample Downloads and Datasets page.

Here are the results of that statement:

The results of this test will be discussed in the next step.

This example tests the hypothesis that HDL cholesterol for non-smokers is the same as that for past smokers.

test _Ismoker_1 - _Ismoker_2 = 0

Here are the results of the statement:

The results of this test will be discussed in the next step.

### Step 9: Review output

In this step, the Stata output is reviewed.

• HDL cholesterol is 6.55 mg/dL higher for overweight adults compared to normal weight adults, as defined by BMI.
• HDL cholesterol is 12.00 mg/dL higher for obese adults compared to normal weight adults, as defined by BMI.
• HDL cholesterol is 2.30 mg/dL lower for underweight adults compared to normal weight adults, as defined by BMI.
• HDL cholesterol is 9.98 mg/dL higher for women than for men, after adjusting for all other variables in the model.
• The F test for gender shows a significant effect (p < 0.001) of gender for HDL cholesterol when controlling for other covariates in the model.
• HDL cholesterol is 4.95 mg/dL higher for non-Hispanic Blacks compared to non-Hispanic Whites, after adjusting for all other variables in the model.
• HDL cholesterol increases 0.11 mg/dL per unit increase in age.

### Special topic: Interactions

If you want to look for interactions, use the xi option to create interaction terms.  The general form for interaction terms is:

i.var1*i.var2

See the sample code in Sample Datasets and Code for a model with interaction term included.