margins and marginsplot for a continuous predictor variable

Stata's margins and marginsplot commands are powerful tools for visualizing the results of regression models. We will use linear regression below, but the same principles and syntax work with nearly all of Stata's regression commands, including probit, logistic, poisson, and others. You will want to review Stata's factor-variable notation if you have not used it before.

Let's begin by opening the nhanes2l dataset. Then let's describe and summarize the variables bpsystol and age.

. webuse nhanes2l
(Second National Health and Nutrition Examination Survey)

. describe bpsystol age


Variable      Storage   Display    Value
    name         type    format    label      Variable label
                                                                                
bpsystol        int     %9.0g                 Systolic blood pressure
age             byte    %9.0g                 Age (years)


. summarize bpsystol age


    Variable 
 
        Obs        Mean    Std. dev.       Min        Max
 
 
 
    bpsystol 
 
     10,351    130.8817    23.33265         65        300
         age 
 
     10,351    47.57965    17.21483         20         74

We are going to fit a series of linear regression models for the outcome variable bpsystol, which measures systolic blood pressure (SBP) with a range of 65 to 300 mmHg, and age measures age with a range of 20 to 74 years.

Let's fit a linear regression model using the continuous outcome variable bpsystol and the continuous predictor variable age.

. regress bpsystol age


      Source 
 
       SS           df       MS  
   Number of obs   =    10,351
 
 
 
   F(1, 10349)     =   3116.79
       Model 
 
  1304200.02         1  1304200.02
   Prob > F        =    0.0000
    Residual 
 
  4330470.01    10,349  418.443328
   R-squared       =    0.2315
 
 
 
   Adj R-squared   =    0.2314
       Total 
 
  5634670.03    10,350  544.412563
   Root MSE        =    20.456




    bpsystol 
 
 Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
 
 
 
         age 
 
   .6520775   .0116801    55.83   0.000     .6291823    .6749727
       _cons 
 
   99.85603   .5909867   168.96   0.000     98.69758    101.0145

The regression output tells us that the intercept, labeled “_cons”, is 99.85603 and the slope coefficient for age is 0.6520775. We can use these estimated coefficients to calculate the expected SBP for a 20-year-old.

. display "E(SBP | age = 20) = " 99.85603 + 0.6520775 * 20
E(SBP | age = 20) = 112.89758

We can also use the estimated coefficients to calculate the expected SBP for a 40-year-old and a 60-year-old.

. display "E(SBP | age = 40) = " 99.85603 + 0.6520775 * 40
E(SBP | age = 40) = 125.93913

. display "E(SBP | age = 60) = " 99.85603 + 0.6520775 * 60
E(SBP | age = 60) = 138.98068

Stata's margins command will estimate the expected SBP for all three values of age along with the standard error, t statistic, p-value, and 95% confidence interval. Note that the “i.” prefix is required in the regress command but not in the margins command.

. margins, at(age=(20 40 60))

Adjusted predictions                                    Number of obs = 10,351
Model VCE: OLS

Expression: Linear prediction, predict()
1._at: age = 20
2._at: age = 40
3._at: age = 60



              
 
            Delta-method                                       
              
 
     Margin   std. err.      t    P>|t|     [95% conf. interval]
 
 
 
         _at 
 
                                                                
          1  
 
   112.8976   .3797296   297.31   0.000     112.1532    113.6419
          2  
 
   125.9391   .2196887   573.26   0.000     125.5085    126.3698
          3  
 
   138.9807   .2479332   560.56   0.000     138.4947    139.4667

We can estimate predictions from age 20 to 60 in 5-year increments using the following syntax:

. margins, at(age=(20(5)60))

Adjusted predictions                                    Number of obs = 10,351
Model VCE: OLS

Expression: Linear prediction, predict()
1._at: age = 20
2._at: age = 25
3._at: age = 30
4._at: age = 35
5._at: age = 40
6._at: age = 45
7._at: age = 50
8._at: age = 55
9._at: age = 60



              
 
            Delta-method                                       
              
 
     Margin   std. err.      t    P>|t|     [95% conf. interval]
 
 
 
         _at 
 
                                                                
          1  
 
   112.8976   .3797296   297.31   0.000     112.1532    113.6419
          2  
 
    116.158   .3316322   350.26   0.000     115.5079     116.808
          3  
 
   119.4184   .2873786   415.54   0.000      118.855    119.9817
          4  
 
   122.6787   .2490265   492.63   0.000     122.1906    123.1669
          5  
 
   125.9391   .2196887   573.26   0.000     125.5085    126.3698
          6  
 
   129.1995   .2033058   635.49   0.000      128.801     129.598
          7  
 
   132.4599   .2030384   652.39   0.000     132.0619    132.8579
          8  
 
   135.7203   .2189455   619.88   0.000     135.2911    136.1495
          9  
 
   138.9807   .2479332   560.56   0.000     138.4947    139.4667

The output also reports a standard error, t statistic, p-value, and 95% confidence interval for each estimate. The t statistic tests the null hypothesis that the expected SBP is zero.

Then we can plot the marginal predictions by typing marginsplot.

. marginsplot

Variables that uniquely identify margins: age

Let's use the ytitle() and title() options to add titles to our graph.

. marginsplot, ytitle("Expected systolic blood pressure (mmHg)")
                title("Expected systolic blood pressure by age")

Variables that uniquely identify margins: age

You can read more about factor-variable notation, margins, and marginsplot in the Stata documentation. You can also watch a demonstration of these commands by clicking on the links to the YouTube videos below.