Indicator Variables With Stata

Andy Grogan-Kaylor

24 Feb 2021 09:24:57

Introduction

Get Data

. use https://www.stata-press.com/data/r16/margex, clear
(Artificial data for margins)

Descriptive Statistics

. summarize y

    Variable │        Obs        Mean    Std. Dev.       Min        Max
─────────────┼─────────────────────────────────────────────────────────
           y │      3,000    69.73357    21.53986          0      146.3

. tabulate sex

        sex │      Freq.     Percent        Cum.
────────────┼───────────────────────────────────
       male │      1,498       49.93       49.93
     female │      1,502       50.07      100.00
────────────┼───────────────────────────────────
      Total │      3,000      100.00

. tabulate group

      group │      Freq.     Percent        Cum.
────────────┼───────────────────────────────────
          1 │      1,199       39.97       39.97
          2 │      1,118       37.27       77.23
          3 │        683       22.77      100.00
────────────┼───────────────────────────────────
      Total │      3,000      100.00

Regressions

“Usual” Regression With Indicator Variables

. regress y i.sex i.group

      Source │       SS           df       MS      Number of obs   =     3,000
─────────────┼──────────────────────────────────   F(3, 2996)      =    152.06
       Model │  183866.077         3  61288.6923   Prob > F        =    0.0000
    Residual │  1207566.93     2,996  403.059723   R-squared       =    0.1321
─────────────┼──────────────────────────────────   Adj R-squared   =    0.1313
       Total │  1391433.01     2,999  463.965657   Root MSE        =    20.076

─────────────┬────────────────────────────────────────────────────────────────
           y │      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
         sex │
     female  │   18.32202   .8930951    20.52   0.000     16.57088    20.07316
             │
       group │
          2  │   8.037615    .913769     8.80   0.000     6.245937    9.829293
          3  │   18.63922   1.159503    16.08   0.000     16.36572    20.91272
             │
       _cons │   53.32146   .9345465    57.06   0.000     51.48904    55.15388
─────────────┴────────────────────────────────────────────────────────────────

. est store M1 // store estimates

Regression With No Constant and No Reference Category For One Independent Variable

. regress y i.sex ibn.group, noconstant

      Source │       SS           df       MS      Number of obs   =     3,000
─────────────┼──────────────────────────────────   F(4, 2996)      =   9162.52
       Model │    14772177         4  3693044.26   Prob > F        =    0.0000
    Residual │  1207566.93     2,996  403.059723   R-squared       =    0.9244
─────────────┼──────────────────────────────────   Adj R-squared   =    0.9243
       Total │    15979744     3,000  5326.58132   Root MSE        =    20.076

─────────────┬────────────────────────────────────────────────────────────────
           y │      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
         sex │
     female  │   18.32202   .8930951    20.52   0.000     16.57088    20.07316
             │
       group │
          1  │   53.32146   .9345465    57.06   0.000     51.48904    55.15388
          2  │   61.35908   .7006367    87.58   0.000      59.9853    62.73285
          3  │   71.96068   .7730326    93.09   0.000     70.44495    73.47641
─────────────┴────────────────────────────────────────────────────────────────

. est store M2 // store estimates

Compare These Approaches

. est table M1 M2, star

─────────────┬────────────────────────────────
    Variable │      M1              M2        
─────────────┼────────────────────────────────
         sex │
     female  │  18.322021***    18.322021***  
             │
       group │
          1  │     (base)       53.321461***  
          2  │  8.0376149***    61.359076***  
          3  │  18.639222***    71.960683***  
             │
       _cons │  53.321461***                  
─────────────┴────────────────────────────────
      legend: * p<0.05; ** p<0.01; *** p<0.001

Display Combinations of Results With margins

. margins sex#group

Adjusted predictions                            Number of obs     =      3,000
Model VCE    : OLS

Expression   : Linear prediction, predict()

─────────────┬────────────────────────────────────────────────────────────────
             │            Delta-method
             │     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
   sex#group │
     male#1  │   53.32146   .9345465    57.06   0.000     51.48904    55.15388
     male#2  │   61.35908   .7006367    87.58   0.000      59.9853    62.73285
     male#3  │   71.96068   .7730326    93.09   0.000     70.44495    73.47641
   female#1  │   71.64348   .6015065   119.11   0.000     70.46407    72.82289
   female#2  │    79.6811   .8022261    99.32   0.000     78.10813    81.25407
   female#3  │    90.2827   1.114023    81.04   0.000     88.09838    92.46703
─────────────┴────────────────────────────────────────────────────────────────

The noconstant Option Does Not Work With Two Indicator Variables

. regress y ibn.sex ibn.group, noconstant
note: 3.group omitted because of collinearity

      Source │       SS           df       MS      Number of obs   =     3,000
─────────────┼──────────────────────────────────   F(4, 2996)      =   9162.52
       Model │    14772177         4  3693044.26   Prob > F        =    0.0000
    Residual │  1207566.93     2,996  403.059723   R-squared       =    0.9244
─────────────┼──────────────────────────────────   Adj R-squared   =    0.9243
       Total │    15979744     3,000  5326.58132   Root MSE        =    20.076

─────────────┬────────────────────────────────────────────────────────────────
           y │      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
         sex │
       male  │   71.96068   .7730326    93.09   0.000     70.44495    73.47641
     female  │    90.2827   1.114023    81.04   0.000     88.09838    92.46703
             │
       group │
          1  │  -18.63922   1.159503   -16.08   0.000    -20.91272   -16.36572
          2  │  -10.60161    1.01299   -10.47   0.000    -12.58783   -8.615381
          3  │          0  (omitted)
─────────────┴────────────────────────────────────────────────────────────────

Display Combinations of Results With margins

. margins sex#group

Adjusted predictions                            Number of obs     =      3,000
Model VCE    : OLS

Expression   : Linear prediction, predict()

─────────────┬────────────────────────────────────────────────────────────────
             │            Delta-method
             │     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
─────────────┼────────────────────────────────────────────────────────────────
   sex#group │
     male#1  │   53.32146   .9345465    57.06   0.000     51.48904    55.15388
     male#2  │   61.35908   .7006367    87.58   0.000      59.9853    62.73285
     male#3  │   71.96068   .7730326    93.09   0.000     70.44495    73.47641
   female#1  │   71.64348   .6015065   119.11   0.000     70.46407    72.82289
   female#2  │    79.6811   .8022261    99.32   0.000     78.10813    81.25407
   female#3  │    90.2827   1.114023    81.04   0.000     88.09838    92.46703
─────────────┴────────────────────────────────────────────────────────────────