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How do I keep all levels of my categorical variable in my model?

How do I specify a cell means model?

In the following example, we use regress as our estimation command, but the same thing applies to other estimation commands that have a noconstant option.

You might try

. sysuse auto, clear
(1978 Automobile Data)

. regress mpg i.rep78, noconstant


      Source 
       SS           df       MS   
   Number of obs   =        69
   F(4, 65)        =    188.12
       Model 
  30942.2129         4  7735.55322
   Prob > F        =    0.0000
    Residual 
  2672.78712        65  41.1198019
   R-squared       =    0.9205
   Adj R-squared   =    0.9156
       Total 
       33615        69  487.173913
   Root MSE        =    6.4125


         mpg 
 
 Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

       rep78 
 

          2  
 
     19.125   2.267151     8.44   0.000     14.59719    23.65281
          3  
 
   19.43333   1.170752    16.60   0.000     17.09518    21.77149
          4  
 
   21.66667   1.511434    14.34   0.000     18.64812    24.68521
          5  
 
   27.36364   1.933433    14.15   0.000      23.5023    31.22497

and then wonder why the first level of rep78 does not appear in your regression table. If you add the baselevels option to your regression command, you will see that the first level is considered a base level and has been omitted from the model.

. regress mpg i.rep78, noconstant baselevels


      Source 
 
       SS           df       MS   
   Number of obs   =        69
   F(4, 65)        =    188.12
       Model 
 
  30942.2129         4  7735.55322
   Prob > F        =    0.0000
    Residual 
 
  2672.78712        65  41.1198019
   R-squared       =    0.9205
   Adj R-squared   =    0.9156
       Total 
 
       33615        69  487.173913
   Root MSE        =    6.4125



         mpg 
 
 Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

       rep78 
 
 
          1  
 
          0  (base)						 
          2  
 
     19.125   2.267151     8.44   0.000     14.59719    23.65281
          3  
 
   19.43333   1.170752    16.60   0.000     17.09518    21.77149
          4  
 
   21.66667   1.511434    14.34   0.000     18.64812    24.68521
          5  
 
   27.36364   1.933433    14.15   0.000      23.5023    31.22497

The ibn. factor-variable operator specifies that a categorical variable should be treated as if it has no base, or, in other words, that all levels of the categorical variable are to be included in the model; see [U] 11.4.3 Factor variables.

What happens when you specify that rep78 should have no base level but leave the constant in the model?

. regress mpg ibn.rep78

note: 5.rep78 omitted because of collinearity

      Source 
 
       SS           df       MS   
   Number of obs   =        69
   F(4, 64)        =      4.91
       Model 
 
  549.415777         4  137.353944
   Prob > F        =    0.0016
    Residual 
 
  1790.78712        64  27.9810488
   R-squared       =    0.2348
   Adj R-squared   =    0.1869
       Total 
 
   2340.2029        68  34.4147485
   Root MSE        =    5.2897



         mpg 
 
 Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

       rep78 
 

          1  
 
  -6.363636   4.066234    -1.56   0.123    -14.48687    1.759599
          2  
 
  -8.238636   2.457918    -3.35   0.001    -13.14889    -3.32838
          3  
 
  -7.930303    1.86452    -4.25   0.000    -11.65511   -4.205497
          4  
 
   -5.69697    2.02441    -2.81   0.006    -9.741193   -1.652747
          5  
 
          0  (omitted)
             
 

       _cons 
 
   27.36364   1.594908    17.16   0.000     24.17744    30.54983

One of the levels of rep78 is omitted from the model despite your request that there be no base level for rep78. If you have the constant and all levels of a categorical variable in a model, something must be dropped because of the collinearity between all the levels and the constant.

You need to use the ibn. operator on your categorical variable and the noconstant option on your estimation command to obtain a cell means model.

. regress mpg ibn.rep78, noconstant


      Source 
 
       SS           df       MS   
   Number of obs   =        69
   F(5, 64)        =    227.47
       Model 
 
  31824.2129         5  6364.84258
   Prob > F        =    0.0000
    Residual 
 
  1790.78712        64  27.9810488
   R-squared       =    0.9467
   Adj R-squared   =    0.9426
       Total 
 
       33615        69  487.173913
   Root MSE        =    5.2897



         mpg 
 
 Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

       rep78 
 

          1  
 
         21   3.740391     5.61   0.000     13.52771    28.47229
          2  
 
     19.125   1.870195    10.23   0.000     15.38886    22.86114
          3  
 
   19.43333   .9657648    20.12   0.000       17.504    21.36267
          4  
 
   21.66667   1.246797    17.38   0.000      19.1759    24.15743
          5  
 
   27.36364   1.594908    17.16   0.000     24.17744    30.54983