factor variables and interactions

[Dominique Chaufree]

Hi,

Suppose, I have three variables: An outcome, a dummy variable D=0,1, and a variable with three values E=1,2,3.

I want to estimate the following interacted model (without constant):

gen E1 = E == 1
gen E2 = E == 2
gen E3 = E == 3
gen D_E1 = E1 * D
gen D_E2 = E2 * D
gen D_E3 = E3 * D

reg Y E1 E2 E3 D_E1 D_E2 D_E3, nocons

I'd like to use the stata factor variable notation for this purpose. However, I am not sure whether or not this is possible. When I type

reg Y i.E##i.D, nocons,

Stata includes a Dummy for E1, for E2, for D1, and interactions for E1#D1 and E2#D1. My model. however, should not include the non-interacted effect of D1 (see above).

Thank you so much!

[Carlo Lazzaro]

Dominique:
I do hope that the following toy-example can be helpful:

. set obs 12
number of observations (_N) was 0, now 12

. g D=0 in 1/6
(6 missing values generated)

. replace D=1 if D==.
(6 real changes made)

. g E=1 in 1/4
(8 missing values generated)

. replace E=2 in 5/8
(4 real changes made)

. replace E=3 if E==.
(4 real changes made)

. g Y=runiform()*1000

. reg Y i.D##i.E
note: 0b.D#3.E identifies no observations in the sample
note: 1.D#1b.E identifies no observations in the sample
note: 1.D#2.E omitted because of collinearity
note: 1.D#3.E omitted because of collinearity

      Source |       SS           df       MS      Number of obs   =        12
-------------+----------------------------------   F(3, 8)         =      2.72
       Model |  552323.622         3  184107.874   Prob > F        =    0.1148
    Residual |   541990.13         8  67748.7663   R-squared       =    0.5047
-------------+----------------------------------   Adj R-squared   =    0.3190
       Total |  1094313.75        11  99483.0684   Root MSE        =    260.29

------------------------------------------------------------------------------
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         1.D |  -412.6576   260.2859    -1.59   0.152    -1012.878    187.5629
             |
           E |
          2  |   414.6539   225.4142     1.84   0.103    -105.1522    934.4601
          3  |    849.558   318.7839     2.66   0.029     114.4411    1584.675
             |
         D#E |
        0 3  |          0  (empty)
        1 1  |          0  (empty)
        1 2  |          0  (omitted)
        1 3  |          0  (omitted)
             |
       _cons |   195.2401    130.143     1.50   0.172    -104.8701    495.3504
------------------------------------------------------------------------------

. reg Y i.D##i.E, nocons
note: 0b.D#3.E identifies no observations in the sample
note: 1.D#1b.E identifies no observations in the sample
note: 1.D#2.E omitted because of collinearity
note: 1.D#3.E omitted because of collinearity

      Source |       SS           df       MS      Number of obs   =        12
-------------+----------------------------------   F(3, 9)         =     10.45
       Model |  2420152.94         3  806717.646   Prob > F        =    0.0027
    Residual |  694464.989         9  77162.7766   R-squared       =    0.7770
-------------+----------------------------------   Adj R-squared   =    0.7027
       Total |  3114617.93        12  259551.494   Root MSE        =    277.78

------------------------------------------------------------------------------
           Y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         1.D |  -412.6576   277.7819    -1.49   0.172    -1041.044    215.7287
             |
           E |
          2  |   609.8941   196.4215     3.11   0.013     165.5579     1054.23
          3  |   1044.798   310.5696     3.36   0.008     342.2409    1747.355
             |
         D#E |
        0 3  |          0  (empty)
        1 1  |          0  (empty)
        1 2  |          0  (omitted)
        1 3  |          0  (omitted)
------------------------------------------------------------------------------

.

[Rich Goldstein]

if you use the "allbase" option in your regression command, you will be shown all terms and will see why Stata is not including certain terms

[Dominique Chaufree]

Thanks a lot for your help!