Re: Re-re-post: Stata 11 - Factor variables in a regression command

[Richard Williams <Williams.NDA@comcast.net>]

At 01:42 AM 5/1/2010, Michael Norman Mitchell wrote:
> Dear Ricardo
>
>   The command
>
> . logistic y a#b
>
>    includes just the interaction of "a by b", and does not include 
> the main effect of a, nor the main effect of b. By contrast, the command
>
> . logistic y a##b
>
>   includes the main effect of a, the main effect of b, as well as 
> the a by b interaction. It is equivalent to typing
>
> . logistic y a#b a b

Incidentally, if the variables are continuous, rather than 
categorical, Mike's description is right, i.e. c.a#c.b only enters 
the interaction term of a*b and not the lower level effects.  But by 
default, Stata assumes the crossed variables are categorical unless 
you indicate otherwise, and the # and ## notations produce different 
parameterizations of the same model.

These factor variables are nice but make sure you understand what 
parameterization you are getting and how to interpret it!!! 
Personally I think there is much to be said for explicitly including 
the main effects so I can make sure they are there and to make my 
commands easier to read, i.e. I prefer

logit y i.a i.b a#b

over

logit y a##b

The following illustrates how the c. notation changes things.  In the 
first syntax, you only get the interaction term, in the other two you 
get both the interaction and the main effects.

. use "http://www.indiana.edu/~jslsoc/stata/spex_data/ordwarm2.dta";, clear
(77 & 89 General Social Survey)

. logit  warmlt2 c.yr89#c.male, nolog

Logistic regression                               Number of obs   =       2293
                                                  LR chi2(1)      =       7.81
                                                  Prob > chi2     =     0.0052
Log likelihood = -880.00359                       Pseudo R2       =     0.0044

------------------------------------------------------------------------------
     warmlt2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      c.yr89#|
      c.male |   -.497305    .186906    -2.66   0.008     -.863634    -.130976
             |
       _cons |  -1.829973   .0666787   -27.44   0.000    -1.960661   -1.699285
------------------------------------------------------------------------------

. logit  warmlt2 c.yr89##c.male, nolog

Logistic regression                               Number of obs   =       2293
                                                  LR chi2(3)      =      64.74
                                                  Prob > chi2     =     0.0000
Log likelihood = -851.54241                       Pseudo R2       =     0.0366

------------------------------------------------------------------------------
     warmlt2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        yr89 |  -1.295833    .229115    -5.66   0.000     -1.74489   -.8467762
        male |   .1816812   .1431068     1.27   0.204     -.098803    .4621655
             |
      c.yr89#|
      c.male |   .4542502   .3050139     1.49   0.136    -.1435661    1.052066
             |
       _cons |  -1.667376   .1021154   -16.33   0.000    -1.867518   -1.467233
------------------------------------------------------------------------------

. logit  warmlt2 yr89 male c.yr89#c.male, nolog

Logistic regression                               Number of obs   =       2293
                                                  LR chi2(3)      =      64.74
                                                  Prob > chi2     =     0.0000
Log likelihood = -851.54241                       Pseudo R2       =     0.0366

------------------------------------------------------------------------------
     warmlt2 |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        yr89 |  -1.295833    .229115    -5.66   0.000     -1.74489   -.8467762
        male |   .1816812   .1431068     1.27   0.204     -.098803    .4621655
             |
      c.yr89#|
      c.male |   .4542502   .3050139     1.49   0.136    -.1435661    1.052066
             |
       _cons |  -1.667376   .1021154   -16.33   0.000    -1.867518   -1.467233
------------------------------------------------------------------------------

.



-------------------------------------------
Richard Williams, Notre Dame Dept of Sociology
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EMAIL:  Richard.A.Williams.5@ND.Edu
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