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


From   Richard Williams <Williams.NDA@comcast.net>
To   statalist@hsphsun2.harvard.edu
Subject   Re: Re-re-post: Stata 11 - Factor variables in a regression command
Date   Sat, 01 May 2010 11:20:05 -0500

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
OFFICE: (574)631-6668, (574)631-6463
HOME:   (574)289-5227
EMAIL:  Richard.A.Williams.5@ND.Edu
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