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

[Ricardo Basurto <ricardobasurto@gmail.com>]

Not the best way to start posting to StataList, is it? I am
re-arranging my message hoping that at least that way my question
won't be cut out. (If anyone has suggestions on how to successfully
submit messages from within Gmail, I would appreciate those as well.)

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I am having trouble understanding the difference between a regression
that uses a cross operator (#) and one that uses a cross factorial
operator (##).
For example, below is the output I get from running two different
regressions.  From the log-likelihood ratio, chi2, etc, it seems clear
to me that both commands are fitting the same regression model.  Also,
I can reproduce the second regression by fitting a regression with
dummies for a=1, b=1, and a variable equal to the multiplication of
those two dummies; however, I just can't figure out what exact model
is being fitted in the first regression. Can anyone explain this?

Thank you,

Ricardo

REGRESSION #1:

. logistic y a#b

Logistic regression                             Number of obs   =      19670
                                              LR chi2(3)      =       7.71
                                              Prob > chi2     =     0.0525
Log likelihood = -1473.1898                     Pseudo R2       =     0.0026

----------------------------------------------------------------------------
         y | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Int.]
-----------+----------------------------------------------------------------
       a#b |
      0 1  |   1.567419   .2804138     2.51   0.012     1.1038    2.2256
      1 0  |   1.447424   .2588797     2.07   0.039     1.0194    2.0551
      1 1  |   1.211988   .2246236     1.04   0.300     .84283    1.7428
----------------------------------------------------------------------------


REGRESSION #2

. logistic y a##b

Logistic regression                             Number of obs   =      19670
                                              LR chi2(3)      =       7.71
                                              Prob > chi2     =     0.0525
Log likelihood = -1473.1898                     Pseudo R2       =     0.0026

----------------------------------------------------------------------------
         y | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Int.]
-----------+----------------------------------------------------------------
       1.a |   1.447424   .2588797     2.07   0.039     1.0194    2.0551
       1.b |   1.567419   .2804138     2.51   0.012     1.1038    2.2256
           |
       a#b |
      1 1  |   .5342167   .1302597    -2.57   0.010     .33125    .86152
----------------------------------------------------------------------------
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