st: multinomial logit using -gllamm-

[Jeph Herrin <stata@spandrel.net>]

This question may be better directed to the authors of -gllamm-, but I thought I should
start with the list before bothering them.

I want to estimate random effects multinomial logit models, and one solution in Stata
is to use -gllamm-. However, there the help file and the -gllamm- manual differ in
describing how to do this, and the results differ.

In the help file, I would estimate an empty model like this:

  gllamm depvar , i(groupvar) link(mlogit) family(binomial)

and this model does in fact converge, producing a single variance for a
single random effect. However, since I have three intercepts (-depvar-
takes 4 values), I went to the -gllamm- manual to understand why, and
found there that this model should be estimated by expanding the data to
4 obs per original measurement, with a new variable -alt- indicating which
obs is the actual outcome, then

 gllamm alt , expand(obsid depvar m) i(groupvar) link(mlogit) fam(binomial) ///
             nrf(3) eqs(a1 a2 a3)

this model also converges, and produces 3 random effect variances, one for
each intercept, which makes sense.

However, the first model produces intercepts that look very much like I would
expect from -mlogit-, whereas the intercepts from the second model are of different
magnitudes and in one case direction, so it seems very suspect.

My question: what is the first model estimating for a random variance, and why does
the second one produce such different results for the fixed effects?

thanks,
Jeph

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