Continuing the thread, Thomas Klausch <[email protected]> points out
slight differences between -xtlogit- and -xtmelogit- on equivalent models,
even when both commands converge to a result:
> Anyways, your guess may be right, because I just included a covariate and
> then -xtmelogit- estimates the model without error. However, the models
> estimated by -xtlogit- and -xtmelogit- still are not equivalent. That is the
> log likelihood in my example is
> xtlogit: approx 15016
> xtmelogit: approx 15009
> and also coefficients deviate by some hundredth...
> Do you know why this is? I thought both programs use conditional ML and
> Gauss-Hermit quadrature optimization. Or is there any difference?
Both commands use adaptive Gauss-Hermite quadrature to approximate the
log likelihood. However, they differ in the default way in which they adapt
the quadrature. By default, -xtlogit- adapts according to posterior means and
variances, whereas -xtmelogit- adapts according to posterior modes and
curvatures. In most cases, the resulting difference is slight and akin to
what Thomas is observing.
-xtmelogit-'s method of adapting quadrature is the only one available to that
command because it most easily generalizes to multiple levels of nested
effects. -xtlogit-, however, supports three quadrature methods:
1. Adaptive with means and variances, option -intmethod(mvaghermite)-, the
default.
2. Adaptive with modes and curvatures, option -intmethod(aghermite)-. Use
this option to most closely duplicate results from -xtmelogit-.
3. Non-adaptive quadrature, option -intmethod(ghermite)-. Use this option
only as a reference; it is not as accurate as the others.
My guess is that if Thomas uses -xtlogit ..., intmethod(aghermite)-, his
results will fall closer in line to those from -xtmelogit-. Even then, he may
still see some slight differences, mostly due to differences in how each
command takes derivatives of the log-likelihood. -xtlogit- does this
analytically; -xtmelogit- does this numerically, again to better generalize to
multiple levels of nested effects.
--Bobby
[email protected]
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