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st: Re: Which random effect estimators use Gauss-Hermite


From   "Scott Merryman" <smerryman@kc.rr.com>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Re: Which random effect estimators use Gauss-Hermite
Date   Sat, 26 Apr 2003 16:43:45 -0500

----- Original Message -----
From: "Cowell, Alexander J." <cowell@rti.org>
To: <statalist@hsphsun2.harvard.edu>
Sent: Friday, April 25, 2003 11:59 AM
Subject: st: Which random effect estimators use Gauss-Hermite


> Hi there
>
> The manual points out that after running xtlogit with random effects, one
> should use quadchck (though I don't see why this isn't just the default in
> xtlogit).  This is because the quadrature method of computing the log
> likelihood and the derivatives may give unstable estimates.  This makes
> sense.
>
> Rather cryptically the manual (version 7.0) also says in the 'quadchck'
> entry "Some random-effects estimators in Stata use Gauss-Hermite
> quadrature...).
>
> My questions are:
> 1.  Which estimators do and which don't use G-H quadrature?

At least in Stata 8 -quadchk- checks the quadrature approximation used in
the random-effects estimators of the following commands:
        xtcloglog
        xtintreg
        xtlogit
        xtpoisson with the normal option
        xtprobit
        xttobit

These estimators all assume a normal distribution for the random effect.

> 2.  Or, if #1 is too much to answer, what does xtnbreg use?
Gaussian quadrature is not used to maximize the log-likelihood but to
approximate integrals that do not exist in closed form.   Stata uses the
Newton-Raphson algorithm to maximize the likelihood function (or if
the -difficult- option is employed then steepest ascent is used in the
problem subspaces). For -xtnbreg , re-  with random effect d(i), it is
assumed that 1(1+d(i)) is distributed as a Beta distribution.  I believe the
integral has a closed form so quadrature approximation is not necessary.

Scott



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