----- Original Message -----
From: "Cowell, Alexander J." <[email protected]>
To: <[email protected]>
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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