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From   Stas Kolenikov <>
Subject   Re: st: GLLAMM versus XTMEPOISSON
Date   Tue, 12 Feb 2013 12:41:41 -0600


You're probably right (about me mixing up things) -- the best advice
would be to look up GLLAMM manuals, of course. I know for sure that
GLLAMM uses Cholesky parameterization somewhere; and I am sure that
Sophia does the back-transformations properly when presenting the
results. So an easy check would be to

nlcom ( exp(_b[lns1_1_1:_cons]) ) ( exp( _b[lns1_1_2:_cons]) )

and see if they agree with the results printed out. If both do, then
that's the parameterization of the whole covariance matrix. If the
first one does, but the second one doesn't, then it is the
parameterization of Cholesky transform.

-- Stas Kolenikov, PhD, PStat (SSC)  ::
-- Senior Survey Statistician, Abt SRBI  ::  work email kolenikovs at
srbi dot com
-- Opinions stated in this email are mine only, and do not reflect the
position of my employer

On Tue, Feb 12, 2013 at 11:54 AM, JVerkuilen (Gmail)
<> wrote:
> On Tue, Feb 12, 2013 at 12:03 PM, Stas Kolenikov <> wrote:
>> Ana,
>> these are the parameters of the Cholesky decomposition of the
>> variance-covariance matrix. The lns are the natural logs of the
>> diagonal elements, and atr is the (hyperbolic?) arctan of the
>> correlation.
> Stas, I think you might be mixing up two different paramaterizations
> for the covariance matrix. The Cholesky is one (essentially
> decomposing the covariance matrix C = TT', where T is a lower
> triangular matrix), and the logarithmic is another, where the
> variances and covariances are expressed as exponential terms with
> estimation on the logs and correlations are Fisher Z (inverse
> hyperbolic tangent), but otherwise spot on advice.
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