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Re: st: Normalization of (standard deviation of) errors in mvprobit


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Normalization of (standard deviation of) errors in mvprobit
Date   Tue, 29 Nov 2011 09:31:42 +0100

On Mon, Nov 28, 2011 at 8:37 PM, saqlain raza wrote:
> Does there exist any command in Stata under -mvprobit- for normalization of (standard deviation of) errors?

-mvprobit- is a user written command, so per the Statalist FAQ you
_must_ say where you got this from. I know several of us have been
pushing you again and again to read the FAQ, and it may feel we are
mean to you, but this is really in your own interest: The FAQ contains
advise on how to ask question that can be answered. For example, the
reason for requiring you to say where you got your version of user
written software from is that there are usually multiple version
floating around in cyber space, and it obviously helps if we are
talking about the same version. So I ask you again to please read the
FAQ. A link to the FAQ can be found at the bottom of this (and any
other) post.

There is no need to normalize, as the results are already normalized
such that the standard deviation of the errors all equal 1. The fact
that Stata (or any other piece of software) gives you a result is
evidence that normalization has taken place, as the model is not
identified without it. Than it should be in the documentation of your
piece of software how the normalization was done. In case of
-mvprobit- this is done in the Stata Journal article that introduces
this program (Cappellari and Jenkins 2003). On page 279 it says:

"e_{im}, m = 1, . . . ,M are error terms distributed as multivariate
normal, each with a mean of zero, and variance-covariance matrix V ,
where V has values of 1 on the leading diagonal and correlations
rho_{jk} = rho_{kj} as off-diagonal elements."

e_{im} are the error terms, the leading diagonal of the
variance-covariance matrix contains the variances, and if the
variances are constrained to be 1 than the standard deviations are
also 1, as sqrt(1)=1.

-- Maarten

L. Cappellari and S.P. Jenkins (2003) "Multivariate probit regression
using simulated maximum likelihood" The Stata Journal, 3(3): 278-294.
<http://www.stata-journal.com/article.html?article=st0045>

--------------------------
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
Germany

http://www.maartenbuis.nl
--------------------------
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