# st: Assumptions of unit variance in multivariate probit: Stephen Jenkins?

 From "Stephen P. Jenkins" To Subject st: Assumptions of unit variance in multivariate probit: Stephen Jenkins? Date Fri, 2 Feb 2007 09:22:11 -0000

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Date: Thu, 1 Feb 2007 08:12:31 -0800 (PST)
From: Kam Kup <kamkupan@yahoo.com>
Subject: st: Assumptions of unit variance in multivariate probit:
Stephen Jenkins?

I have a multivariate probit model with one selection
equation and three other outcome variable across time.

That is,
selection equation: y1*=x*b1
if y1*>0 for a given individual, we also observe the
following over three points in time:
z1*=w1*theta z2*=w2*theta z3*=w3*theta

To compute the multivariate normal probabilities, I am
using Stephen Jenkin's excellent mvnp progrma.  My
question is about the restrictions that should be
placed on the 4x4 Cholesky matrix.

The problem: the Cholesky matrix in my case seems to
converge for some specifications and not others.  In
particular, convergence is not achieved if even one
variable is included in both stages, even if there are
several exclusion restrictions.  When the variables
are totally different, the model converges and the
results make sense.

What is apparently happening is that the sum of the
squares of the cholesky elements (other than the
diagonal) sum to more than 1.

Would you suggest using atanh to transform the
elements of the Cholesky matrix, as heckprob.ado does
to the covariance matrix?

Thank you,
Kam
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Kam refers to the code distributed with Stata Journal 6-2 article by
Lorenzo Cappellari and myself: package st0101          accompanying
"Calculation of multivariate normal probabilities by simulation, with
applications to maximum                     simulated likelihood
estimation".  [Preprint version of article available as ISER WP at
http://www.iser.essex.ac.uk/pubs/workpaps/pdf/2006-16.pdf] The main
programs are -_gmvnp()-, an egen function with associated plug-in for
calculating multivariate normal probabilities using the GHK simulator,
and -mdraws- for creating pseudo-random and Halton draw variables.

Your penultimate paragraph suggests that you have not imposed the
appropriate constraints on the elements of the Cholesky matrix.  Look
at the code for the trivariate probit with one selection (p. 178 of SJ
article, and note the lines placing restrictions on scalars `cf22',
`cf33'

Stephen
-------------------------------------------------------------
Professor Stephen P. Jenkins <stephenj@essex.ac.uk>
Institute for Social and Economic Research
University of Essex, Colchester CO4 3SQ, U.K.
Tel: +44 1206 873374.  Fax: +44 1206 873151.
http://www.iser.essex.ac.uk
Survival Analysis using Stata:
http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/