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

 From Kam Kup To statalist@hsphsun2.harvard.edu Subject Re: st: Assumptions of unit variance in multivariate probit: Stephen Jenkins? Date Fri, 2 Feb 2007 09:00:53 -0800 (PST)

```Professor Jenkins,

Thanks for your response.  In fact, I did place the
same restrictions on the diagonal elements of the
matrices.  However, when the independent variables in
the selection and outcome equations overlap by more
than one variable (as the theory suggests), Stata
estimates the sum of the non-diagonal elements in
certain rows to be more than one, thus violating the
restriction.

Heckprob  estimates the selection and first outcome
equation just fine.

My questions are:

1. I am unclear on which elements of the cholesky
Matrix need to be restricted, since, if an observation
is selected, I have multiple observations on the
outcome variable over time.  (I'm using d0 as a
result.)

For example, in your final panel example in that
paper, you do not impose any restrictions on the
diagonal elements except for the first one.

I am unclear on why this is different from the earlier
multivariate probit cases.  Perhaps this would help me
understand which restrictions I should place.

2. Heckprob explicitly uses atanh(rho) in it's the
likelihood evaluator to ensure that constrain rho to
the appropriate interval.  Would you recommend doing
htis?  (I notice that you did not use this in your
programs, perhaps to avoid the issues with calculating
confidence intervals.)

Thanks again,
Kam

--- "Stephen P. Jenkins" <stephenj@essex.ac.uk> wrote:

>
=======================================================
>
> 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
>
==========================================================
>
> 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/
>
> http://ideas.repec.org/e/pje7.html
>
>
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