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Re: st: [multivariate ordered probit models in Stata]


From   Joseph Coveney <jcoveney@bigplanet.com>
To   Statalist <statalist@hsphsun2.harvard.edu>
Subject   Re: st: [multivariate ordered probit models in Stata]
Date   Sat, 22 May 2004 13:27:18 +0900

Mouratidis Kostas wrote:

Dear all,

I want to estimate a Mutivariate ordered probit model. The ado program written
from {HYPERLINK "/RAS/pca117.htm"}Lorenzo Cappellari and {HYPERLINK 
"/RAS/pje7.htm"}Stephen Jenkins allow you to estimate a
mutivariate binary probit models. So Has any body extent their program
from binary to ordered probit model?

-------------------------------------------------------------------------------

I believe that it might be doable using -gllamm-.  

It's my understanding that a multivariate binary probit or logit model is 
fitted in -gllamm- by (i) generating indicator (dummy) variables to identify 
the multiple dependent variables, (ii) creating equations corresponding to each 
of the dummy variables for use in defining random effects in -gllamm-'s -nrf() 
eqs()- options, and (iii) using the dummy variables also as the predictors 
(independent variables) in a no-constant model.  This sets up the indicator for 
each response variable to be included in both fixed- and random-effect design 
matrixes, which in turn allows a general (unstructured) variance-covariance 
matrix of the latent variables (behind the manifest categories) to be fitted as 
for a multivariate model.

But ordered categorical models are parameterized in Stata with the intercept 
assumed to be zero in order to identify the model; the first cut-point takes 
the place normally held by the intercept in other models, such as binary probit 
or logistic, which do the converse, i.e., hold the threshold at zero and fit 
the intercept.  -gllamm- follows this convention, so the -nocons- option is not 
permitted in -gllamm- for the ordered-probit or ordered-logit link.  It might 
be possible, i.e., legitimate, to use -constraint define- to fix the first cut-
point at zero in order to identify the model (as is done normally behind the 
scenes for -logit- or -probit-), and then to proceed with -gllamm- analogously 
as for multivariate binary probit or logit models as described above. (Look at 
the discussion earlier this month on Statalist in the thread "bivariate random 
effects meta-analysis of diagnostic test" for an example of fitting a 
multivariate logistic model with -gllamm-.)

With more than a few dependent variables, fitting a multivariate model with 
-gllamm- can be time-consuming with a dozen or more integration points and with 
adaptive quadrature.  

In my experience, ordered categorical models are sometimes difficult to fit 
(attain convergence); those with random effects, e.g., -reoprob-, -gllamm-, are 
even more often so.  Depending upon your scientific objective, for example, if 
it's to test a hypothesis of group differences and not to fit the completely 
specified multivariate ordered categorical model, then -oprobit , score()- 
coupled with -estimates store- and -suest , cluster()- is a faster alternative 
to -gllamm-.

Joseph Coveney
 

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