[Limdep Nlogit List] Problems when Estimating Multivariate Probit Model

[William Greene]

Professor Savilainen. The model you have listed below is not a multivariate probit 
model. An MVP model has only "X" variables on the RHS.  The simultaneous equations
model you have written below is not identified - this is a longstanding
problem.  This means it is not estimable.  Sometimes the optimizer can compute
what look like estimates, but they are not meaningful.  Authors who have written 
on this identification issue are Amemiya in several papers in the late 1970s and
Maddala in his famous 1983 book on limited and qualitatie dependent variables.
   If the model is recursive - that is each equation can be written
with, on its RHS only X variables and Y variables from earlier equations, 
then the model does become identifiable and estimable.  Your model does not
meet that criterion.
The error 130 is occurring when at a particular set of parameter estimates
during iterations, the number of observations with joint probability that
enters the likelihood function greater than 10^(-38) (i.e., greater than
zero) is less than the number of parameters.  This is probably happening 
because of the problem noted above.
/B. Greene



----- Original Message -----
From: "Peter Tarmo Savolainen" <bb2725 at wayne.edu>
To: limdep at limdep.itls.usyd.edu.au
Sent: Tuesday, October 12, 2010 2:09:24 PM GMT -05:00 US/Canada Eastern
Subject: [Limdep Nlogit List] Problems when Estimating Multivariate Probit Model

Hello all,

I am trying to estimate a multivariate probit model for six interrelated binary outcomes.  My model has been structured as follows:

MVPROBIT;
LHS = Y1,Y2,Y3,Y4,Y5,Y6;
EQ1 = X1,Y2,Y3,Y4,Y5,Y6;
EQ2 = X2,Y4;
EQ3 = X3,Y6;
EQ4 = X4,Y2;
EQ5 = X5,Y3,Y6;
EQ6 = X6,Y3;
PTS = 50$

X1 through X6 correspond to vectors of independent variables (the specific variables included in X differ among the six models).  When running the model in NLOGIT, I receive the following error messages:

"Error   130: Models - Regression; insufficient degrees of freedom.
Line search does not improve fn. Exit iterations. Status=3
Check derivatives (with ;OUTPUT=3). This may be a solution
if several iterations have been computed, not if only one.
Error   806: (The log likelihood is flat at the current estimates.)"

I am particularly concerned with Error 130, which is reported five times in a row.  From the structure presented above, does it appear that I have over-specified my model?  Is there something else that leads to this particular error message?  I did not run into any issues previously when dealing with a smaller number of outcomes and fewer simulations points.  My dataset includes 4,962 observations and the less-frequent of the 6 outcomes occur slightly over 100 times.  Any insight would be very much appreciated.

Sincerely,
Peter

---
Peter T. Savolainen, Ph.D., P.E.
Assistant Professor
Department of Civil and Environmental Engineering
Wayne State University-Transportation Research Group
5050 Anthony Wayne Drive, EDC 0504.01
Detroit, MI 48202
Phone: (313) 577-9950
Fax: (313) 577-8126
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