[Limdep Nlogit List] Ask for help on Probit estimation results

[William Greene]

Lixian Qian.  A number of restrictions on the covariance matrix are needed
for
identification of the multivariate probit model.  There are many ways to
impose the
restrictions.  Sufficient restrictions are (1) the last row equals the last
row of the
identity matrix, plus (b), one more of the diagonal elements is fixed at
1.0. That
would leave one free covariance and one free scale parameter.
That is what you see for your 3x3 problem.  There are 6 parameters in the
covariance matrix.  Restriction (a) fixes 3 of them.  Restriction (b) fixes
one
more.
(Note, if there are two choices instead of three, there are no free
parameters.)
Note, because these are identification restrictions, the other model
estimates are
invariant to the form of the normalization.)
Your question mentions a different set of reported results.  The parameters
labeled
c(...) sound like the elements of the Cholesky matrix that are used to
compute the
covariance matrix.  In general, R = CC' where C is lower triangular. C is
what
is actually estimated - R is computed using the estimated C.
Regards
William Greene

On Wed, Feb 28, 2024 at 10:38 PM Lixian Qian <Lixian.Qian at xjtlu.edu.cn>
wrote:

> Hello,
>
> We are estimating a Multinomial Probit model.
> Different from the example in the NLogit handbook, our results also
> include a few more estimated parameters in the section of "correlations in
> the Normal Distribution".
> Suppose we have three alternatives, A, B, and C.
> These new parameters are named as c[A], c[B] and c[C], and cA,B; cA,C;
> cB,C. Specifically, only c[A] and c[B] have estimated parameters while
> others have fixed parameters.
>
> We didn't find such items in the Probit example of Nlogit Handbook [p.,
> N487]. Can anyone please explain what they are?
>
> Many thanks.
>
>
> Best Regards,
> Lixian
>
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-- 
William Greene
Department of Economics, emeritus
Stern School of Business, New York University
URL: https://url.au.m.mimecastprotect.com/s/alNIC4QOPEizD8KQ3sOUfzm?domain=people.stern.nyu.edu
Email: wgreene at stern.nyu.edu
Editor in Chief: Foundations and Trends in Econometrics
Associate Editor: Economics Letters
Associate Editor: Journal of Business and Economic Statistics