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Re: st: How to save a hessian matrix for post-estimation analysis?


From   Gordon Hughes <G.A.Hughes@ed.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: How to save a hessian matrix for post-estimation analysis?
Date   Thu, 23 Aug 2012 11:19:46 +0100

Sorry about the delay in responding. Unfortunately, the real answer to your question is that it all depends on what you are trying to do. I think that the best advice is to try and remove the source of the degeneracy - i.e. remove collinear variables or whatever. If there is some reason why this can't be done (I can't think of an obvious example), then the generalised inverse is pretty robust so that the non-missing diagonal elements might be used for tests on the relevant coefficients.

I would give one warning. Degeneracy in the variance-covariance matrix is commonly a sign that the maximisation has failed - i.e. the likelihood function does not have a single local maximum and the gradient procedure has headed off to a region that is infeasible or degenerate for some reason. Any inferences based on estimates of this kind are worthless. This brings us back full circle to the question of why you have degenerate variance-covariance matrix.

Gordon Hughes
g.a.hughes@ed.ac.uk

============================

Dear Gordon,

Thanks for the answer. It seems that there is no easy way to use the official command, e.g. "logit", "mprobit", etc., and save the original hessian.

By the way, I wonder that, if the negative hessian is singular or not positive definite, is there any drawback to using the generalised inverse hessian? I know that some standard errors in the output will be labelled with a dot, which means we can't do the statistical tests for those predictors. How about the other standard errors appearing as usual? We can use them to do the test, but will them cause invalid results?

Thanks for the help.

Best Regards,

Chi-lin Tsai


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