Regarding Hessian


I am having trouble figuring out which global holds the Hessian (the information matrix) while estimating a model using maxlik.

As far I can figure out from the documentation _max_HessCov  should hold the matrix, but it seems that _max_HessCov returns a scalar, while it should return a KxK matrix.

Please let me know if I am missing something here.

Thanks and Regards



2 Answers


First, _max_covPar must equal 3 and then _max_HessCov will contain the covariance matrix of the parameters, not the Hessian.  If you want the Hessian it will be stored in _max_FinalHess.

If _max_CovPar = 3, and _max_HessCov is a scalar missing value, then the Hessian failed to invert indicating a linear dependency in the model.   To diagnose this problem check the eigenvalues of the Hessian stored in _max_FinalHess.  The Hessian must be positive definite, i.e., no negative eigenvalues.  If there are eigenvalues equal to or nearly equal to zero, then it is singular and you have a linear dependency.  To analysis this see the final section in the article, Optimization with the Quasi-Newton Method.




Thanks for your answer.

I have couple more questions here then.

1. Does _max_FinalHess varies depending on what value I specify for _max_CovPar? It believe the answer is yes.

2. If yes then what are the three different matrices supplied by _max_FinalHess for

_max_CovPar = 1, _max_CovPar = 2, and _max_CovPar = 3.

I understand that _max_CovPar = 1 calculates covariance of the parameters by inverse of hessian, _max_CovPar = 2 calculates covariance of the parameters

by outer product of the score and  _max_CovPar = 3 calculates covariance of the parameters by Hessian_inv*outer_product*Hessian_inv.

I look forward to your response.



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