Regarding _max_FinalHess


I posted this question yesterday but have not got any response yet. I would appreciate if someone could take the time to answer the question. The question is regarding the _max_FinalHess returned by maxlik.

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.



4 Answers


_max_FinalHess contains the Hessian used in the calculation of the covariance matrix of the parameters.  _max_CovPar determines the type of Covariance Matrix of the Parameters and has nothing to do with _max_FinalHess.   The calculation of the covariance matrix of the parameters is as you describe where the Hessian used in the calculations is stored in _max_FinalHess.


Thanks for your clarification.

But I think you contradict in your answer. _max_CovPar determines how to calculate the covariance matrix of the parameter and I do not think that its right to say that, _max_FinalHess stores the "Hessian" always.

Rather if  _max_CovPar is 1  _max_FinalHess stores Hessian and if _max_CovPar is 2 _max_FinalHess stores the outer product of the gradient or the score. So, there is a definite relationship between the value taken by _max_CovPar and the value stored in _max_FinalHess.

Also, Hessian of a function at convergence is always the Hessian of a function, no matter what you use for the getting the covariance of the parameters.


In looking at the Maxlik source code, it appears that you are correct.  If you select _max_CovPar = 2, the cross-product is returned and not the Hessian.   The current optimization Applications, CMLMT and MaxlikMT, return the cross-product and the Hessian in separate locations, so I was assuming Maxlik did the same.   I apologize for getting that wrong.


No problem at all.

Thanks much for the clarification. I appreciate it.

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