Hello,
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.
Thanks
Annesha
4 Answers
0
_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.
0
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.
0
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.
Your Answer
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.