How is the covariance matrix calculated in the MAXLIK?

Hi I have a question about how the covariance is estimated in MAXLIK. I have calculated the hessian by :

vread(_max_Diagnostic,"hessian");

which gives me:

0.098854902 -0.044789408 0.21265749 -0.098746774
-0.044789408 0.097216091 -0.097149608 0.21118073
0.21265749 -0.097149608 0.66755658 -0.33440959
-0.098746774 0.21118073 -0.33440959 0.66921942

The inverse of this matrix is:

45.059278 24.224743 -15.109826 -8.5460929
24.224743 45.880519 -8.6733621 -15.237785
-15.109826 -8.6733621 7.0742131 4.0424484
-8.5460929 -15.237785 4.0424484 7.0617510

However when I use cov, I get:

 0.057190334  0.030671550 -0.018652539 -0.010151653  . . . . .
 0.030671550  0.057763764 -0.010134082 -0.019056447  . . . . .
-0.018652539 -0.010134082  0.0081342988 0.0043459482 . . . . .
-0.010151653 -0.019056447  0.0043459482 0.0083873686 . . . . .
            .           .            .             . . . . . .
            .           .            .             . . . . . .
            .           .            .             . . . . . .
            .           .            .             . . . . . .
            .           .            .             . . . . . .

which is different from the inverse of the Hessian matrix.

I have 1000 observations, _max_CovPar is set to 1, and the gradient is calculated numerically. This is the gradient:

-0.00033315205
-0.00010445805
-0.00079539564
-0.00014439259

4 Answers



0



accepted

The version of the Hessian retrieved in _max_diagnostic is an intermediary calculation of the Hessian in the iterations.  It is not the final one.  The covariance matrix returned in cov is computed after convergence and will differ from the ones computed during the iterations.

If you are interested in the Hessian computed after convergence, you will find that in the global, _max_FinalHess.



0



The covariance matrix in the cov return argument takes into account the number of observations.

cov = {
 0.057190334  0.030671550 -0.018652539 -0.010151653,
 0.030671550  0.057763764 -0.010134082 -0.019056447,
-0.018652539 -0.010134082  0.0081342988 0.0043459482,
-0.010151653 -0.019056447  0.0043459482 0.0083873686 };

 
Here is invpd(cov)/1000 and you'll notice that it closely resembles the Hessian retrieved in _max_diagnostic.

 0.0908 -0.0441  0.2049 -0.0964
-0.0441  0.0906 -0.0964  0.2024
 0.2049 -0.0964  0.6321 -0.2985
-0.0964  0.2024 -0.2985  0.6170

 

Here is 1000*cov and you'll notice that it resembles the inverse of the Hessian in _max_diagnostic.

 57.1903  30.6715 -18.6525 -10.1517
 30.6715  57.7638 -10.1341 -19.0564
-18.6525 -10.1341   8.1343   4.3459
-10.1517 -19.0564   4.3459   8.3874



0



Thank you for the response. However, still there is some discrepancy between  the inverse of hessian and 1000*cov :

This is inverse of the Hessian

45.059278 24.224743 -15.109826 -8.5460929
24.224743 45.880519 -8.6733621 -15.237785
-15.109826 -8.6733621 7.0742131 4.0424484
-8.5460929 -15.237785 4.0424484 7.0617510

and  this is 1000*cov :

 57.1903  30.6715 -18.6525 -10.1517
 30.6715  57.7638 -10.1341 -19.0564
-18.6525 -10.1341   8.1343   4.3459
-10.1517 -19.0564   4.3459   8.3874

Is there anything else that is factored in calculating cov?

 



0



Thank you very much. Now it makes sense.

 

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