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?
Your Answer
4 Answers
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.
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
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?