R users; A question about optimization within R.
I've been using both optim() and nlminb() to estimate parameters and all seems to be working fine. For context (but without getting into specifics - sorry), I'm working with a problem that is known to have correlated parameters, and parameter estimation can be difficult. I have a question on optim() - I'm using method="L-BFGS-B" to accommodate box constraints. For my dataset, I obtain parameter estimates using a few iterations of optim() - iterations in that I'm simply taking the results from a previous optim() call and using these as starting values in the next function call. The final call to optim() returns the following: $par [1] 0.2272361 0.8037642 26.8591998 3.0631280 0.2224566 $value [1] -46.13906 $counts function gradient 4 4 $convergence [1] 0 $message [1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH" $hessian [,1] [,2] [,3] [,4] [,5] [1,] 1.267070e+17 1.012691e+17 1.348054e+15 625551.58724 9.359559e+07 [2,] 1.012691e+17 8.189877e+16 1.144248e+15 569562.44945 8.699072e+07 [3,] 1.348054e+15 1.144248e+15 2.457323e+05 3426.60293 -2.297009e+03 [4,] 6.255516e+05 5.695624e+05 3.426603e+03 99.06880 -6.750806e+01 [5,] 9.359559e+07 8.699072e+07 -2.297009e+03 -67.50806 1.905247e+03 i.e. convergence and message report that things look "ok". However; if I take the hessian and compute eigenvalues and eigenvectors, the result is: $values [1] 2.080357e+17 5.889416e+14 1.907746e+03 9.648828e+01 -1.886641e+13 $vectors [,1] [,2] [,3] [,4] [,5] [1,] 7.797175e-01 6.246383e-01 -5.024932e-09 -2.214316e-10 -4.321721e-02 [2,] 6.260739e-01 -7.768497e-01 5.917821e-09 2.637892e-10 6.734993e-02 [3,] 8.496067e-03 -7.957109e-02 9.710924e-08 4.049691e-09 -9.967930e-01 [4,] 4.058779e-12 -8.828316e-11 3.729724e-02 -9.993042e-01 -4.192523e-10 [5,] 6.125907e-10 -1.547717e-08 -9.993042e-01 -3.729724e-02 -9.626469e-08 Optim() indicates convergence when one of the eigenvalues is negative !?!? Any reason to not be concerned? (Possibly the Hessian is simply computed at the solution and not used to arrive at the estimate?) Thanks in advance for any helpful feedback. B Healey ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
