Aah – I see that I misunderstood Santosh’s question. I thought Santosh was asking about reporting standard errors at each iteration step within the estimation algorithm.
Best, Ken From: Leonid Gibiansky <lgibian...@quantpharm.com> Sent: Saturday, July 27, 2024 4:18 PM To: Ken Kowalski <kgkowalsk...@gmail.com> Cc: Santosh <santosh2...@gmail.com>; nmusers <nmusers@globomaxnm.com> Subject: Re: [NMusers] Obtaining RSE% It can be done if you add extra $cov statement after each estimation method record Thank you Leonid On Sat, Jul 27, 2024, 12:47 PM <kgkowalsk...@gmail.com <mailto:kgkowalsk...@gmail.com> > wrote: Dear Santosh, There is a good reason for this. Wald (1943) has shown that the inverse of the Hessian (R matrix) evaluated at the maximum likelihood estimates is a consistent estimator of the covariance matrix. It is based on Wald’s approximation that the likelihood surface locally near the maximum likelihood estimates can be approximated by a quadratic function in the parameters. This theory does not hold for any set of parameter estimates along the algorithm’s search path prior to convergence to the maximum likelihood estimates. Moreover, inverting the Hessian evaluated at an interim step prior to convergence would likely be a poor approximation especially early in the search path where the gradients are large (i.e., large changes in OFV for a given change in the parameters would probably have substantial curvature and not be well approximated by a quadratic model in the parameters). Thus, the COV step in NONMEM is only applied once convergence is obtained during the EST step. Wald, A. “Tests of statistical hypotheses concerning several parameters when the number of observations is large.” Trans. Amer. Math. Soc. 1943;54:426. Best, Ken Kenneth G. Kowalski President Kowalski PMetrics Consulting, LLC Email: kgkowalsk...@gmail.com <mailto:kgkowalsk...@gmail.com> Cell: 248-207-5082 From: owner-nmus...@globomaxnm.com <mailto:owner-nmus...@globomaxnm.com> <owner-nmus...@globomaxnm.com <mailto:owner-nmus...@globomaxnm.com> > On Behalf Of Santosh Sent: Friday, July 26, 2024 3:38 AM To: nmusers@globomaxnm.com <mailto:nmusers@globomaxnm.com> Subject: [NMusers] Obtaining RSE% Dear esteemed experts! When using one or more estimation methods & covariance step in a NONMEM control stream, the resulting ext file contains final estimate (for all estimation steps) & standard error (only for the last estimation step). Is there a way that standard error is generated for every estimation step? TIA Santosh
