Re: Effect of FOCE vs FOCE INTER on success of covariance step within a model with additive error
From: "Gastonguay, Marc" marcg@metrumrg.com
Subject: Re: [NMusers] Effect of FOCE vs FOCE INTER on success of covariance step within a model with additive error
Date: Fri, 10 Mar 2006 10:31:57 -0500
Hi, Sameer. These results are a bit puzzling, but I'll offer a possible explanation below. The NONMEM documentation for
INTERACTION states: "The dependence on etas of the model for intra-individual random error is preserved in the
computation of the objective function". In your case there is no ETA-EPS interaction because the individual prediction
is not involved in the calculation of the residual variance, but INTERACTION may still play a small role.
I did investigate a couple of additive residual model examples, and although the starting OFV, min OFV and parameters
were identical (up to the precision reported) under FOCE vs FOCE INT, I did observe that some of the RES and WRES were
different in the 4th decimal place and some parameter gradients near the minimum were different in the second (or higher)
digit when comparing FOCE and FOCE INT. Did you observe similar differences? This could result in the difference you've
seen in the successful calculation of the VAR-COV matrix of the estimates during $COV.
Here's one possible explanation: The residuals in a NONMEM population model are weighted by the square root of the total
variance (inter-individual and intra-individual and inter-occasion, etc.), which is represented by the Individual
Covariance Matrix (C[i]). C[i] is a function of all variability terms; something like
C[i] = G*OMEGA*transpose(G) + H*SIGMA*transpose(H);
where G is the partial derivative matrix w.r.t. ETAs and H is the partial deriv matrix w.r.t. EPS.
Although the intra-individual variance is additive and ETA does not play a role in that portion of C[i], it may be
that INTERACTION imposes a difference in the way that the G matrix is calculated (evaluated at individual ETA, rather than ETA=0).
This discrepancy between FOCE and FOCE INT with additive residual var. is probably most evident when OMEGA is large, relative
to SIGMA. The NONMEM documentation is not clear on this topic, and I'll leave it up to someone with more intimate knowledge
of NONMEM internals to confirm my explanation.
The kind of behavior you've described could also be indicative of differences due to NONMEM bug fixes, hardware/OS, compiler
type, version and/or optimization settings. Were all of these identical in your 2 runs?
Marc
Marc R. Gastonguay, Ph.D.
www.metrumrg.com
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