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[NMusers] RE: Standard errors of estimates for strictly positive parameters

From: Bob Leary <Bob.Leary_at_certara.com>
Date: Thu, 12 Feb 2015 14:04:02 +0000

Dear Aziz -
The approximate likelihood methods in NONMEM such as FO, FOCE,and LAPLACE =
 optimize an objective function than is parameterized internally
by the Cholesky factor L of Omega, regardless of whether the matrix is diag=
onal (the EM -based methods do something considerably different and work di=
rectly with Omega rather than
the Cholesky factor.)
 
Thus for the approximate likelihood methods, the SE's computed internally b=
y $COV from the Hessian or Sandwich or Fisher score methods
are first computed with respect to these Cholesky parameters , and then the=
 corresponding SE's of the full Omega=LL' are computed by a 'propagation =
of errors' approach
which skews the results, particularly if the SE's are large. Thus in a sen=
se regarding your dilemma about whether Model 1 or Model 2 is better with r=
espect to applicability of $COV results, one answer is that both are fundam=
entally distorted by the propagation of errors method with respect to the =
Omega elements.

But regarding your fundamental question 'can we trust the output of $COV '=
- all of this makes very little difference. Standard errors computed by $C=
OV are inherently dubious - the applicability of the usual asymptotic argum=
ents is very questionable for the types/sizes of data sets we often deal wi=
th.
As Lewis Sheiner used to say of these results, 'they are not worth the elec=
trons used to compute them'. They are the best we can do for the level o=
f computational investment put into them -
If you want something better, try a bootstrap or profiling method.



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Received on Thu Feb 12 2015 - 09:04:02 EST

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