From: "Stephen Duffull" <sduffull@fs1.pa.man.ac.uk>
Subject: Cross product matrix
Date: Thu, 18 Nov 1999 11:37:59 -0000

Hi All

In fear of changing the topic. I have a fairly specific question about the cross product matrix (R^(-1)SR^(-1)) used as the source of the asymptotic standard errors. The R and S matrices seem straightforward - but I do not (yet) understand the implied intricacies of the cross product matrix. Part II of the guide says "When the normality assumption is not made, the [cross product matrix] estimates the true covariance matrix". Is there a reference that someone could point me to so that I can read about this? (I have read part IV of the guide without further enlightenment.)

I ask this because on occasion when the cross product matrix is not available due to difficulties in its computation then the S matrix may offer a conservative guide to the SEs (since this matrix is almost always invertible). However I need to understand the difference between the assumptions in the output of S versus R^(-1)SR^(-1) - indeed it would also help when comparing matrices gained from theoretical approaches to approximation of the information matrix with those of NONMEM.

Regards

Steve
=====================
Stephen Duffull
School of Pharmacy
University of Manchester
Manchester, M13 9PL, UK
Ph +44 161 275 2355
Fax +44 161 275 2396

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Date: Thu, 18 Nov 1999 13:13:50 -0800
From: Lewis Sheiner <lewis@c255.ucsf.edu>
Subject: Re: Cross product matrix

I think Davidian & Giltinan discuss the "sandwich" estimate of covar& perhaps provide references ... this is old stuff, but I admit that I don't recall where it comes from ...
LBS.
--
Lewis B Sheiner Professor, Lab. Med., Biopharmaceut. Sci, Med.
Box 0626 - UCSF 415-476-1965 (voice)
San Francisco, CA 415-476-2796 (fax)
94143 lewis@c255.ucsf.edu

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Date: Mon, 22 Nov 1999 14:25:29 -0800 (PST)
From: ABoeckmann <alison@c255.ucsf.edu>
Subject: Re: Cross product matrix

A few remarks from Stuart Beal ...
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In reference to paragraph 1 of Steve's note:

See NONMEM References, Methodological, Item 2.

In reference to paragraph 2 of Steve's note:

It is not always the case that the S matrix is invertible. When it is invertible, and when the R matrix is also computable and invertible, it does not follow that the SE using one of the two methods is related to the SE using the other method. If the R matrix is not invertible, one better stop and ask why this is, rather than plow ahead and compute the inverse of S.

Stu Beal