From: "Stephen Duffull" <>
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.


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






Date: Thu, 18 Nov 1999 13:13:50 -0800
From: Lewis Sheiner <>
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 ...
Lewis B Sheiner Professor, Lab. Med., Biopharmaceut. Sci, Med.
Box 0626 - UCSF 415-476-1965 (voice)
San Francisco, CA 415-476-2796 (fax)





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

A few remarks from Stuart Beal ...
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