Re: Centering (was Re: Missing covariates)

From: Nick Holford <n.holford@auckland.ac.nz> Subject: Re: Centering (was Re: Missing covariates) Date: Wed, 04 Jul 2001 16:52:05 +1200 Lewis, I asked earlier in this thread if centering was expected to change precision or bias. The answer from you ( http://www.cognigencorp.com/nonmem/nm/99mar021999.html) and from Ken Kowalski was that centering would not affect the estimates (i.e. no bias) if a local minimum was avoided. I am afraid I mistakenly inferred that you also meant that precision (standard error) was also unaffected because that is an issue relating to Joga Gobburu's assertion that statistical inference is not altered by centering and which prompted my question. Your reductio ad absurdam example does illustrate that the SE of the estimate will depend on centering. So now that means that Joga's assertion that "Centering is done for convenience, it does not alter statistical inference" needs to be qualified. I would accept that if the same objective function minimum is reached then model building inferences would not be affected but inferences about the parameters e.g. credible intervals, would be. There is also the issue that I was hoping that Alan Xiao might throw some light on i.e. the empirical evidence (e.g. using NONMEM) for differences in the standard errors depending on the use of centering or not. There is clearly room for a difference between theory and experiment when one has to rely on NONMEM to obtain estimates. It would be of interest to know the size of the standard error as well as the magnitude of parameter bias and or false acceptance rate of one parameterization being superior to another with a practical example. Finally, let me repeat your previous advice contained in the link above: "Bottom line: There is nothing to lose with centering, and much to gain. Hence, ALWAYS do it! " Nick -- Nick Holford, Divn Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556 http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm