Re: Reporting Modeling Results

Hi Jeroen, I cannot see any extra covariance introduced by scaling by a fixed numbers. Moreover, I even not sure that the term "centered" is applicable to this model. It came from the linear model where the model Y=ax+b was called centered if presented in the form Y=a1*(x-meanX)+b1 (here and below a and b are parameters, THETAs, while x is random) Indeed, it is more stable in the second, centered form. If you assume that a1 and b1 are normally distributed without correlation, then a = a1 and b = b1-a1*meanX are correlated, and correlation is higher for large meanX. In this regard, the model that consist of several equations of the type Y=b*x^0.75 is equivalent to the model with Y=b'*(x/10)^0.75, no extra correlations added. However, the model Y=b*x^a is more like the linear model because it can be presented in the log scale as log(Y)=a*log(x) + log(b) and then it is better be centered: log(Y)= a1*(log(x)-mean(log(x))) + log(b1) or equivalently Y=b1*(x/x0)^a1 where x0 is geometric mean of x. Thus, these two (examples only!) models need to be centered: CL=THETA()+(WT-70)*THETA() or CL=THETA()*(WT/70)^THETA() but this one can be used in any shape and form CL=THETA()*(WT/10)^0.75 = (THETA()/10^0.75) WT^0.75 =~ THETA() WT^0.75 This is just a scheme, not exact derivation/proof, but the bottom line is that scaling by a constant should not influence the standard errors, there should be another reason (may be, just insufficient sample size of the bootstrap process? or bounds on the parameters?) for the discrepancy. May be we need to stratify it into more than two age groups, to guarantee sufficient coverage of the entire age range of interest in each and every bootstrap set. Leonid Elassaiss - Schaap, J. (Jeroen) wrote: > Hi Leonid, > > The aspect of the results that John describes as being dependent on > scaling are the (bootstrap) confidence intervals, not the parameter > estimates. I actually agree with John's original statements about not > being surprised by the inflated standard errors when the model is not > centered. Removal of normalization induces covariance in the estimation > of affected parameters. This covariance naturally leeds to inflated > standard errors (w/o bootstrapping). And as we all know, high > correlation between parameters can result in matrix singularity and > consequently failing covariance steps, consistent with John's > statements. > > Best regards, > Jeroen > > J. Elassaiss-Schaap > Scientist PK/PD > Organon NV > PO Box 20, 5340 BH Oss, Netherlands > Phone: + 31 412 66 9320 > Fax: + 31 412 66 2506 > > e-mail: [EMAIL PROTECTED] >