[R-sig-ME] Interpretation of heteroscedastic structures for the within group error

[Christos Argyropoulos]

Hi, 
I apologise if the question is stupid, but I was wondering about the proper interpretation of the ratio of variances reported by heteroscedastic structures (varIdent).
Could one (within reason) interpret them as the intrinsic variability of the processes generating the data ? Stated otherwise, can one view Mixed Models as a generative 
model?

The background of my problem is the following:
I have data regarding mood, daytime performance and quality of sleep assessed sequentially over 14 days in three (unbalanced) groups of patients under different non-psychiatric treatments.
When the data are examined with a "population averaged" method such as a GEE or GLS there is evidence that the standard deviation of the repeated measures differ in these groups.
Since this relationship between standard deviations in the three groups could be due to the unbalanced nature of the data (different number of patients in each of the three groups) , I would like to explore
it further with a LMM. The call to lme looks like this:

lme(fixed=response~TREATMENT+ContCovars+OtherFactors,random=pdDiag(~1+ContCovar+OtherFactors|ID,weights=varIdent(form=~1|TREATMENT)) 

(I tried to put TREATMENT in the pdDiag wrapper but lme complained about positive-definitess of the covariate matrix, so I used the varIdent construct instead)

Even though I do get a reasonable output from LME  i.e. the relation of the variances reported by the intervals function is in line with the understanding of the biology/clinical problem I'm still worried about the interpretation of these variances. Can one interpet these variances as estimates of the intrinsic variability in the three outcomes under the treatment assignment?

Christos Argyropoulos
University of Pittsburgh
 
PS There is very little evidence of a consistent cycling behaviour, linear or general trend in these longitudinal data and thus I do not have to use the time series correlation structures for the analyses.

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