[R-sig-ME] : estimating AR1 parameters of level one error using lme

[Steve Candy]

I question whether this model of dependency between residuals in repeated
measures analysis is sensible

> >   /RANDOM=INTERCEPT Time | SUBJECT(Subject)

corresponds to a random coefficients approach which implies a correlation
between time points within subjects which varies with time (also called
"the growth curve model" cf:  Diggle et al 2002 pg 98-99) while

> >   /REPEATED=Time | SUBJECT(Subject)COVTYPE(AR1)

also implies a correlation between time points within subjects which varies
with time (if the Phi1 is positive it implies a positive serial correlation
exponentially decaying to zero as the time lag increases).

Therefore these two error models compete with each other in explaining
correlation that varies with time which is very messy (i.e. what does the
theoretical semivariogram look like?)  and possibly over-parameterised.

However, it makes sense to combine random intercepts with an AR1 process
(Diggle et al. 2002, Section 5.2.3, Figure 5.4)

> >   /RANDOM=INTERCEPT | SUBJECT(Subject)
> >   /REPEATED=Time | SUBJECT(Subject)COVTYPE(AR1).

My understanding is that the above SPSS error model is the same as the  lme
error model below  

> lme(
> fixed=conc~Time,
> random=~1|Subject,
> method="REML",
> data=fGlucose,
> na.action="na.omit",
> correlation=corAR1(form=~Time|Subject))

*Diggle, D. J., P. J. Heagerty, K. Y. Liang, and S. L. Zeger. 2002. Analysis
of Longitudinal Data. . Oxford University Press, Oxford, England.

Dr Steven G. Candy
Director/Consultant
SCANDY STATISTICAL MODELLING PTY LTD
(ABN: 83 601 268 419)
70 Burwood Drive
Blackmans Bay, TASMANIA, Australia 7052
Mobile: (61) 0439284983