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

[Viechtbauer Wolfgang (STAT)]

It is certainly possible to have a model with random intercepts and slopes (for time) and also AR(1) correlated residuals over time within individuals. The random slopes model differences in the trend between individuals, while the AR(1) structure models how the residuals are fluctuating around the person-specific slopes within individuals. Of course, you need to have a sufficient number of follow-up measurements within individuals to distinguish those two elements. But this is certainly possible. And in fact, ignoring serial correlation in the residuals when it is present could lead to inflated Type I error rates for the mean trend effect.

Best,
Wolfgang

> -----Original Message-----
> From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-
> project.org] On Behalf Of Steve Candy
> Sent: Wednesday, May 20, 2015 13:14
> To: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] : estimating AR1 parameters of level one error
> using lme
> 
> 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
> 
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