[R-sig-ME] Autocorrelation in a growth curve model

[Andrew Robinson]

Hi Tim,

I'm not certain that there is a problem.  I infer that the original
estimate of the residual sd was biased low because of the ignored
autocorrelation.

Best wishes

Andrew

On Wed, Jul 17, 2013 at 11:38 PM, Cole, Tim <tim.cole at ucl.ac.uk> wrote:
> I have a mixed effects growth model I call SITAR, modified from Ken Beath's (Stat Med 2007;26:2547-64), which consists of a spline curve in transformed age with random intercept (a).  Transformed age TA is a linear function of age, TA = (age – b) * exp(c), where b and c are also random effects.
>
> Using nlme, the model provides an excellent fit to pubertal height data, explaining ~99% of the variance of the corresponding fixed effects model. However there is appreciable autocorrelation as shown by the ACF function. If I adjust for it by adding corr=corAR1() the likelihood increases by 985 units  but the residual SD also increases from 0.006 to 0.039, and the residuals are correspondingly larger. Using corr=corCAR1(~x) gives similar results.
>
> I don't understand what's going on, and wonder if I'm missing something?
>
> The nlme code for a curve with 5 df is as follows:
>
>
> fitnlme <- function(x, s1, s2, s3, s4, s5, a, b, c) {
>
>     splinecoefs <- as.matrix(cbind(s1, s2, s3, s4, s5))
>
>     as.vector(a + (splinecoefs * as.matrix(ns((x-b)*exp(c),
>
>     knots=knots, Boundary.knots=bounds))) %*% matrix(rep(1, df),  ncol=1))
>
> }
>
> nlme1 <- nlme(y ~ fitnlme(x, s1, s2, s3, s4, s5, a, b, c),
>
> fixed = s1 + s2 + s3 + s4 + s5 + a + b + c ~ 1,
>
> random = a + b + c ~ 1 | id,
>
> …)
>
> nlme2 <- update(nlme1, corr=corAR1())
>
> Thanks,
> Tim Cole
> --
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-- 
Andrew Robinson
Deputy Director, CEBRA
Senior Lecturer in Applied Statistics                      Tel: +61-3-8344-6410
Department of Mathematics and Statistics            Fax: +61-3-8344 4599
University of Melbourne, VIC 3010 Australia
Email: a.robinson at ms.unimelb.edu.au    Website: http://www.ms.unimelb.edu.au

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