[R] Measuring correlations in repeated measures data

[Brant Inman]

Ben,

Thanks for the response.  Your method generates an answer that is slightly different than what I was looking for.  In the Orthodont dataset there are 4 age groups (8, 10, 12, 14).  I would like to calculate the correlation of "distance" for all combinations of the categorical variable "age".  The anticipated output would therefore be a matrix with 4 columns and 4 rows and a diagonal of ones.

For example, in such a table I would be able to look at the mean within individual correlation coefficient for distance b/t ages 8 and 10 or, alternatively, ages 10 and 14.  Is there a function in nlme or lme4 that does this?

Brant

On Feb 28, 2011, at 02:24 AM, Ben Bolker <bbolker at gmail.com> wrote:

> Brant Inman <brant.inman <at> mac.com> writes:
>
> >
> > R-helpers:
> >
> > I would like to measure the correlation coefficient between the repeated
> measures of a single variable
> > that is measured over time and is unbalanced. As an example, consider the
> Orthodont dataset from package
> > nlme, where the model is:
> >
> > fit <- lmer(distance ~ age + (1 | Subject), data=Orthodont)
> >
> > I would like to measure the correlation b/t the variable "distance" at
> different ages such that I would have
> > a matrix of correlation coefficients like the following:
> >
> > age08 age09 age10 age11 age12 age13 age14
> > age08 1
> > age09 1
> > age10 1
> > age11 1
> > age12 1
> > age13 1
> > age14 1
> >
> > The idea would be to demonstrate that the correlations b/t
> > repeated measures of the variable "distance"
> > decrease as the time b/t measures increases. For example,
> > one might expect the correlation
> > coefficient b/t age08 and age09 to be higher than that
> > between age08 and age14.
> >
>
> This stuff is not currently possible in lmer/lme4 but is
> easy in nlme:
>
> library(nlme)
> Orthodont$age0 <- Orthodont$age/2-3
> ## later code requires a time index of consecutive integers
> ## (which apparently must also start at 1, although not stated)
>
> fit <- lme(distance~age,random=~1|Subject,data=Orthodont)
>
> ## compute autocorrelation on the basis of lag only, plot
> a <- ACF(fit)
> plot(a,alpha=0.05)
>
>
> fit2 <- update(fit, correlation=corSymm(form=~age0|Subject))
> fit3 <- update(fit, correlation=corAR1(form=~age0|Subject))
>
> AIC(fit,fit2,fit3)
> ## at least on the basis of AIC, this extra complexity is
> ## not warranted
>
> anova(fit,fit2) ## likelihood ratio test
>
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