[R] Measuring correlations in repeated measures data

[Ben Bolker]

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