Kickstarting R - Repeated measures

## Repeated measures

One of the most common statistical questions in psychology is whether something has changed over time, for example, whether the rats learned the task or whether the clients in the intervention group got better. Such questions are typically tested by comparing observations before and after some treatment. It is inappropriate to just compare the before and after observations as if they were independent, because they are not. The "after" observations are usually dependent upon the "before" observations and the effect of order. That is, a client who was very anxious at the initial occasion of measurement is likely to be less anxious at subsequent occasions, and because of the selection of clients on the basis of their disturbed psychological state and the change that state over time, our clients (who tended to be more disturbed than usual when they were recruited) will be likely to get somewhat better even if we just tell them to come back in six weeks.

There are a number of ways to perform repeated measures analysis in R. Here, we'll just examine two - the univariate method using ANOVA and that using linear mixed effects analysis.

## Univariate ANOVA

Many simple repeated measures analyses can be performed as a "univariate" ANOVA using `aov()` if the "circularity" property (the equivalence of variances of the differences between repeat observations) is met. For two repeats, of course, this is not a problem. Assume you have a data frame like this:

```subid	age	test1	test2
S001	23	17	21
S002	32	16	24
...```

The function `make.rm()` will reformat a data frame that contains repeats as multiple columns so that a call of the form:

```myexpr.df<-make.rm(constant=c("subid","age"),repeated=c("test1","test2"),data=myexp.df) summary(aov(repdat~age*contrasts+Error(subid),myexpr.df))```

will perform a simple repeated measures analysis.

Analyzing repeated measures using ANOVA involves stretching out the matrix of observations in a way that `aov()` is able to appropriately partition the variance for this problem. It is not always appropriate to use this method, and the reader should not just blindly plug their repeated measures problem into the cookbook method outlined here and expect to get the correct answer.

## Linear Mixed Effects

A more general method for repeated measures is to use the Linear Mixed Effects functions found in the `nlme` package. These functions expect the data to be in the "stretched-out" form produced by make.rm(), so that you may use this function to transform data that is in a "subject x repeat" format. Try the example using the data set `ergoStool` as follows:

```> library(nlme)
> data(ergoStool)
> summary(lme(effort ~ Type, data = ergoStool, random = ~ 1 | Subject))
```

This shows that there are differences between type T1 (the reference category) and types T2 and T3, but not T4. Perhaps the contrast of interest to you is whether types T1 and T4, made by manufacturer X, are different from types T2 and T3, made by manufacturer Y.

```> XvY<-ifelse(ergoStool\$Type=="T1",1,0)+
+ ifelse(ergoStool\$Type=="T4",1,0)+
+ ifelse(ergoStool\$Type=="T2",-1,0)+
+ ifelse(ergoStool\$Type=="T3",-1,0)
> summary(lme(effort ~ XvY, data = ergoStool, random = ~ 1 | Subject))
```

While not as "good" a model as the one in the example, this may be more informative in a particular case.

For a much more detailed treatment of ANOVAs and other methods, get the VR package or Notes on the use of R..." in the Contributed documentation page.