Repeated Measurements

Abstract

Suppose that several measurements are taken on a number of individuals, usually over time. We wish to compare the way in which the measurements change for different individuals or groups of individuals. We are, then, comparing growth curves or time series, and testing for differences among them. Since observations are taken from the same individual, they will usually be correlated. (As is often the case for such models, we ignored this correlation in the chapter on growth curves.) Note, however, that the number of observations is usually very much smaller than for a single time series or growth curve. In such a case, the covariances among observations often can be modelled by a simple autoregression. The further apart in time are the observations on an individual, the less closely related they are. The values on the minor diagonals of the variance-covariance matrix, for an individual, decrease the farther they are from the main diagonal, while off diagonal elements between individuals are zero. In this sense, repeated measurements models are very closely related to the models of the previous three chapters. The difference is that more than one individual is involved. We shall deal with this case in the second and fourth sections.