10.1 - Historical Methods

Repeated measures were historically handled as either a multivariate analysis, or alternatively as a univariate split-plot in time.

The multivariate approach is one where we have (by strict definition) several dependent variables, i.e., \(y_{time1}, y_{time2}, y_{time3} = \text{treatments}\), etc. This approach is difficult to work with and not very satisfactory. The method assumes a multivariate normal distribution (difficult to assess), the F-test is an approximate test, and the method evaluates the suite of dependent variables, making it difficult to evaluate what is happening to individual treatments over time.

A split-plot in time approach looks at each subject (experimental unit) as a main plot (receiving a treatment) and then is split into sub-plots (time periods). The split-plot in time is how Minitab analyzes repeated measures. The split plot in time assumes that the correlations among time periods are the same for all treatments and time periods (compound symmetry). This assumption is not a good one and often there are other correlation structures that are more appropriate when using repeated measures (e.g. autoregressive lag 1).

The evolution of methodology for repeated measures had been driven by the need to consider the nature of potentially correlated residuals. The current state of the art for repeated measures can be seen in SAS and SPSS. There may be others, but I work with these two. In the mixed model program in SAS we can explore and specify the correlation structure for our model.