Computing for Unbalanced Repeated Measures Experiments

Repeated measures experiments involve two or more intended measurements per subject. If the within-subjects design is the same for each subject, and if no data are missing, then the analysis is not very hard and there are readily available programs that do the analysis automatically. Huwever, if the data are not balanced, with the same arrangement for eaeh subject, then the analysis becomes much more difficult. Beginning with procedures which are not optimal but are fairly simple, we move on to unbalanced linear model analysis, and then normal maximum likelihood procedures, We discuss ML and REML estimators for the mixed mouel and also maximum likelihood estimators for a model which allows arbitrary within-subjects covariances. We give a program which uses SAS MATRIX to do generalized least squares based on the output of BMDPAN, which gives a maximum likelihood estimate for the covariance matrix.