Using projection for testing goodness-of-fit in regression models for repeated measures

Repeated measures data often occur in practice. This has led to considerable progress in the development of methods for inference in models for such data. In this paper, projection methods are proposed for examining goodness-of-fit in regression models for repeated measures. Rao's (1959, Biometrika 46, 49-58) F-test for testing a postulated mean structure using an independently identically normally distributed random sample is extended to a broad class of models including both fixed and random effects. The paper also shows how projection methods may be utilized for checking multivariate normality. In addition, application of projection to test the adequacy of extremely unbalanced models is considered. Two examples are given to demonstrate the underlying techniques.