PRESS model selection in repeated measures data

Abstract

Model selection is central to the art of data analysis, as any final inference depends strongly upon the chosen model. Repeated measures data is a common form of multivariate data, and linear models with correlated errors are widely used in modeling repeated measures data. Compared with linear regression, relatively few model selection methods have been studied for selecting the linear predictor in these models. In this paper, we generalize a cross-validation based model selection method, the Predicted Residual Sum of Squares (PRESS), to multivariate linear models with correlated errors. We present theorems about the expected value of PRESS, and about the differences in expected values of PRESS calculated under a larger and a smaller model given that the larger or smaller model is true. These theorems aid in understanding the behavior of PRESS in multivariate linear models and show that PRESS can be used as a model selection method for these models. An efficient scheme is given for calculating and updating PRESS when adding or deleting predictors. A data example is given which shows how PRESS model selection works in practice.