A discriminant analysis extension to mixed models

Abstract

Discriminant analysis is commonly used to classify an observation into one of two (or more) populations on the basis of correlated measurements. Classical discriminant analysis approaches require complete data for all observations. Our extension enables the use of all available longitudinal data, regardless of completeness. Traditionally a linear discriminant function assumes a common unstructured covariance matrix for both populations, which may be taken from a multivariate model. Here, we can model the correlated measurements and use a structured covariance in the discriminant function. We illustrate cases in which the estimated covariance structure is either compound symmetric, heterogeneous compound symmetric or heterogeneous autoregressive. Thus a structured covariance is incorporated into the discrimination process in contrast to standard discriminant analysis methodology. Simulations are performed to obtain a true measure of the effect of structure on the error rate. In addition, the usual multivariate expected value structure is altered. The impact on the discrimination process is contrasted when using the multivariate and random-effects covariance structures and expected values. The random-effects covariance structure leads to an improvement in the error rate in small samples. To illustrate the procedure we consider repeated measurements data from a clinical trial comparing two active treatments; the goal is to determine if the treatment could be unblinded based on repeated anxiety score measurements.