A discriminant analysis extension to mixed models

Discriminant analysis is commonly used to classify an observation into one of two (or more) populations on the basis of correlated measurements. Class ical discriminant analysis approaches require complete data for all observa tions. Our extension enables the use of all available longitudinal data, re gardless of completeness. Traditionally a linear discriminant function assu mes a common unstructured covariance matrix for both populations, which may be taken from a multivariate model. Here, we can model the correlated meas urements and use a structured covariance in the discriminant function. We i llustrate cases in which the estimated covariance structure is either compo und symmetric, heterogeneous compound symmetric or heterogeneous autoregres sive. Thus a structured covariance is incorporated into the discrimination process in contrast to standard discriminant analysis methodology. Simulati ons are performed to obtain a true measure of the effect of structure on th e error rate. In addition, the usual multivariate expected value structure is altered. The impact on the discrimination process is contrasted when usi ng the multivariate and random-effects covariance structures and expected v alues. The random-effects covariance structure leads to an improvement in t he error rate in small samples. To illustrate the procedure we consider rep eated measurements data from a clinical trial comparing two active treatmen ts; the goal is to determine if the treatment could be unblinded based on r epeated anxiety score measurements. Copyright (C) 1999 John Wiley & Sons, L td.