GENERALIZED COVARIANCE-ADJUSTED DISCRIMINANTS - PERSPECTIVE AND APPLICATION

When discriminant analysis is used in practice for assessing the usefu lness of diagnostic markers, the lack of control over covariates motiv ates the need for their adjustment in the analysis. This necessity for adjustment arises especially when the researcher's aim is classificat ion based on a set of diagnostic markers and is not based on a set of covariates for which there exists known heterogeneity among the subjec ts with respect to the groups under consideration. The traditional cov ariance-adjusted approach is restrictive for such applications in that they assume linear covariates and a normal distribution for the the f eature vector. Further, there is no available method for variable sele ction in using such covariance-adjusted models. In this paper, we gene ralize the traditional covariance-adjusted model to a general normal a nd logistic model, where these generalized models not only relax the d istributional assumptions on the feature vector but also allow for non linear covariates. Exact and asymptotic tests are also derived for the problem of variable selection for these new models. The methodology i s illustrated with both simulated data and an actual data set from a p sychiatric study on using the Social Rhythm Metric for patients with a nxiety disorders.