Robust descriptive discriminant analysis for repeated measures data

Discriminant analysis (DA) procedures based on parsimonious mean and/or covariance structures have recently been proposed for repeated measures data. However, these procedures rest on the assumption of a multivariate normal distribution. This study examines repeated measures DA (RMDA) procedures based on maximum likelihood (ML) and coordinatewise trimming (CT) estimation methods and investigates bias and root mean square error (RMSE) in discriminant function coefficients (DFCs) using Monte Carlo techniques. Study parameters include population distribution, covariance structure, sample size, mean configuration, and number of repeated measurements. The results show that for ML estimation, bias in DFC estimates was usually largest when the data were normally distributed, but there was no consistent trend in RMSE. For non-normal distributions, the average bias of CT estimates for procedures that assume unstructured group means and structured covariances was at least 40% smaller than the values for corresponding procedures based on ML estimators. The average RMSE for the former procedures was at least 10% smaller than the average RMSE for the latter procedures, but only when the data were sampled from extremely skewed or heavy-tailed distributions. This finding was observed even when the covariance and mean structures of the RMDA procedure were mis-specified. The proposed robust procedures can be used to identify measurement occasions that make the largest contribution to group separation when the data are sampled from multivariate skewed or heavy-tailed distributions.