Predictive discriminant analysis versus logistic regression for two-group classification problems in educational settings.

The cross-validated classification accuracy of predictive discriminant analysis (PDA) and logistic regression (LR) models was compared for the two-group classification problem. Thirty-four real data sets varying in number of cases, number of predictor variables, degree of group separation, relative group size, and equality of group covariance matrices were employed for the comparison. PDA models were built based on assumptions of multivariate normality and equal covariance matrices, and cases were classified using Tatsuoka's (1988, p. 351) minimum chi square rule. LR models were built using the International Mathematical and Statistical Library (IMSL) subroutine Categorical Generalized Linear Model (CTGLM), available with the 32-bit Microsoft Fortran v4.0 Powerstation. CTGLM uses a nonlinear approximation technique (Newton-Raphson) to determine maximum likelihood estimates of model parameters. The group with the higher log-likelihood probability was used as the LR prediction. Cross-validated hit-rate accuracy of PDA and LR models was estimated using the leave-one-out procedure. McNemar's (1947) statistic for correlated proportions was used in the statistical comparisons of PDA and LR hit rate estimates for separate-group and total-sample proportions (z = 2.58, $\alpha$ =.01).