Discriminant Analysis Using Mixed Continuous, Dichotomous, and Ordered Categorical Variables

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This article proposes an intuitive approach for predictive discriminant analysis with mixed continuous, dichotomous, and ordered categorical variables that are defined via an underlying multivariate normal distribution with a threshold specification. The classification rule is based on the comparison of the observed data logarithm probability density functions. To reduce the computational burden, the analysis is conducted in the context of a confirmatory factor analysis model with independent error measurements. Identification of the dichotomous and ordered categorical variables is discussed. Results are obtained by implementations of a Monte Carlo expectation maximization (MCEM)algorithm and a path sampling procedure. Probabilities of misclassification are estimated via the idea of the “jackknife” method. A real example is given to illustrate the proposed method.