Discriminant analysis based on binary and continuous variables
Abstract An observation consisting of both binary and continuous variables may be classified into one of two populations by the double-discriminant function based on the point-biserial model. When the parameters are unknown or partially known, a sample double-discriminant function is obtained by replacing the unknown parameters by their sample estimates. A sampling scheme referred to as the double inverse sampling is proposed to ensure nonsingularity of the sample covariance matrices. An asymptotic expansion for the distribution of the sample double-discriminant function is given under the double inverse sampling scheme. Comparisons of three classification procedures—double-discriminant function, X-out procedure, and X-continuous procedure—are made.