Variables Extraction on Large Binary Variables in Discriminant Analysis based on Mixed Variables Location Model

The natural performance of the location model is a potential tool for allocating an object into one of the two observed groups involving mixtures of continuous and binary variables. In constructing location model, continuous variable is used to estimate parameters while binary variable is utilized to create segmentation in each group. Such segmentation is called as multinomial cells. Basically, the multinomial cells will grow exponentially according to the number of the binary variable. These multinomial cells will become empty when there is no object can be assigned into some of them. Then the occurring of empty cells will lead to unreliable parameter estimation. Consequently, the construction of the discriminant rule based on location model is impossible. Therefore, this paper attempts to discuss how the location model based on maximum likelihood estimation can be constructed even dealing with many measured binary variables. In other word, how is location model able to deal with the issue of many empty cells for classifying an object into correct group? For remedy this problem, this paper adapts nonlinear principal component analysis in order to reduce large binary variables considered in the study. This new strategy can be expected as an alternative discriminant tool practically when large number of binary variables are considered in a classification tasks.