Diagnostic Measures for Multinomial Distance Model

Qualitative data are more and more present in any ?eld of research. For example, in medicine one can be interested in predicting an illness based on some symptoms (e.g. presence/absence of physical characteristics), in psychology one can be interested in classifying di?erent types of mental status of human being through behaviors, or in economy ?rms are interested in splitting customers into di?erent groups based on their purchasing preferences to address marketing researches. Many techniques are developed to handle these type of data. Most of them allow only a detailed model evaluation (e.g. Discriminant Analysis) while others (e.g. multidimensional procedures) produce graphical representation of the data. Ideal Point Discriminant Analysis proposed by Takane (Takane, Bozdogan & Shibayama, 1987) is a semi-parametric model that allows both detailed evaluation and graphical representation of the data and it handles with all of kinds of predictors (categorical and numerical one). Multinomial Distance Model is an extension of IPDA and it has been proved (De Rooij, 2009) that it allows to a better graphical representation of the data than ideal point discriminant analysis. The main weakness of this model is that diagnostic statistics to evaluate the fit as well as outliers are not available. This work focuses on diagnostics to detect outliers for these kind of models. We will show that, even if Multinomial Distance Model is not a generalized linear model (it is a bilinear model), it can be regarded as a constrained baseline category logit model and based on this fact we will extend the diagnostics of multiple-group logistic regression to it.