An Index for Selecting Mixed Explanatory Variables in the Analysis of Dependence

In the analysis of multivariate dependence, two main objectives may be pursued: descriptive and decisional. In the descriptive approach, the selection of explanatory variables is determined by the researcher’s objectives and form the nature of the problem at hand. The decisional approach requires a parsimonious model where only the variables with the highest explanatory power are included. This is done in order to achieve the highest possible rate of correctly classified units. In the case of numerical explanatory variables, the problem has been widely treated in discriminant analysis (Huberty, 1994) and in regression analysis (Cox e Snell, 1989). In the analysis of dependence for contingency tables, two approaches are known in literature: modelling by means of log-linear models and factorial methods. Within the framework of factorial methods, depending on the sampling scheme, we can refer to Baricentric Discriminant Analysis (BDA, Nakache, 1981) with a retrospective sampling, or to Non Symmetrical Correspondence Analysis (NSCA, Lauro e D’Ambra, 1984) with a prospective sampling (Palumbo, 1995), i.e. when no a priori information is available on the distribution of the explanatory variable. In the context of BDA for variables selection, the chi-square criterion is adopted (Nakache et al., 1977). On the other side, in NSCA, its Authors proposed a selection criterion based on the multiple τ index by Gray and Williams. This index, some conditions be given, approximately follows the chi-square distribution. However, the computation of the latter criterion is heavy. This paper aims at developing an alternative criterion, more efficient from a computational point of view, for the variables selection in decisional NSCA.