In this contribution we aim at improving ordinal variable selection in the context of causal models. In this regard, we propose an approach that provides a formal inferential tool to compare the explanatory power of each covariate, and, therefore, to select an effective model for classification purposes. Our proposed model is Bayesian nonparametric, and, thus, keeps the amount of model specification to a minimum. We consider the case in which information from the covariates is at the ordinal level. A noticeable instance of this regards the situation in which ordinal variables result from rankings of companies that are to be evaluated according to different macro and micro economic aspects, leading to different ordinal covariates that correspond to different ratings, that entail different magnitudes of the probability of default. For each given covariate, we suggest to partition the statistical units in as many groups as the number of observed levels of the covariate. We then assume individual defaults to be homogeneous within each group and heterogeneous across groups. Our aim is to compare and, therefore, select, the partition structures resulting from the consideration of different explanatory covariates. The metric we choose for variable comparison is the calculation of the posterior probability of each partition. The application of our proposal to a European credit risk database shows that it performs well, leading to a coherent and clear to explain method for variable averaging the estimated default probabilities.
