Nonparametric multivariate inference via permutation tests for CUB models

A new approach for modelling discrete choices in rating or ranking problems is represented by a class of mixture models with covariates (Combination of Uniform and shifted Binomial distributions, CUB models), proposed by Piccolo (2003, Quaderni di Statistica, 5, 85-104), D'Elia & Piccolo (2005, Computational Statistics & Data Analysis, 49, 917-934), Piccolo (2006, Quaderni di Statistica, 8, 33-78) and Iannario (2010, Metron, LXVIII, 87-94). In case of a univariate response, a permutation solution to test for covariates effects has been discussed in Bonnini et al. (2012, Communication in Statistics: Theory and Methods), together with parametric inference. We propose an extension of this nonparametric test to deal with the multivariate case. The good performances of the method are showed trough a simulation study and the procedure is applied to real data regarding the evaluation of the Ski School of Sesto Pusteria (Italy).