Nonparametric inference via permutation tests for Cub models

Abstract In statistical surveys, respondents are often asked to express evaluations on several topics. The rating problem can be often faced in many fields. A new approach is represented by a class of mixture models with covariates (CUB models). Together with parametric inference, a permutation solution to test for covariates effects, when an univariate response is considered, has been discussed in [1], where the preference for a permutation test as compared to asymptotic ones when the sample size is moderate or even small has been justified through a simulation study. We propose an extension of this nonparametric inference to deal with the multivariate case. The method is applied to a real data set.