Permutation inference for a class of mixture models

In statistical surveys, people are often asked to express evaluations on several topics or to make an ordered arrangement in a list of objects (items, services, sentences, etc.); thus, the analysis of ratings and rankings is receiving a growing interest in many fields. In this framework, we develop a testing procedure for a class of mixture models with covariates (defined as cub models), proposed by Piccolo (2003) and D'Elia and Piccolo (2005) and generally developed in a parametric context. Instead, we propose a nonparametric solution to perform inference on cub models, specifically on the coefficients of the covariates. A simulation study proves that this approach is more appropriate in some specific data settings, mostly for small sample sizes.