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 Piccolo , D. ( 2003 ). On the moments of a mixture of uniform and shifted binomial random variables . Quaderni di Statistica 5 : 85 – 104 . [Google Scholar]) and D'Elia and Piccolo (2005 D'Elia , A. , Piccolo , D. ( 2005 ). A mixture model for preference data analysis . Computat. Statist. Data Anal. 49 : 917 – 934 .[Crossref], [Web of Science ®] , [Google Scholar]) 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.