A Permutation and Combination-Based Solution on the Ranking of Multivariate Populations in the Case of Ordered Categorical Responses with Application to the Evaluation of the Indoor Environment

This article deals with the problem of classifying and ranking several multivariate populations of interests using the permutation and combination approach providing also an inferential validity of the procedure. The need to define an appropriate classification of populations, i.e., products, services, teaching courses, degree programs, and so on, is very common within many areas of applied research. Many times the populations of interest are multivariate in nature meaning that many aspects of that populations can be simultaneously observed on the same unit/subject. From a statistical point of view, when the response variable of interest is multivariate in nature, the problem may become quite difficult to cope with especially in case of ordered categorical responses, due to the large dimensionality of the parametric space. Nonparametric inference based on the NPC methodology however, allows us to overcome these limitations, without the need of referring to assume any specified random distribution.