Bayesian factor models for multivariate categorical data obtained from questionnaires

TL;DR

This paper introduces a Bayesian factor model tailored for multivariate categorical data, enabling factor analysis of questionnaire responses where traditional methods are unsuitable, demonstrated through simulations and real data.

Contribution

It develops a novel Bayesian factor analysis method for categorical data, extending factor analysis to non-scaled variables with MCMC inference.

Findings

The method accurately estimates factors in simulations.

It effectively analyzes questionnaire data on emotions.

Provides a flexible tool for categorical data analysis.

Abstract

Factor analysis is a flexible technique for assessment of multivariate dependence and codependence. Besides being an exploratory tool used to reduce the dimensionality of multivariate data, it allows estimation of common factors that often have an interesting theoretical interpretation in real problems. However, standard factor analysis is only applicable when the variables are scaled, which is often inappropriate, for example, in data obtained from questionnaires in the field of psychology,where the variables are often categorical. In this framework, we propose a factor model for the analysis of multivariate ordered and non-ordered polychotomous data. The inference procedure is done under the Bayesian approach via Markov chain Monte Carlo methods. Two Monte-Carlo simulation studies are presented to investigate the performance of this approach in terms of estimation bias, precision and assessment of the number of factors. We also illustrate the proposed method to analyze participants' responses to the Motivational State Questionnaire dataset, developed to study emotions in laboratory and field settings.