Bayesian factor analysis for mixed data on management studies

In: RAUSP management journal, Band 54, Heft 4, S. 430-445

Abstract

Purpose
Factor analysis is the most used tool in organizational research and its widespread use in scale validations contribute to decision-making in management. However, standard factor analysis is not always applied correctly mainly due to the misuse of ordinal data as interval data and the inadequacy of the former for classical factor analysis. The purpose of this paper is to present and apply the Bayesian factor analysis for mixed data (BFAMD) in the context of empirical using the Bayesian paradigm for the construction of scales.


Design/methodology/approach
Ignoring the categorical nature of some variables often used in management studies, as the popular Likert scale, may result in a model with false accuracy and possibly biased estimates. To address this issue, Quinn (2004) proposed a Bayesian factor analysis model for mixed data, which is capable of modeling ordinal (qualitative measure) and continuous data (quantitative measure) jointly and allows the inclusion of qualitative information through prior distributions for the parameters' model. This model, adopted here, presents considering advantages and allows the estimation of the posterior distribution for the latent variables estimated, making the process of inference easier.


Findings
The results show that BFAMD is an effective approach for scale validation in management studies making both exploratory and confirmatory analyses possible for the estimated factors and also allowing the analysts to insert a priori information regardless of the sample size, either by using the credible intervals for Factor Loadings or by conducting specific hypotheses tests. The flexibility of the Bayesian approach presented is counterbalanced by the fact that the main estimates used in factor analysis as uniqueness and communalities commonly lose their usual interpretation due to the choice of using prior distributions.


Originality/value
Considering that the development of scales through factor analysis aims to contribute to appropriate decision-making in management and the increasing misuse of ordinal scales as interval in organizational studies, this proposal seems to be effective for mixed data analyses. The findings found here are not intended to be conclusive or limiting but offer a useful starting point from which further theoretical and empirical research of Bayesian factor analysis can be built.