Bayesian Constrained-Model Selection for Factor Analytic Modeling

TL;DR

This paper develops Bayesian methods for constrained model selection in factor analysis, addressing both dimensionality determination and inequality restrictions, with applications to exploratory and confirmatory factor analysis.

Contribution

It introduces a Bayesian framework for constrained model selection in factor analysis, linking model dimensionality and inequality restrictions to EFA and CFA.

Findings

Bayesian approach effectively determines model dimensionality.

Method incorporates inequality constraints into factor loadings.

Results demonstrate improved model selection accuracy.

Abstract

My dissertation revolves around Bayesian approaches towards constrained statistical inference in the factor analysis (FA) model. Two interconnected types of restricted-model selection are considered. These types have a natural connection to selection problems in the exploratory FA (EFA) and confirmatory FA (CFA) model and are termed Type I and Type II model selection. Type I constrained-model selection is taken to mean the determination of the appropriate dimensionality of a model. This type of constrained-model selection connects with EFA in the sense of selecting the optimal dimensionality of the latent vector. Type II model selection is taken to mean the determination of appropriate inequality, order or shape restrictions on the parameter space. The dissertation connects Type II constrained-model selection to CFA by focusing on the determination of linear inequality constraints as expressions of the direction and (relative) strength of factor loadings. The figures accompanying this article are taken from the slides of my Division 5 Awards Symposium Invited address at the APA 2015 Annual Convention in Toronto. These slides can be retrieved from \url{https://github.com/CFWP/ConventionTalk}.