A Relabeling Procedure for Dealing with Rotational Invariance in Bayesian Confirmatory Factor Analysis

• Activity Number: 517
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Elena Erosheva*+ and S. McKay Curtis
• Companies: University of Washington and University of Washington
• Keywords: Bifactor models ; identifiability constraints ; label-switching ; Markov chain Monte Carlo ; reflection ; rotational invariance

Abstract

A well-known inherent ambiguity in factor models is that factors and factor loadings can only be identified up to an orthogonal rotation. In confirmatory factor analysis (CFA), different options exist for placing constraints aimed at ensuring unique identification of the model parameters. For simple CFA structures, when each observed variable loads on exactly one factor, different sets of constraints are equivalent with respect to model fit. However, this may no longer be the case when some variables are permitted to load on more than one factor. Following a Bayesian approach to factor analysis, we illustrate that constraining some loadings to be one or positive may result in nontrivial multimodality in the likelihood and in mode-switching behavior with Markov chain Monte Carlo samplers that can be problematic for Bayesian inference. We present a simple relabeling procedure for dealing with rotational invariance in Bayesian CFA and demonstrate it on simulated data and on a classic CFA bifactor data set measuring the subjects' spatial, verbal, mental speed, memory, and mathematical abilities.