Applications of Bayesian Confirmatory Factor Analysis in Behavioral Measurement: Strong Convergence of a Bayesian Parameter Estimator

ABSTRACT This article is concerned with the large-sample parameter estimatorbehavior in applications of Bayesian confirmatory factor analysis in behavioral measurement. The property of strong convergence of the popular Bayesian posterior median estimator is discussed, which states numerical convergence with probability 1 of the resulting estimates to the population parameter value as sample size increases without bound. This property is stronger than the consistency and convergence in distribution of that estimator, which have been commonly referred to in the literature. A numerical example is utilized to illustrate this almost sure convergence of a Bayesian latent correlation estimator. The paper contributes to the body of research on optimal statistical features of Bayesian estimates and concludes with a discussion of the implications of this large-sample property of the Bayesian median estimator for empirical measurement studies.