JOINT BAYESIAN ANALYSIS OF FACTOR SCORES AND STRUCTURAL PARAMETERS IN THE FACTOR ANALYSIS MODEL

SIK-YUM LEE^{1} AND JIAN-QING SHI^{2}

1Department of Statistics, Chinese University of Hong Kong, China 2Department of Statistics, University of Warwick, U.K.

(Received June 25, 1998; revised May 14, 1999)

Abstract. A Bayesian approach is developed to assess the factor analysis model. Joint Bayesian estimates of the factor scores and the structural parameters in the covariance structure are obtained simultaneously. The basic idea is to treat the latent factor scores as missing data and augment them with the observed data in generating a sequence of random observations from the posterior distributions by the Gibbs sampler. Then, the Bayesian estimates are taken as the sample means of these random observations. Expressions for implementing the algorithm are derived and some statistical properties of the estimates are presented. Some aspects of the algorithm are illustrated by a real example and the performance of the Bayesian procedure is studied using simulation.

Key words and phrases: Posterior distributions, conjugate prior, hyper-parameters, factor scores, Gibbs sampler, posterior mean, posterior covariance matrix, simulation study.