Bayesian Factor Analysis.
Abstract
A new Bayesian procedure for factor analysis is developed in which factor scores as well as factor loadings and error variances are treated as parameters of interest. The presentation is fully Bayesian in the sense that all the parameters have prior distributions and the posterior mode of a subset of the parameters is used as the point estimate. The model is a standard one where the observations are expressed as the sum of the linear combination of factor scores, with factor loadings being the weights, and a normal error term. As the prior distribution the following exchangeable form is assumed: A factor score vector for each observation has a common normal distribution. A factor loading vector for each variable has a common normal distribution. A error variance for each variable has a common inverted chi square distribution. When the exchangeability of all the observations/variables is in question observations/variables may be divided into several subsets and the observations/variables within each subset may be treated as exchangeable. Since the posterior marginal distribution of factor loadings and error variances can be expressed as the product of the covariance-based likelihood and the prior distributions of factor loadings and error variances the proposed method includes both the random and the fixed factor analysis models. Keywords include: Factor analysis, Bayesian estimation, and EM algorithm.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 23, 1985
- Accession Number
- ADA154184
Entities
People
- S. I. Mayekawa
Organizations
- University of Iowa