Year: 2008
Type: preprint
Abstract: Factor analysis provides a useful tool for exploring the covariance structure among a set of observed random variables by construction of a smaller number of random variables called common factors. In maximum likelihood factor analysis, the estimates of unique or error variances can turn out to be zero or negative, which makes no sense from a statistical point of view. In order to overcome the problem of these so-called improper solutions, we use a Bayesian approach by specifying a prior distribution for the variances of specific factors, i.e., we introduce a prior distribution for the parameters to prevent the occurrence of improper solutions. Crucial aspects of Bayesian factor analysis include the choice of adjusted parameters, in particular, the hyper-parameters for the prior distribution and also choosing an appropriate number of factors. The choice of these parameters can be viewed as a model selection and evaluation problem. We derive a model selection criterion for a Bayesian factor analysis model. Monte Carlo simulations are conducted to investigate the efficiency of the proposed procedures. A real data example is also given to illustrate our procedures.
Authors: Kei Hirose, Shuichi Kawano, Sadanori Konishi, Masanori Ichikawa, 秀一 川野, 貞則 小西, 雅教 市川
Institutions: Kyushu University, Tokyo University of Foreign Studies
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W620055873