Bayesian estimation in unrestricted factor analysis: A treatment for heywood cases

The Number-of-Factors Problem in Least-Squares Factor Analysis With a Random Loading Model

“…This possibility suggests that some alternative methods motivated to eliminate improper solutions may give rise to good competitors to the former. Hopeful candidates will be penalty function method due to Lee(1980), Lagrange multiplier method by Lee(1981) and Lee and Poon(1985) and also Bayes method by Martin and McDonald(1975) and Akaike(1987). The random loading model dealt with in this paper belongs to the family of formal models christened by Tucker, Koopman and Linn(1969), which include only major factors and unique factors.…”

A survey of some studies in methods for the structural analysis of multivariate data in the social sciences

“…This device is commonly employed to this day but cannot be recommended. Martin and McDonald (1975) showed that Bayesian estimation, with a prior distribution such that a nonpositive residual variance has zero probability and" small" residual variances have small probabilities, gives more reasonable values and does not grossly distort the parameter values of the variables yielding negative residual variances by maximum likelihood.…”

Bayesian factor analysis for spatially correlated data: application to cancer incidence data in Scotland

“…Despite the acknowledged advantages, Bayesian approaches to factor analysis have been so far quite limited. Bayesian factor analysis was introduced by Martin and McDonald (1975) and Press and Shigemasu (1989). They had to use rather restrictive model assumptions since most of the computational techniques for Bayesian data analysis were not available yet.…”