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

A Bayesian procedure is given for estimation in unrestricted common factor analysis. A choice of the form of the prior distribution is justified. It is shown empirically that the procedure achieves its objective of avoiding inadmissible estimates of unique variances, and is reasonably insensitive to certain variations in the shape of the prior distribution.

[1]  H. B. Heywood,et al.  On finite sequences of real numbers , 1931 .

[2]  D. Lawley.  VI.—The Estimation of Factor Loadings by the Method of Maximum Likelihood , 1940 .

[3]  W. G. Emmett.  FACTOR ANALYSIS BY LAWLEY'S METHOD OF MAXIMUM LIKELIHOOD , 1949 .

[4]  Louis Guttman,et al.  Image theory for the structure of quantitative variates , 1953 .

[5]  Calyampudi R. Rao.  Estimation and tests of significance in factor analysis , 1955 .

[6]  Louis Guttman,et al.  “Best possible” systematic estimates of communalities , 1956 .

[7]  Irving John Good,et al.  The Estimation of Probabilities: An Essay on Modern Bayesian Methods , 1965 .

[8]  B. M. Hill,et al.  Inference about Variance Components in the One-Way Model , 1965 .

[9]  K. Jöreskog.  Some contributions to maximum likelihood factor analysis , 1967 .

[10]  B P Frost,et al.  Anxiety and educational achievement. , 1968, The British journal of educational psychology.

[11]  Stephen M. Robinson,et al.  A Newton-Raphson algorithm for maximum likelihood factor analysis , 1969 .

[12]  M. Degroot.  Optimal Statistical Decisions , 1970 .

[13]  M. R. B. Clarke,et al.  A RAPIDLY CONVERGENT METHOD FOR MAXIMUM-LIKELIHOOD FACTOR ANALYSIS , 1970 .

[14]  Dorothy T. Thayer,et al.  Bayesian inference and the classical test theory model: Reliability and true scores , 1971 .

[15]  E. Polak.  Introduction to linear and nonlinear programming , 1973 .

[16]  S. J. Press,et al.  Applied Multivariate Analysis. , 1973 .