In confirmatory factor analysis (CFA), model parameters are usually estimated by iteratively minimizing the Maximum Likelihood (ML) fit function. In optimal circumstances, the ML estimator yields the desirable statistical properties of asymptotic unbiasedness, efficiency, normality, and consistency. In practice, however, real-life data tend to be…

Confirmatory factor analysis is considered from a Bayesian viewpoint, in which prior information concerning parameters is incorporated in the analysis. An interactive algorithm is developed to obtain the Bayesian estimates. A numerical example is presented. (Author/JKS)

A longitudinal factor analysis model that is entirely exploratory is proposed for use with multiple populations. Factorial collapse, period/practice effects, and an invariant and/or stationary factor pattern are allowed. The model is formulated stochastically and implemented via a stage-wise EM algorithm. (TJH)

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. An example is presented to demonstrate potential problems in other approaches to maximum likelihood factor analysis. (Author/JKS)

A jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Examples are given to demonstrate the feasibility of the method. (Author/JKS)

Rubin and Thayer recently presented equations to implement maximum likelihood estimation in factor analysis via the EM algorithm. It is argued here that the advantages of using the EM algorithm remain to be demonstrated. (Author/JKS)

The authors respond to a criticism of their earlier article concerning the use of the EM algorithm in maximum likelihood factor analysis. Also included are the comments made by the reviewers of this article. (JKS)

A method of item factor analysis is described, which is based on Thurstone's multiple-factor model and implemented by marginal maximum likelihood estimation and the EM algorithm. Also assessed are the statistical significance of successive factors added to the model, provisions for guessing and omitted items, and Bayes constraints. (TJH)

A method is proposed for constructing a population covariance matrix as the sum of a particular model plus a nonstochastic residual matrix, with the stipulation that the model holds with a prespecified lack of fit. The procedure is considered promising for Monte Carlo studies. (SLD)

A two-level model for factor analysis is defined, and formulas for a scoring algorithm for this model are derived. A simple noniterative method based on decomposition of total sums of the squares and cross-products is discussed and illustrated with simulated data and data from the Second International Mathematics Study. (SLD)

This paper discusses the use of latent class structure as a modelling framework for tests in which much of the data conforms to a relatively small number of systematic patterns. Application of this framework to the analysis of tests has been limited because available parameter estimation algorithms can only handle a relatively small number of…