Similarities between latent class models with K classes and linear factor models with K-1 factors are investigated. Specifically, the mathematical equivalence between the covariance structure of the two models is discussed, and a Monte Carlo simulation is performed using generated data that represents both latent factors and latent classes with…

Extension analysis allows for the investigation of relationships between factors from a core set of variables and the variables from an additional, extension set. This frequently results in obtaining negative residual variances, called Heywood cases. Procedures for checking for that problem are presented here. (Author/JKS)

Gives a set of minimally sufficient axioms to define and distinguish common factor theory, image theory, and component theory and analyzes claims that have been made for image theory as a device for improving factor theory. (Author/RC)

Demonstrates the advantages for test construction, validity studies, and extensions of unidimensional item response theory (IRT) of applying classical factor-analytic treatments, based on the independent clusters concept, of confirmatory (restricted) models and exploratory (unrestricted) models to multidimensional IRT and obtaining standard…

It is shown that if a behavior domain can be described by the common factor model with a finite number of factors, the squared correlation between the sum of a selection of items and the domain total score is actually greater than coefficient alpha. (Author/JKS)

Problems in avoiding the singularity problem in analyzing matrices for optimal scaling are addressed. Conditions are given under which the stationary points and values of a ratio of quadratic forms in two singular matrices can be obtained by a series of simple matrix operations. (Author/JKS)

The use of an independent clusters basis for restricted factor analysis can be recommended in cases where the known structure of a subset of variables serves to determine the structure of the remaining variables in the set. A comparison of this technique with an appropriate form of restricted factor analysis is illustrated on a large set of…

A Bayesian procedure is given for estimation in unrestricted common factor analysis. A choice of the form of the prior distribution is justified. 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. (Author/BJG)

If the factor loadings of a core set of variables (fitting the general factor model) are the same when analyzed alone, and when analyzed along with the rest of the variables in an infinite behavior domain, there is only one factor variable in the domain that is a possible factor variable of the core set. If the condition of consistency of factor…

The relationship between the factor structure of a convariance matrix and the factor structure of a partial convariance matrix when one or more variables are partialled out of the original matrix is given in this brief note. (JKS)

An expression is given for weighted least squares estimators of oblique common factors of factor analyses, constrained to have the same covariance matrix as the factors they estimate. A proof of the uniqueness of the solution is given. (Author/JKS)

Solutions for the indeterminate common factor of a group of variables satisfying the single common factor model are not unique. This paper examines a number of thereoms concerning that problem and draws conclusions from them for factor analysis in general. (Author/JKS)

The extent to which a scale score generalizes to a latent variable common to all of the scale's indicators is indexed by the scale's general factor saturation. Seven techniques for estimating this parameter--omega[hierarchical] (omega[subscript h])--are compared in a series of simulated data sets. Primary comparisons were based on 160 artificial…

It is shown that goodness-of-fit criteria developed for the evaluation of multivariate structural models can be applied to assist in evaluating the dimensionality of a test consisting of binary items, and correlative methods regularly used in factor analysis can be employed to diagnose causes of misfit. (Author)