PARAFAC is a generalization of principal components analysis in a factor score matrix and in a factor loadings matrix. How PARAFAC behaves when applied to positive manifold data is examined, and a constrained PARAFAC method is offered for use when PARAFAC does not produce a positive manifold solution. (SLD)

A method is proposed for detecting influential observations in iterative principal factor analysis. Theoretical influence functions are derived for two components of the common variance decomposition. The major mathematical tool is the influence function derived by Tanaka (1988). (SLD)

Arguments by J. Levin (1988) challenging the convergence properties of the Harman and Jones (1966) method of Minres factor analysis are shown to be invalid. Claims about the invalidity of a rank-one version of the Harman and Jones method are also refuted. (TJH)

Relations between latent trait and latent class models for item response data are examined. Conditions are given for two-latent class and two-parameter normal ogive models to agree, and relations between their item parameters are presented. Results are illustrated with data from the Law School Admission Test. (SLD)

Structural models that yield circumplex inequality patterns are reviewed, focusing on a model developed by T. W. Anderson (1960). A modification is proposed to this model to allow for negative correlations. This model may be reparameterized as a factor analysis model with nonlinear constraints on the factor loadings. (SLD)

The distance approach to nonlinear multivariate analysis proposed by J. J. Meulman (1986) is reviewed. Several generalizations are discussed by combining features from the conventional multivariate analysis approach, which seeks weighted sums of variables, with the alternative approach, which seeks to fit distances. (SLD)

A model is proposed for empirically testing the appropriateness of using tetrachoric correlations for a set of dichotomous variables. A testing method is proposed that uses information from trivariate marginal tables. Assumptions are tested with real and simulated data. (SLD)

An item-response model for binary response data exhibiting the bi-factor structure is derived, and a practical parameter estimation method is developed. The model, which provides an alternate to the traditional conditionally independent unidimensional item response theory model, is illustrated with an example from psychiatric research. (SLD)

R. A. Bailey and J. C. Gower explored approximating a symmetric matrix "B" by another, "C," in the least squares sense when the squared discrepancies for diagonal elements receive specific nonunit weights. A solution is proposed where "C" is constrained to be positive semidefinite and of a fixed rank. (SLD)

The scree test and its linear regression technique are reviewed, and results of its use in factor analysis and Delphi data sets are described. The scree test was originally a visual approach for making judgments about eigenvalues, which considered the relationships of the eigenvalues to one another as well as their actual values. The graph that is…

Canonical weights and structure correlations are used to construct low dimensional views of the relationships between two sets of variables. These views, in the form of biplots, display familiar statistics: correlations between pairs of variables, and regression coefficients. (SLD)

A simple procedure for establishing convergent and discriminant validity is presented, as an alternative to the LISREL-based nested model used by R. P. Bagozzi (1978) and K. F. Widaman (1985). Ordinary least-squares regression is used, with the correlation between measures as the dependent variable. (SLD)

Several methods for the analysis of three-way data (data classified three ways) are described and shown to be variants of principal components analysis of the two-way supermatrix in which each two-way slice is strung out into a column vector. Direct fitting and fitting derived data are considered. (SLD)

The fundamental mathematical model of L. L. Thurstone's common factor analysis is reviewed, and basic covariance matrices of maximum likelihood factor analysis and alpha factor analysis are presented. The methods are compared in terms of computational and scaling contrasts. Weighting and the appropriate number of common factors are considered.…

Across conditions, differences between population parameters defined by common factor analysis and component analysis are demonstrated. Implications for data analytic and theoretical issues related to choice of analytic model are discussed. Results suggest that principal components analysis should not be used to obtain parameters reflecting latent…