Reise, Cook, and Moore proposed a "comparison modeling" approach to assess the distortion in item parameter estimates when a unidimensional item response theory (IRT) model is imposed on multidimensional data. Central to their approach is the comparison of item slope parameter estimates from a unidimensional IRT model (a restricted model), with…

In three-mode principal components analysis, the P x Q x R core matrix "G" can be transformed to simple structure before it is interpreted. This paper shows that, when P=QR-1, G can be transformed to have nearly all the elements equal to values specified a priori. A closed-form solution for this transformation is offered. (SLD)

For two given vectors of the three-dimensional Euclidean space we investigate the problem of identifying all rotations that transform them into each other. For this purpose we consider three types of rotation matrices to obtain a complete characterization. Finally some attention is paid to the problem of obtaining all rotations taking two vectors…

A general factor analysis computer algorithm is briefly discussed. The algorithm is highly transportable with minimum limitations on the number of observations. Both singular and non-singular data can be analyzed. (Author/JKS)

Examples are presented in which it is either necessary or desirable to transform two sets of orthogonal axes to simple structure positions by means of the same transformation matrix. A solution is outlined which represents a two-matrix extension of the general "orthomax" orthogonal rotation criterion. (Author/RC)

A procedure is outlined showing how the axiom of local independence for latent structure models can be weakened. (CK)

Relations between maximum likelihood factor analysis and factor indeterminacy are discussed. (CK)

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)

Prediction for a number of criteria from a set of predictor variables in a system of regression equations is studied with the possibilities of linear transformations applied to both the criterion and predictor variables. Predictive composites representing a battery of predictor variables provide identical estimates of criterion scores as do the…

This report describes a test of the robustness of factor-analytic methods in the face of various types of scale transformations on the data. Because of the complexities that would be involved in an exact analytical investigation, the tests were done with simulated sets of data having different factor structures. After factor analyzing the original…

To study the applicability of simple structure logic for factorial data from scientific disciplines outside psychology, four correlation matrices from each of six scientific areas were factor analyzed by five factoring methods. Resulting factor matrices were compared on two objective criteria of simple structure before and after rotation.…

Applications to the Promax Rotation are discussed, and it is shown that these procedures solve Thurstone's hitherto intractable "invariant" box problem as well as other more common problems based on real data. (Author/RC)

In this article, new arguments and empirical evidence are presented justifying the use of Standardized R - analysis (or equivalently Q - technique) in certain types of factor-analytic studies. The standardized R - analysis analyses the intercorrelations among respondents based on their "ipsative" scores, as opposed to the unstandardized…