Demonstrated that the extra-factor phenomenon (the two-dimensional solution produced when linear factor analysis is applied to a set of unfoldable items) arises because the metric unidimensional unfolding model is equivalent to the unidimensional quadratic factor model and the unidimensional quadratic factor model is not distinguishable from the…

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)

Path analytic techniques for assessing the validity of indicators in multitrait-multimethod matrices represent improvements on Campbell and Fiske's early procedures for testing for validity. The diagnosis of indicator ills by means of confirmatory factor analysis is especially useful. An empirical example of these techniques is presented.…

The Cartesian theory of dimensionality (defined in terms of geometric distances between points in the test space) and Leibnitzian theory (defined in terms of order-generative connected, transitive, and asymmetric relations) are contrasted in terms of the difference between a factor analysis and an order analysis of the same data. (Author/CTM)

Two sets of five items each from the Law School Admission Test were analyzed by two methods of factor analysis, and by the Krus-Bart ordering theoretic method of multidimensional scaling. The results indicated a conceptual gap between latent trait theoretic procedures and order theoretic procedures. (Author/CTM)

Path analyses of two multitrait-multimethod matrices are used as examples of the kind of information afforded by application of the technique. It is concluded that the technique should be of considerable aid to researchers who want to evaluate the convergent and discriminant validity of their measures. (Author/CTM)

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)

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.…

After a brief review of the contributions of factor analysis and regional analysis to the elaboration of the structures of spatial abilities, a facet design and regional model for spatial abilities are presented. A cylindrical-wedge model is proposed to represent the correlational structure of spatial ability tests. (SLD)

The form of item log-likelihood surface was investigated under two-parameter and three-parameter logistic models. Results confirm that the LOGIST program procedures used to locate the maximum of the likelihood functions are consistent with the form of the item log-likelihood surface. (SLD)

A group of covariance structure models was examined to ascertain the similarity between conventionally administered and computerized adaptive versions of the Differential Aptitude Test (DAT). Results for 332 students indicate that the computerized version of the DAT is an adequate representation of the conventional test battery. (TJH)

A mathematical model is proposed to describe how group differences in distributions of abilities, which are distinct from the target ability, influence the probability of a correct item response. In the multidimensional approach, differential item functioning is considered a function of the educational histories of the examinees. (SLD)

The validity of the assumptions under which the ordinal true score test theory was derived was examined using (1) simulation based on classical test theory; (2) a long empirical test with data from 321 sixth graders; and (3) an extensive simulation with 480 datasets based on the 3-parameter model. (SLD)