A combination is achieved of two lines of psychometric interest: a) multidimensional scaling and b) factor analysis. This is accomplished with the use of three-mode factor analysis of scalar product matrices, one for each subject. Two of the modes are the groups of objects scaled and the third mode is the sample of subjects. Results are an object space, a person space, and a system for changing weights given to dimensions and of angles between dimensions in the object space for individuals located at different places in the person space. The development is illustrated with data from an adjective similarity study.

A multivariate logistic latent trait model for items scored in two or more nominal categories is proposed. Statistical methods based on the model provide 1) estimation of two item parameters for each response alternative of each multiple choice item and 2) recovery of information from “wrong” responses when estimating latent ability. An application to a large sample of data for twenty vocabulary items shows excellent fit of the model according to a chi-square criterion. Item and test information curves are compared for estimation of ability assuming multiple category and dichotomous scoring of these items. Multiple scoring proves substantially more precise for subjects of less than median ability, and about equally precise for subjects above the median.

A local independence latent structure model, which assumes m latent classes, requires a minimum of 2m-1 items for the solution of the 2m2 latent parameters. If one adds 3 items to the test and if one assumes local “dependence” between pairs of items, thereby adding\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\left( {\begin{array}{*{20}c} {2m + 2}\\ 2\\ \end{array} } \right)$$\end{document} additional latent parameters, ξij, representing the association between items i and j, then it is possible to obtain estimates for all of the latent parameters: latent class frequencies latent probabilities, and measures of association between pairs of items. The solution consists of (1) forming (m + 1) × (m + 1) matrices of manifest data, which are singular, (2) solving for the ξij in equations that result from the singularity of the data matrices, (3) “correcting” the manifest data by removing the “contamination” due to local dependence, and (4) estimating the remaining latent parameters from the corrected data, using methods outlined in earlier literature.

Some relations between maximum likelihood factor analysis and factor indeterminacy are discussed. Bounds are derived for the minimum average correlation between equivalent sets of correlated factors which depend on the latent roots of the factor intercorrelation matrix Ψ. Empirical examples are presented to illustrate some of the theory and indicate the extent to which it can be expected to be relevant in practice.

Given three variables, x, y, z, univariate selection on x, usually reduces the correlation ry z. However, in some cases, when rx y or rx z assumes extreme values, ry z may increase. This reversal is explained by comparison to the effects of suppressor variables and predictors of predictability.

It is shown that McDonald’s generalization of classical Principal Components Analysis to groups of variables maximally channels the total variance of the original variables through the groups of variables acting as groups. A useful equation is obtained for determining the vectors of correlations of the L2 components with the original variables. A calculation example is given.

A computational short cut suggested by Feldman and Klinger for the one-sided Fisher-Yates exact test is clarified and is extended to the calculation of probability values for certain two-sided tests when sample sizes are unequal.