A model of Bradley-Terry type for paired comparisons is considered. In addition to the usual parameters, the model allows for individual parameters and corresponding parameters for the choice-alternatives. The model is applied to a set of data from a Danish investigation of the attitude of blue collar workers towards alternative social gains. The proposed model is finally compared to a model recently suggested by Schönemann and Wang.

Extending the definitions of part and bipartial correlation to sets of variates, the notion of part and bipartial canonical correlation analysis are developed and illustrated.

A general question is raised concerning the possible consequences of employing the very popular INDSCAL multidimensional scaling model in cases where the assumptions of that model may be violated. Simulated data are generated which violate the INDSCAL assumption that all individuals perceive the dimensions of the common object space to be orthogonal. INDSCAL solutions for these various sets of data are found to exhibit extremely high goodness of fit, but systematically distorted object spaces and negative subject weights. The author advises use of Tucker’s three-mode model for multidimensional scaling, which can account for non-orthogonal perceptions of the object space dimensions. It is shown that the INDSCAL model is a special case of the three-mode model.

A probabilistic model for the validation of behavioral hierarchies is presented. Estimation is by means of iterative convergence to maximum likelihood estimates, and two approaches to assessing the fit of the model to sample data are discussed. The relation of this general probabilistic model to other more restricted models which have been presented previously is explored and three cases of the general model are applied to exemplary data.

This article is concerned with estimation of components of maximum generalizability in multifacet experimental designs involving multiple dependent measures. Within a Type II multivariate analysis of variance framework, components of maximum generalizability are defined as those composites of the dependent measures that maximize universe score variance for persons relative to observed score variance. The coefficient of maximum generalizability, expressed as a function of variance component matrices, is shown to equal the squared canonical correlation between true and observed scores. Emphasis is placed on estimation of variance component matrices, on the distinction between generalizability- and decision-studies, and on extension to multifacet designs involving crossed and nested facets. An example of a two-facet partially nested design is provided.

The earlier two-sample procedure of Feldt [1969] for comparing independent alpha reliability coefficients is extended to the case of K ≥ 2 independent samples. Details of a normalization of the statistic under consideration are presented, leading to computational procedures for the overall K-group significance test and accompanying multiple comparisons. Results based on computer simulation methods are presented, demonstrating that the procedures control Type I error adequately. The results of a power comparison of the case of K = 2 with Feldt’s [1969] F test are also presented. The differences in power were negligible. Some final observations, along with suggestions for further research, are noted.

A quadratic programming algorithm is presented for fitting Carroll’s weighted unfolding model for preferences to known multidimensional scale values. The algorithm can be applied directly to pairwise preferences; it permits nonnegativity constraints on subject weights; and it provides a means of testing various preference model hypotheses. While basically metric, it can be combined with Kruskal’s monotone regression to fit ordinal data. Monte Carlo results show that (a) adequacy of “true” preference recovery depends on the number of data points and the amount of error, and (b) the proportion of data variance accounted for by the model sometimes only approximately reflects “true” recovery.

Guttman’s index of indeterminacy (2ρ2 − 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ρ2 for predicting the factor from the observed variables is the average correlation ρAB between independently selected alternative solutions A and B, while var (ρAB) = (1 − ρ2)2/s, where s is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ρ2 is the lower bound for E(ρAB); however, E(ρAB) need not be a modal value in the distribution of ρAB. Guttman’s index and E(ρAB) measure different aspects of the same indeterminacy problem.

A summary and interpretation of the recent literature on the indeterminacy of factor scores is given in simple terms. A good index of factor score determinacy is the squared multiple correlation of the factor with the observed variables.

Examples are presented in which it is either desirable or necessary to transform two sets of orthogonal axes to simple structure positions by means of the same transformation matrix. A solution is then outlined which represents a two-matrix extension of the general “orthomax” orthogonal rotation criterion. In certain circumstances, oblique two-matrix solutions are possible using the procedure outlined and the Harris-Kaiser [1964] logic. Finally, an illustrative example is presented in which the preceding technique is applied in the context of an inter-battery factor analysis.

This note extends and elaborates Hubert’s attempt to provide an interpretation of Freeman’s measure of association, θ. The θ measure is used in a contingency table when observations are ordered on one variable and unordered on the other. No attempt is made explore the distribution of θ.

A recent comparison of methods for estimating missing data concluded that when there is sufficient redundancy to justify using a more elaborate method than the mean of each variable, the principal components and regression methods are equally good and superior to the other methods investigated. Principal components was preferred because of its “tremendous computational savings over the regression method.” This note proposes an alternate implementation of the regression method which should be slightly faster than the principal components method.