A general procedure is provided for comparing correlation coefficients between optimal linear composites. The procedure allows computationally efficient significance tests on independent or dependent multiple correlations, partial correlations, and canonical correlations, with or without the assumption of multivariate normality. Evidence from some Monte Carlo studies on the effectiveness of the methods is also provided.

This study formulates a property of a quantification method, the principle of equivalent partitioning (PEP). When the PEP is used together with Guttman's principle of internal consistency (PIC) in a simple way, the combination offers an interesting way of analyzing categorical data in terms of the variate(s) chosen by the investigator, a type of canonical analysis. The study discusses applications of the technique to multiple-choice, rank-order, and paired comparison data.

The most widely-used computer programs for structural equation models analysis are the LISREL series of Jöreskog and Sörbom. The only types of constraints which may be made directly are fixing parameters at a constant value and constraining parameters to be equal. Rindskopf (1983) showed how these simple properties could be used to represent models with more complicated constraints, namely inequality constraints on unique variances. In this paper, two new concepts are introduced which enable a much wider variety of constraints to be made. The concepts, “phantom” and “imaginary” latent variables, allow fairly general equality and inequality constraints on factor loadings and structural model coefficients.

Methods for orthogonal Procrustes rotation and orthogonal rotation to a maximal sum of inner products are examined for the case when the matrices involved have different numbers of columns. An inner product solution offered by Cliff is generalized to the case of more than two matrices. A nonrandom start for a Procrustes solution suggested by Green and Gower is shown to give better results than a random start. The Green-Gower Procrustes solution (with nonrandom start) is generalized to the case of more than two matrices. Simulation studies indicate that both the generalized inner product solution and the generalized Procrustes solution tend to attain their global optima within acceptable computation times. A simple procedure is offered for approximating simple structure for the rotated matrices without affecting either the Procrustes or the inner product criterion.

In the application of clustering methods to real world data sets, two problems frequently arise: (a) how can the various contributory variables in a specific battery be weighted so as to enhance some cluster structure that may be present, and (b) how can various alternative batteries be combined to produce a single clustering that “best” incorporates each contributory set. A new method is proposed (SYNCLUS, SYNthesized CLUStering) for dealing with these two problems.

A family of solutions for linear relations among k sets of variables is proposed. It is shown how these solutions apply for k = 2, and how they can be generalized from there to k ≥ 3.

The family of solutions depends on three independent choices: (i) to what extent a solution may be influenced by differences in variances of components within each set; (ii) to what extent the sets may be differentially weighted with respect to their contribution to the solution—including orthogonality constraints; (iii) whether or not individual sets of variables may be replaced by an orthogonal and unit normalized basis.

Solutions are compared with respect to their optimality properties. For each solution the appropriate stationary equations are given. For one example it is shown how the determinantal equation of the stationary equations can be interpreted.

A new family of indices was introduced earlier as a link between two approaches: One based on item response theory and the other on sample statistics. In this study, the statistical properties of these indices are investigated and then the relationships to Guttman Scales, and to item and person response curves are discussed. Further, these indices are standardized, and an example of their potential usefulness for diagnosing students' misconceptions is shown.

It is shown that Kruskal's multidimensional scaling loss function is differentiable at a local minimum. Or, to put it differently, that in multidimensional scaling solutions using Kruskal's stress distinct points cannot coincide.

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.

The use of U-statistics based on rank correlation coefficients in estimating the strength of concordance among a group of rankers is examined for cases where the null hypothesis of random rankings is not tenable. The studentized U-statistics is asymptotically distribution-free, and the Student-t approximation is used for small and moderate sized samples. An approximate confidence interval is constructed for the strength of concordance. Monte Carlo results indicate that the Student-t approximation can be improved by estimating the degrees of freedom.

FACTALS is a nonmetric common factor analysis model for multivariate data whose variables may be nominal, ordinal or interval. In FACTALS an Alternating Least Squares algorithm is utilized which is claimed to be monotonically convergent.

In this paper it is shown that this algorithm is based upon an erroneous assumption, namely that the least squares loss function (which is in this case a nonscale free loss function) can be transformed into a scalefree loss function. A consequence of this is that monotonical convergence of the algorithm can not be guaranteed.

This paper proposes test statistics based on the likelihood ratio principle for testing equality of proportions in correlated data with additional incomplete samples. Powers of these tests are compared through Monte Carlo simulation with those of tests proposed recently by Ekbohm (based on an unbiased estimator) and Campbell (based on a Pearson-Chi-squared type statistic). Even though tests based on the maximum likelihood principle are theoretically expected to be superior to others, at least asymptotically, results from our simulations show that the gain in power could only be slight.