Multidimensional rotation and scaling of configurations to optimal agreement

An integrated method for rotating and rescaling a set of configurations to optimal agreement in subspaces of varying dimensionalities is developed. The approach relates existing orthogonal rotation techniques as special cases within a general framework based on a partition of variation which provides convenient measures of agreement. In addition to the well-known Procrustes and inner product optimality criteria, a criterion which maximizes the consensus among subspaces of the configurations is suggested. Since agreement of subspaces of the configurations can be examined and compared, rotation and rescaling is extended from a data transformation technique to an analytical method.     

The rank of reduced dispersion matrices

Psychometricians working in factor analysis and econometricians working in regression with measurement error in all variables are both interested in the rank of dispersion matrices under variation of the diagonal elements. Psychometricians concentrate on cases in which low rank can be attained, preferably rank one, the Spearman case. Econometricians cocentrate on cases in which the rank cannot be reduced below the number of variables minus one, the Frisch case. In this paper we give an extensive historial discussion of both fields, we prove the two key results in a more satisfactory and uniform way, we point out various small errors and misunderstandings, and we present a methodological comparison of factor analysis and regression on the basis of our results.Financial support by the Netherlands Organization for the Advancement of Pure Research (ZWO) is gratefully acknowledged.     

Application of model-selection criteria to some problems in multivariate analysis

A review of model-selection criteria is presented, with a view toward showing their similarities. It is suggested that some problems treated by sequences of hypothesis tests may be more expeditiously treated by the application of model-selection criteria. Consideration is given to application of model-selection criteria to some problems of multivariate analysis, especially the clustering of variables, factor analysis and, more generally, describing a complex of variables.     

Some properties of the correlation matrix of dichotomous guttman items

Both the elements and the eigenvalues of the Pearson correlation matrix of dichotomous Guttman-scalable items can be expressed as simple functions of the number of items if the score distribution is uniform and there is an equal number of items at each difficulty level. Even when these special conditions do not hold, the correlations can often be expressed in a simple form by assuming a particular score distribution.The author thanks Neil Dorans, Bob Mislevy, Ledyard R Tucker, and Howard Wainer for their comments.     

Parent-perceived child behavior problems: Comparison of normative and clinical factors of the Adelaide-Conners Parent Rating Scale

The Adelaide-Conners Parent Rating Scale (APRS), an instrument developed by studying a large, representative group of schoolchildren, was used with a group of psychiatry attenders. Multimethod factor analysis found satisfactory agreement between the factor structures of the clinical and the normative groups. The patterns of scores on the 12 APRS scales were also compared. Two higher-order factors (Conflict with the Environment and Conflict within the Self) were identified in the clinical sample as previously found in the normative group. Comparison of the factor solutions with previous empirical efforts to identify parent-perceived patterns of child behavior disorder showed that the APRS compares well with other instruments and supports the strategy of proceeding from the study of normative populations to the study of clinically defined groups.This work was supported in part by a grant from the Department of Health, Canberra.     

BENEFITS AND COSTS OF SUPPORTED EMPLOYMENT: AN ANALYSIS OF THE ILLINOIS SUPPORTED EMPLOYMENT PROJECT

This investigation presents a cost-benefit analysis completed for one of 27 states implementing supported employment as a result of federal funding. Based upon the benefits and costs detailed, society realized a $0.75 return for every $1.00 invested in supported employment in Illinois. Supported employees realized a 37% increase in their earnings over a comparable period. The results of this study are discussed and recommendations are made for similar analyses across states.     

DOES CONDITIONAL DISCRIMINATION LEARNING BY PIGEONS NECESSARILY INVOLVE HIERARCHICAL RELATIONSHIPS?

Four experiments demonstrate that when putative conditional and discriminative cues are presented simultaneously in the single reversal procedure, it is not possible to ascribe a uniquely conditional or uniquely discriminative function to either of the cues. In Experiment 1, pigeons were trained to respond to a blue key and not to a red key while the houselight was on; then in a different session they learned the reversal of this discrimination with the houselight off (single reversal). Separate groups were tested for color generalization with houselight conditions alternating in blocks of trials or for houselight intensity generalization with blue and red key colors alternating in blocks of trials. Both test procedures revealed a conditional relationship between houselight and key color conditions. Experiment 2 produced the same result following training in which the key colors were held constant across training sessions while the houselight and no houselight conditions varied within sessions. In Experiment 3, separate groups were trained with the two procedures but were tested with randomly ordered combinations of key colors and houselight intensities. The two groups yielded indistinguishable bidimensional generalization gradients with peaks at both previously reinforced stimulus combinations. In Experiment 4 the subjects were switched from one of these training procedures to the other with no decrement in their discriminative performance. We conclude that for successive discriminations between conditional- and discriminative-stimulus combinations, the notion of a hierarchical relation between conditional and discriminative stimuli must be extended to include a symmetrical relationship or the notion should be abandoned altogether.     

An alternating least squares algorithm for fitting the two- and three-way dedicom model and the idioscal model

The DEDICOM model is a model for representing asymmetric relations among a set of objects by means of a set of coordinates for the objects on a limited number of dimensions. The present paper offers an alternating least squares algorithm for fitting the DEDICOM model. The model can be generalized to represent any number of sets of relations among the same set of objects. An algorithm for fitting this three-way DEDICOM model is provided as well. Based on the algorithm for the three-way DEDICOM model an algorithm is developed for fitting the IDIOSCAL model in the least squares sense.The author is obliged to Jos ten Berge and Richard Harshman.     

An investigation of the normative and factor analytic composition of six questionnaires used for subject selection

Six self-report instruments which have been widely used for subject screening were administered to large samples of males and female college students. Normative information and bivariate correlations between scales were derived. Principal components analysis was applied to the individual scales to determine substructures. Finally, factor scores from the scales were examined in terms of second-order factors from an additional principal components analysis. The results are discussed in terms of comparisons with the results of previously published reports and implications for the discriminant validity of the scales and factor scores. The use of factor scores for more homogeneous subject selection is suggested.We wish to thank Arnold Holzman, Cynthia Volinsky, Ellen Tuckner, and Patricia Tolchin for their assistance in administering the questionnaires. Appreciation is also extended to Paul Malloy for his aid and suggestions concerning data analysis and to an anonymous reviewer for insightful comments which improved the quality of the final report. This study was conducted while the first author was at the State University of New York at Binghamton.     

Factor analysis by instrumental variables methods

Three alternative estimation procedures for factor analysis based on the instrumental variables method are presented. These procedures are justified by the method of least squares. Formulas for asymptotic standard errors of factor loadings are derived. The procedures are empirically compared to the method of maximum likelihood. The conclusion, based on the data used in this study, is that two of the procedures seem to work well.