Psychometric evaluation of the dating anxiety survey: A self-report questionnaire for the assessment of dating anxiety in males and females

The Dating Anxiety Survey (DAS) was constructed to assess dating anxiety in males and females. Factor analysis of the survey revealed three factors: passive contact, active intentions for dating, and dating interactions. The reliabilities of the three subscales, as determined by coefficient alpha, were .87, .91, and .93 for males and .90, .90, and .92 for females, respectively. Correlations with dating history and a measure of social anxiety were generally of a low but significant magnitude, providing some support for concurrent validity. The results of the factor analysis lend support to the construct validity of the DAS. These findings suggest that the DAS is a potentially useful instrument in the self-report of dating anxiety.Portions of this paper were presented at the meeting of the Southeastern Psychological Association, Atlanta, GA, March 1983.     

A loss function for alpha factor analysis

Most of the factor solutions can be got by minimizing a corresponding loss function. However, up to now, a loss function for the alpha factor analysis (AFA) has not been known. The present paper establishes such a loss function for the AFA. Some analogies to the maximum likelihood factor analysis are discussed.The author is greatly indebted to Prof. Henry F. Kaiser (University of California, Berkeley) for his kind encouragement. He is also indebted to an anonymous referee ofPsychometrika for having confronted him with the problem in 1977. Financial support by the Wiener Hochschuljubiläumsstiftung is gratefully acknowledged.     

More factors than subjects,tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling

Some methods that analyze three-way arrays of data (including INDSCAL and CANDECOMP/PARAFAC) provide solutions that are not subject to arbitrary rotation. This property is studied in this paper by means of the triple product [A, B, C] of three matrices. The question is how well the triple product determines the three factors. The answer: up to permutation of columns and multiplication of columns by scalars—under certain conditions. In this paper we greatly expand the conditions under which the result is known to hold. A surprising fact is that the nonrotatability characteristic can hold even when the number of factors extracted is greater thanevery dimension of the three-way array, namely, the number of subjects, the number of tests, and the number of treatments.This paper is being published in place of Dr. Kruskal's presidential address to the Psychometric Society, April, 1975. Further results like those in this paper, as well as a surprising connection with an area of mathematics called arithmetic complexity theory, will be found in a more recent paper [Kruskal, in press].     

Two-matrix orthogonal rotation procedures

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.The work reported herein was supported by Grant S72-1886 from the Canada Council. The author acknowledges the helpful contributions of Nancy Reid and Lawrence Ward to parts of this paper.     

Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm

Maximum likelihood estimation of item parameters in the marginal distribution, integrating over the distribution of ability, becomes practical when computing procedures based on an EM algorithm are used. By characterizing the ability distribution empirically, arbitrary assumptions about its form are avoided. The Em procedure is shown to apply to general item-response models lacking simple sufficient statistics for ability. This includes models with more than one latent dimension.Supported in part by NSF grant BNS 7912417 to the University of Chicago and by SSRC (UK) grant HR6132 to the University of Lancaster.We are indebted to Mark Reiser and Robert Gibbons for computer programming. David Thissen clarified a number of points in an earlier draft.     

The extension of component analysis to four-mode matrices

A model for four-mode component analysis is developed and presented. The developed model, which is an extension of Tucker's three-mode factor analytic model, allows for the simultaneous analysis of all modes of a four-mode data matrix and the consideration of relationships among the modes. An empirical example based upon viewer perceptions of repetitive advertising shows the four-mode model applicable to real data.This research was supported by the University of Kansas School of Business Research Fund provided by the Fourth National Bank & Trust Company, Wichita. The ideas and opinions expressed herein are solely those of the author.     

EM algorithms for ML factor analysis

The details of EM algorithms for maximum likelihood factor analysis are presented for both the exploratory and confirmatory models. The algorithm is essentially the same for both cases and involves only simple least squares regression operations; the largest matrix inversion required is for aq ×q symmetric matrix whereq is the matrix of factors. The example that is used demonstrates that the likelihood for the factor analysis model may have multiple modes that are not simply rotations of each other; such behavior should concern users of maximum likelihood factor analysis and certainly should cast doubt on the general utility of second derivatives of the log likelihood as measures of precision of estimation.     

Linear structural equations with latent variables

An interdependent multivariate linear relations model based on manifest, measured variables as well as unmeasured and unmeasurable latent variables is developed. The latent variables include primary or residual common factors of any order as well as unique factors. The model has a simpler parametric structure than previous models, but it is designed to accommodate a wider range of applications via its structural equations, mean structure, covariance structure, and constraints on parameters. The parameters of the model may be estimated by gradient and quasi-Newton methods, or a Gauss-Newton algorithm that obtains least-squares, generalized least-squares, or maximum likelihood estimates. Large sample standard errors and goodness of fit tests are provided. The approach is illustrated by a test theory model and a longitudinal study of intelligence.This investigation was supported in part by a Research Scientist Development Award (KO2-DA00017) and a research grant (DA01070) from the U. S. Public Health Service.     

Principal component analysis of three-mode data by means of alternating least squares algorithms

A new method to estimate the parameters of Tucker's three-mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. A special case of the general Tucker model, in which the principal component analysis is only performed over two of the three modes is briefly outlined as well. The Miller & Nicely data on the confusion of English consonants are used to illustrate the programs TUCKALS3 and TUCKALS2 which incorporate the algorithms for the two models described.     

Uniqueness proof for a family of models sharing features of Tucker's three-mode factor analysis and PARAFAC/candecomp

Some existing three-way factor analysis and MDS models incorporate Cattell's “Principle of Parallel Proportional Profiles”. These models can—with appropriate data—empirically determine a unique best fitting axis orientation without the need for a separate factor rotation stage, but they have not been general enough to deal with what Tucker has called “interactions” among dimensions. This article presents a proof of unique axis orientation for a considerably more general parallel profiles model which incorporates interacting dimensions. The model, X_k=A^AD_k H^BD_k B', does not assume symmetry in the data or in the interactions among factors. A second proof is presented for the symmetrically weighted case (i.e., where^AD_k=^BD_k). The generality of these models allows one to impose successive restrictions to obtain several useful special cases, including PARAFAC2 and three-way DEDICOM. We want to express appreciation for the contributions of several colleagues: Jos M. F. ten Berge and Henk A. L. Kiers carefully went through more than one version of this article, found an important error, and contributed many improvements. J. Douglas Carroll and Shizuhiko Nishisato acted with unusual editorial preserverance and flexibility, thereby making possible the successful completion of a difficult assessment and revision process. Joseph B. Kruskal has long provided crucial mathematical insights and inspiration to those working in this area, but this is particularly true for us. His contributions to this specific article include early discussion of basic questions and careful examination of some earlier attempted proofs, finding them to be invalid. The anonymous reviewers also made useful suggestions. Some portions of this work were supported in part by a grant from the Natural Sciences and Engineering Research Council of Canada.