Iterative least squares estimates of communality: Initial estimate need not affect stabilized value

A common criticism of iterative least squares estimates of communality is that method of initial estimation may influence stabilized values. As little systematic research on this topic has been performed, the criticism appears to be based on cumulated experience with empirical data sets. In the present paper, two studies are reported in which four types of initial estimate (unities, squared multiple correlations, highestr, and zeroes) and four levels of convergence criterion were employed using four widely available computer packages (BMDP, SAS, SPSS, and SOUPAC). The results suggest that initial estimates have no effect on stabilized communality estimates when a stringent criterion for convergence is used, whereas initial estimates appear to affect stabilized values employing rather gross convergence criteria. There were no differences among the four computer packages for matrices without Heywood cases.     

Finite mixtures in confirmatory factor-analysis models

In this paper, various types of finite mixtures of confirmatory factor-analysis models are proposed for handling data heterogeneity. Under the proposed mixture approach, observations are assumed to be drawn from mixtures of distinct confirmatory factor-analysis models. But each observation does not need to be identified to a particular model prior to model fitting. Several classes of mixture models are proposed. These models differ by their unique representations of data heterogeneity. Three different sampling schemes for these mixture models are distinguished. A mixed type of the these three sampling schemes is considered throughout this article. The proposed mixture approach reduces to regular multiple-group confirmatory factor-analysis under a restrictive sampling scheme, in which the structural equation model for each observation is assumed to be known. By assuming a mixture of multivariate normals for the data, maximum likelihood estimation using the EM (Expectation-Maximization) algorithm and the AS (Approximate-Scoring) method are developed, respectively. Some mixture models were fitted to a real data set for illustrating the application of the theory. Although the EM algorithm and the AS method gave similar sets of parameter estimates, the AS method was found computationally more efficient than the EM algorithm. Some comments on applying the mixture approach to structural equation modeling are made.Note: This paper is one of the Psychometric Society's 1995 Dissertation Award papers.—EditorThis article is based on the dissertation of the author. The author would like to thank Peter Bentler, who was the dissertation chair, for guidance and encouragement of this work. Eric Holman, Robert Jennrich, Bengt Muthén, and Thomas Wickens, who served as the committee members for the dissertation, had been very supportive and helpful. Michael Browne is appreciated for discussing some important points about the use of the approximate information in the dissertation. Thanks also go to an anonymous associate editor, whose comments were very useful for the revision of an earlier version of this article.     

An alternative to the methodology for analysis of covariance

A general statistical model for simultaneous analysis of data from several groups is described. The model is primarily designed to be used for the analysis of covariance. The model can handle any number of covariates and criterion variables, and any number of treatment groups. Treatment effects may be assessed when the treatment groups are not randomized. In addition, the model allows for measurement errors in the criterion variables as well as in the covariates. A wide variety of hypotheses concerning the parameters of the model can be tested by means of a large sample likelihood ratio test. In particular, the usual assumptions of ANCOVA may be tested.Research reported in this paper has been partly supported by the Swedish Council for Social Science Research under project Statistical methods for analysis of longitudinal data, project director Karl G. Jöreskog, and partly by the Bank of Sweden Tercentenary Foundation under project Structural Equation Models in the Social Sciences, project director Karl G. Jöreskog.     

A note on sufficient conditions that a common factor will be determinate in an infinite domain of variables

It is proved for the common factor model withr common factors that under certain condition s which maintain the distinctiveness of each common factor a given common factor will be determinate if there exists an unlimited number of variables in the model each having an absolute correlation with the factor greater than some arbitrarily small positive quantity.The author is indebted to R. P. McDonald for suggesting the proof of Guttman's determinantal equation for the squared multiple correlation in predicting a factor from the observed variables used in the parenthetical note.     

Minimum rank and minimum trace of covariance matrices

This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented.     

The Headache Symptom Questionnaire: Discriminant classificatory ability and headache syndromes suggested by a factor analysis

A brief Headache Symptom Questionnaire was administered to 129 chronic headache Sufferers. The questionnaire accurately classified 68.42% of headache subjects in their proper diagnostic category, comparable to, but statistically less accurate than, the 86.4% agreement between expert headache diagnosticians using clinical interviews. Results of a factor analysis of the Headache Symptom Questionnaire lend support for their being two commonly accepted global headache categories—vascular/migraine and muscle contraction—and one headache dimension concerned with duration of headache pain. Combined migraine-muscle contraction headache was found to be related more to migraine than to muscle contraction headache, and cluster headaches emerged as a separate clinical entity, not loading positively on any factor and loading negatively on all three.This research was supported in part by Grant NS-15235 from the National Institute of Neurological and Communicative Disorders and Stroke.     

On rotating to smooth functions

Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. Simple structure is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.Portions of this research were supported by the National Research Council of Canada, Grant A8615 to the second author. We thank Jagdeth Sheth for supplying his raw data.     

A look,by simulation,at the validity of some asymptotic distribution results for rotated loadings

In the last few years, a number of asymptotic results for the distribution of unrotated and rotated factor loadings have been given. This paper investigates the validity of some of these results based on simulation techniques. In particular, it looks at principal component extraction and quartimax rotation on a problem with 13 variables. The indication is that the asymptotic results are quite good.     

大学生网名命名动机的研究

本研究自编的“大学生网名命名动机量表”有较高的信度和效度。大学生的网名命名的动机按重要程度依次为:张扬个性、便捷自然、寻求自我价值感、祟尚流行和宣泄情感。网名命名动机在性别间存在显著差异,女生命名网名时,认为“张扬个性”与“便捷自然”较重要,而男生认为“寻求自我价值感”、“宣泄情感”与“崇尚流行”更重要。年级因素在命名动机上存在显著差异。低年级学生认为网名应当“张扬个性”、“寻求自我价值感”和“宣泄情感”,而高年级认为网名应“崇尚流行”和“便捷自然”。文理科学生仅在“便捷自然”动机上有差异。     

Confirmatory Factor Analyses of the Full and Short Versions of the Marlowe-Crowne Social Desirability Scale

Abstract

Over the years, researchers have developed various short versions of the Marlowe-Crowne Social Desirability Scale (D. P. Crowne & D. Marlowe, 1960). The authors used confirmatory factor analyses (J. L. Arbuckle, 1997) as well as item and scale analyses to evaluate the adequacy of the full version and various short versions. Overall, the results from 232 Canadian undergraduates showed (a) that all the short versions in the present study are a significant improvement in fit over the 33-item full scale and (b) that W. M. Reynolds's (1982) Forms A and B are the best fitting short versions. No gender differences were found for the full scale or any of the short versions. The results show that the full scale could be improved psychometrically and that the psychometrically sound short versions should be available because they require less administration time than the full scale.