Accounting for common method variance in cross-sectional research designs

Cross-sectional studies of attitude-behavior relationships are vulnerable to the inflation of correlations by common method variance (CMV). Here, a model is presented that allows partial correlation analysis to adjust the observed correlations for CMV contamination and determine if conclusions about the statistical and practical significance of a predictor have been influenced by the presence of CMV. This method also suggests procedures for designing questionnaires to increase the precision of this adjustment.     

The varimax criterion for analytic rotation in factor analysis

An analytic criterion for rotation is defined. The scientific advantage of analytic criteria over subjective (graphical) rotational procedures is discussed. Carroll's criterion and the quartimax criterion are briefly reviewed; the varimax criterion is outlined in detail and contrasted both logically and numerically with the quartimax criterion. It is shown that thenormal varimax solution probably coincides closely to the application of the principle of simple structure. However, it is proposed that the ultimate criterion of a rotational procedure is factorial invariance, not simple structure—although the two notions appear to be highly related. The normal varimax criterion is shown to be a two-dimensional generalization of the classic Spearman case, i.e., it shows perfect factorial invariance for two pure clusters. An example is given of the invariance of a normal varimax solution for more than two factors. The oblique normal varimax criterion is stated. A computational outline for the orthogonal normal varimax is appended.Part of the material in this paper is from the writer's Ph.D. thesis. I am indebted to my committee, Professors F. T. Tyler, R. C. Tryon, and H. D. Carter, chairman, for many helpful suggestions and criticisms. Dr. John Caffrey suggested the namevarimax, and wrote the original IBM 602A computer program for this criterion.I am also indebted to the staff of the University of California Computer Center for help in programming the procedures described in the paper for their IBM 701 electronic computer. Since their installation is partially supported by a grant from the National Science Foundation, the assistance of this agency is acknowledged.     

An improved solution for factals: A nonmetric common factor analysis

In FACTALS an alternating least squares algorithm is utilized. Mooijaart (1984) has shown that this algorithm is based upon an erroneous assumption. This paper gives a proper solution for the loss function used in FACTALS.     

A paradox for significant freedom

International Journal for Philosophy of Religion -     

Three common factor models for groups of variables

For the case of two or more groups of variables (batteries), generalizations on three common factor models, the Equal Residual Variances model, the Image model of Jöreskog, and the Canonical Factor Analysis model, are described and illustrated with empirical examples.The author is indebted to Dr. E. J. Burr for his valuable criticisms.     

A statistical model which combines features of factor analytic and analysis of variance techniques

This paper describes a method of matrix decomposition which retains the ability of factor analytic techniques to summarize data in terms of a relatively low number of coordinates; but at the same time, does not sacrifice the useful analysis of variance heuristic of partitioning data matrices into independent sources of variation which are relatively simple to interpret. The basic model is essentially a two-way analysis of variance model which requires that the matrix of interaction parameters be decomposed by using factor analytic techniques. Problems of judging statistical significance are discussed; and an illustrative example is presented.Much of the work on this paper was completed while the author held a U.S.P.H.S. Postdoctoral Fellowship at Yale University (1964–65). Many of the ideas in this paper have been discussed in the author's doctoral dissertation which was submitted to Yale University in 1965.Special thanks are due to Robert P. Abelson for his encouragement and for many helpful and stimulating discussions about problems which arose in the preparation of this paper. I would also like to thank Francis J. Anscombe and Alan T. James for their valuable suggestions and constructive criticism of an earlier draft of this article.     

The nonconvergence of factals: A nonmetric common factor analysis

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.     

Assessing the impact of common method variance on higher order multidimensional constructs

Researchers are often concerned with common method variance (CMV) in cases where it is believed to bias relationships of predictors with criteria. However, CMV may also bias relationships within sets of predictors; this is cause for concern, given the rising popularity of higher order multidimensional constructs. The authors examined the extent to which CMV inflates interrelationships among indicators of higher order constructs and the relationships of those constructs with criteria. To do so, they examined core self-evaluation, a higher order construct comprising self-esteem, generalized self-efficacy, emotional stability, and locus of control. Across 2 studies, the authors systematically applied statistical (Study 1) and procedural (Study 2) CMV remedies to core self-evaluation data collected from multiple samples. Results revealed that the nature of the higher order construct and its relationship with job satisfaction were altered when the CMV remedies were applied. Implications of these findings for higher order constructs are discussed.     

A common factor in the MMPI scales of married couples.

Using canonical analysis, a common factor in the MMPI scales of husbands and wives was found. The Sc, Pd, and Hs scales for both the husbands and the wives contributed heavily to the relationship. Other scales contributing to the correlation between the personality components of the pairs were F, Hy Pt, and Si for the husbands and Pa for the wives. The results were interpreted as indicating areas of homogeneity and heterogeneity in the personalities of married couples.     

A weighted procrustes criterion

The Procrustes criterion is a common measure for the distance between two matricesX andY, and can be interpreted as the sum of squares of the Euclidean distances between their respective column vectors. Often a weighted Procrustes criterion, using, for example, a weighted sum of the squared distances between the column vectors, is called for. This paper describes and analyzes the performance of an algorithm for rotating a matrixX such that the column-weighted Procrustes distance toY is minimized. The problem of rotatingX intoY such that an aggregate measure of Tucker's coefficient of congruence is maximized is also discussed.We wish to thank Richard A. Harshman and C. F. Jeff Wu for valuable discussions in the early stages of this work. We would also like to thank Jos ten Berge, John Gower, and the Editor, Associate Editor, and referees whose comments and suggestions greatly improved this paper.     

A multiscale Griffith criterion

In this letter, a compatibility-momentum tensor is proposed based on the strain compatibility condition of continuum mechanics. By rescaling the compatibility-momentum tensor, we construct a so-called multiscale energy-momentum tensor and the corresponding L-integral, which is path-independent if the interior region of the integration contour is dislocation-free. By applying the invariant L-integral to the field of a mode III elastoplastic crack under small-scale yielding condition, we derive a multiscale criterion for macroscopically brittle fractures.