Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-08T12:16:01.088Z Has data issue: false hasContentIssue false
  • English
  • Français

The Analysis of Multitrait-Multimethod Matrices Via Constrained Components Analysis

Published online by Cambridge University Press:  01 January 2025

Henk A. L. Kiers ,
Yoshio Takane  and
Jos M. F. ten Berge
Henk A. L. Kiers*
Affiliation:
University of Groningen
Yoshio Takane
Affiliation:
McGill University
Jos M. F. ten Berge
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Henk A.L. Kiers, Department of Psychology (SPA), Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.
Get access Rights & Permissions [Opens in a new window]

Abstract

Multitrait-Multimethod (MTMM) matrices are often analyzed by means of confirmatory factor analysis (CFA). However, fitting MTMM models often leads to improper solutions, or non-convergence. In an attempt to overcome these problems, various alternative CFA models have been proposed, but with none of these the problem of finding improper solutions was solved completely. In the present paper, an approach is proposed where improper solutions are ruled out altogether and convergence is guaranteed. The approach is based on constrained variants of components analysis (CA). Besides the fact that these methods do not give improper solutions, they have the advantage that they provide component scores which can later on be used to relate the components to external variables. The new methods are illustrated by means of simulated data, as well as empirical data sets.

Keywords

principal components analysiscommon factor analysisalternating least squares algorithmsidentificationuniquenesspartitioning of fit
Type
Original Paper
Information
Psychometrika , Volume 61 , Issue 4 , December 1996 , pp. 601 - 628
Copyright
Copyright © 1996 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences to the first author. The authors are obliged to three anonymous reviewers and an associate editor for constructive suggestions on the first version of this paper.

References

Algina, J. (1980). A note on identification in the oblique and orthogonal factor analysis models. Psychometrika, 45, 393–396.CrossRefGoogle Scholar
Anderson, T. W., Rubin, H. (1956). Statistical inference in factor analysis. In Neymann, J. (Eds.), Proceedings of the third Berkeley symposium on mathematical statistics and probability (Vol. 5), Berkeley CA: University of California Press.Google Scholar
Bagozzi, R. P., Yi, Y. (1990). Assessing method variance in multitrait-multimethod matrices: The case of self-reported affect and perceptions at work. Journal of Applied Psychology, 75, 547–560.CrossRefGoogle Scholar
Bekker, P. A. (1986). A note on the identification of restricted factor loading matrices. Psychometrika, 51, 607–611.CrossRefGoogle Scholar
Brannick, M. T., Spector, P. E. (1990). Estimation problems of the block diagonal model of the multitrait-multimethod matrix. Applied Psychological Measurement, 14, 325–340.CrossRefGoogle Scholar
Browne, M. W. (1984). The decomposition of multitrait-multimethod matrices. British Journal of Mathematical and Statistical Psychology, 37, 1–21.CrossRefGoogle ScholarPubMed
Browne, M. W. (1993). Models for multitrait-multimethod matrices. In Steyer, R., Wender, K. F., Widaman, K. F. (Eds.), Psychometric Methodology. Proceedings of the 7th European Meeting of the Psychometric Society in Trier (pp. 61–73). Stuttgart and New York: Gustav Fischer Verlag.Google Scholar
Campbell, D. T., Fiske, D. W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. Psychological Bulletin, 56, 81–105.CrossRefGoogle ScholarPubMed
Cliff, N. (1966). Orthogonal rotation to congruence. Psychometrika, 31, 33–42.CrossRefGoogle Scholar
Dudgeon, P. (1994). A reparameterization of the restricted factor analysis model for multitrait-multimethod matrices. British Journal of Mathematical and Statistical Psychology, 47, 283–308.CrossRefGoogle Scholar
Grayson, D., Marsh, H. W. (1994). Identification with deficient rank loading matrices in confirmatory factor analysis: Multitrait-multimethod models. Psychometrika, 59, 121–134.CrossRefGoogle Scholar
Jöreskog, K. G., Sörbom, D. (1989). LISREL 7. A guide to the program and applications, Chicago: Scientific Software.Google Scholar
Kenny, D. A. (1979). Correlation and Causality, New York: Wiley.Google Scholar
Kenny, D. A., Kashy, D. A. (1992). Analysis of the multitrait-multimethod matrix by confirmatory factor analysis. Psychological Bulletin, 112, 165–172.CrossRefGoogle Scholar
Kiers, H. A. L., Takane, Y. (1993). Constrained DEDICOM. Psychometrika, 58, 339–355.CrossRefGoogle Scholar
Kruskal, J. B., Harshman, R. A., Lundy, M. E. (1989). How 3-MFA data can cause degenerate PARAFAC solutions, among other relationships. In Coppi, R., Bolasco, S. (Eds.), Multiway Data Analysis (pp. 115–122). Amsterdam: Elsevier Science Publishers.Google Scholar
Lawler, E. E. (1967). The multitrait-multimethod approach to measuring managerial job performance. Journal of Applied Psychology, 51, 369–381.CrossRefGoogle Scholar
Marsh, H. W. (1989). Confirmatory factor analysis of multitrait-multimethod data: Many problems and a few solutions. Applied Psychological Measurement, 13, 335–361.CrossRefGoogle Scholar
Marsh, H. W., Bailey, M. (1991). Confirmatory factor analyses of multitrait-multimethod data: A comparison of alternative models. Applied Psychological Measurement, 15, 47–70.CrossRefGoogle Scholar
Marsh, H. W., Byrne, B. M., Craven, R. (1992). Overcoming problems in confirmatory factor analyses of MTMM data: The correlated uniqueness model and factorial invariance. Multivariate Behavioral Research, 27, 489–507.CrossRefGoogle ScholarPubMed
Marsh, H. W., Hocevar, D. (1983). Confirmatory factor analysis of multitrait-multimethod matrices. Journal of Educational Measurement, 20, 231–248.CrossRefGoogle Scholar
Millsap, R. E. (1992). Sufficient conditions for rotational uniqueness in the additive MTMM model. British Journal of Mathematical and Statistical Psychology, 45, 125–138.CrossRefGoogle Scholar
Penrose, R. (1956). On best approximate solutions of linear matrix equations. Proceedings of the Cambridge Philosophical Society, 52, 17–19.CrossRefGoogle Scholar
Schmitt, N., Stults, D. M. (1986). Methodology review: Analysis of multitrait-multimethod matrices. Applied Psychological Measurement, 10, 1–22.CrossRefGoogle Scholar
Takane, Y., Kiers, H. A. L., de Leeuw, J. (1995). Component analysis with different sets of constraints on different dimensions. Psychometrika, 60, 259–280.CrossRefGoogle Scholar
Werts, C. E., Linn, R. L. (1970). Path analysis: Psychological examples. Psychological Bulletin, 74, 193–212.CrossRefGoogle Scholar
Widaman, K. F. (1985). Hierarchically nested covariance structure models for multitrait-multimethod data. Applied Psychological Measurement, 9, 1–26.CrossRefGoogle Scholar
Widaman, K. F. (1990). Bias in pattern loadings represented by common factor analysis and component analysis. Multivariate Behavioral Research, 25, 89–95.CrossRefGoogle ScholarPubMed
Widaman, K. F. (1993). Common factor analysis versus principal component analysis: Differential bias in representing model parameters. Multivariate Behavioral Research, 28, 263–311.CrossRefGoogle ScholarPubMed
Wothke, W. (1987). Multivariate linear models of the multitrait-multimethod matrix. Paper presented at the meeting of the American Educational Research Association. (ERIC ED 283850, TM 870369).Google Scholar
Wothke, W., Browne, M. W. (1990). The direct product model for the MTMM matrix parameterized as a second order factor analysis model. Psychometrika, 55, 255–262.CrossRefGoogle Scholar