Hostname: page-component-6766d58669-kn6lq Total loading time: 0 Render date: 2026-05-23T10:44:04.963Z Has data issue: false hasContentIssue false
  • English
  • Français

A Multitrait-Multimethod Model with Minimal Assumptions

Published online by Cambridge University Press:  01 January 2025

Michael Eid
Michael Eid*
Affiliation:
University of Trier
*
Requests for reprints should be sent to Michael Eid, Fachbereich I - Psychologie, Universitaet Trier, D-54286 Trier, Germany. E-mail: eid@uni-trier.de
Get access Rights & Permissions [Opens in a new window]

Abstract

A new model of confirmatory factor analysis (CFA) for multitrait-multimethod (MTMM) data sets is presented. It is shown that this model can be defined by only three assumptions in the framework of classical psychometric test theory (CTT). All other properties of the model, particularly the uncorrelatedness of the trait with the method factors are logical consequences of the definition of the model. In the model proposed there are as many trait factors as different traits considered, but the number of method factors is one fewer than the number of methods included in an MTMM study. The covariance structure implied by this model is derived, and it is shown that this model is identified even under conditions under which other CFA-MTMM models are not. The model is illustrated by two empirical applications. Furthermore, its advantages and limitations are discussed with respect to previously developed CFA models for MTMM data.

Keywords

multitrait-multimethod modelsconstruct validityclassical test theorystructural equation modeling

Information

Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 2 , June 2000 , pp. 241 - 261
Copyright
Copyright © 2000 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.)

Article purchase

Temporarily unavailable

References

Arbuckle, J.L. (1995). Amos for Windows. Analysis of moment structures (Version 3.5). Chicago, IL: Smallwaters.Google Scholar
Bagozzi, R.P. (1993). Assessing construct validity in personality research: Applications to measures of self-esteem. Journal of Research in Personality, 27, 49–87.CrossRefGoogle Scholar
Bentler, P. (1992). EQS structural equations program manual. Los Angeles: BMDP Statistical Software.Google Scholar
Brannick, M.T., & Spector, P.E. (1990). Estimation problems in the block-diagonal model of the multitrait-multimethod matrix. Applied Psychological Measurement, 14, 325–339.CrossRefGoogle Scholar
Browne, M.W. (1984). The decomposition of multitrait-multimethod matrices. British Journal of Mathematical and Statistical Psychology, 37, 1–21.CrossRefGoogle ScholarPubMed
Campbell, D.T., & Fiske, D.W. (1959). Convergent and discriminant validation by multitrait-multimethod matrix. Psychological Bulletin, 56, 81–105.CrossRefGoogle ScholarPubMed
Cudeck, R. (1988). Multiplicative models and MTMM matrices. Journal of Educational Statistics, 13, 131–147.Google Scholar
Eid, M. (1996). Longitudinal confirmatory factor analysis for polytomous item responses: Model definition and model selection on the basis of stochastic measurement theory. Methods of Psychological Research—Online, 1, 65–85.Google Scholar
Eid, M. (1997). Sonnenschutzverhalten: Ein typologischer Ansatz. Zeitschrift für Gesundheitspsychologie, 5, 73–90 [Sun-protection behavior: A typological approach]Google Scholar
Eid, M., Klusemann, J., & Schwenkmezger, P. (1996). Motivation zum Sonnenschutz: Ein Experiment zu den Auswirkungen von Aufklrungsbotschaften auf die Intention zum Sonnenschutz und das Sonnenschutzverhalten. Zeitschrift für Gesundheitspsychologie, 4, 270–289 [Sun-protection motivation: An experiment on the effects of messages on sun-protection intentions and behavior]Google Scholar
Eid, M., Schneider, C., & Schwenkmezger, P. (1995). Do you feel better or worse? On the validity of perceived deviations of mood states from mood traits. European Journal of Personality, 13, 283–306.3.0.CO;2-0>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. (1993). LISREL 8: User's reference guide. Chicago: Scientific Software.Google Scholar
Kenny, D.A. (1979). Correlation and causality. New York: Wiley.Google Scholar
Kenny, D.A., & Kashy, D.A. (1992). The analysis of the multitrait-multimethod matrix by confirmatory factor analysis. Psychological Bulletin, 112, 165–172.CrossRefGoogle Scholar
Lord, F.M., & Novick, M.R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.Google Scholar
Marsh, H.W. (1989). Confirmatory factor analyses of multitrait-multimethod data: Many problems and a few solutions. Applied Psychological Measurement, 13, 335–361.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., & Grayson, D. (1995). Latent variable models of multitrait-multimethod data. In Hoyle, R.H. (Eds.), Structural equation modeling. Concepts, issues, and applications (pp. 177–198). Thousand Oaks, CA: Sage.Google Scholar
Marsh, H.W., & Hocevar, D. (1988). A new, more powerful approach to multitrait-multimethod analyses: Application of second-order confirmatory factor analysis. Journal of Applied Psychology, 73, 107–117.CrossRefGoogle Scholar
Millsap, R.E. (1995). The statistical analysis of method effects in multitrait-multimethod data: A review. In Shrout, P.E., & Fiske, S.T. (Eds.), Personality research, methods, and theory. A festschrift honoring D.W. Fiske (pp. 93–109). Hillsdale, NJ: Erlbaum.Google Scholar
Mount, M.K. (1984). Psychometric properties of subordinate ratings of managerial performance. Personnel Psychology, 37, 687–702.CrossRefGoogle Scholar
Muthén, L.K., & Muthén, B.O. (1998). Mplus: The comprehensive modeling program for applied researchers. Los Angeles, CA: Muthén & Muthén.Google Scholar
Saris, W.E., & Andrews, F.M. (1991). Evaluation of measurement instruments using a structural modeling approach. In Biemer, P.P., Groves, R.M., Lyberg, L.E., Mathiowetz, N.A., & Sudman, S. (Eds.), Measurement errors in surveys (pp. 575–597). New York: Wiley.Google Scholar
Saris, W.E., & van Meurs, A. (1991). Evaluation of measurement instruments by meta-analysis of multitrait-multimethod studies. Amsterdam: North Holland.Google Scholar
Schmitt, N., & Stults, D.M. (1986). Methodological review: Analysis of multitrait-multimethod matrices. Applied Psychological Measurement, 10, 1–22.CrossRefGoogle Scholar
Shrout, P.E., & Fiske, S.T. (1995). Personality research, methods, and theory. A festschrift honoring D.W. Fiske (pp. 93–109). Hillsdale, NJ: Erlbaum.Google Scholar
Steyer, R. (1988). Conditional expectations: An introduction to the concept and its applications in empirical sciences. Methodika, 2, 53–78.Google Scholar
Steyer, R. (1989). Models of classical psychometric test theory as stochastic measurement models: Representation, uniqueness, meaningfulness, identifiability, and testability. Methodika, 3, 25–60.Google Scholar
West, S.G., Finch, J.F., & Curran, P.J. (1995). Structural equation models with nonnormal variables: Problems and remedies. In Hoyle, R.H. (Eds.), Structural equation modeling. Concepts, issues, and applications (pp. 56–75). Thousand Oaks: Sage.Google Scholar
Widaman, K.F. (1985). Hierarchically nested covariance structure models for multitrait-multimethod data. Applied Psychological Measurement, 9, 1–26.CrossRefGoogle Scholar
Wothke, W. (1996). Models for multitrait-multimethod matrix analysis. In Marcoulides, G.A., & Schumacker, R E. (Eds.), Advanced structural equation modeling (pp. 7–56). Mahwah, NJ: Erlbaum.Google Scholar
Zimmerman, D.W. (1975). Probability spaces, Hilbert spaces, and the axioms of test theory. Psychometrika, 40, 395–412.CrossRefGoogle Scholar
Zimmerman, D.W. (1976). Test theory with minimal assumptions. Educational and Psychological Measurement, 36, 85–96.CrossRefGoogle Scholar