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A Multilevel CFA-MTMM Model for Nested Structurally Different Methods

Author

Listed:
  • Tobias Koch

    (Leuphana Universität Lüneburg)

  • Martin Schultze

    (Freie Universität Berlin)

  • Jeremy Burrus

    (Professional Examination Service)

  • Richard D. Roberts

    (Professional Examination Service)

  • Michael Eid

    (Freie Universität Berlin)

Abstract

The numerous advantages of structural equation modeling (SEM) for the analysis of multitrait–multimethod (MTMM) data are well known. MTMM-SEMs allow researchers to explicitly model the measurement error, to examine the true convergent and discriminant validity of the given measures, and to relate external variables to the latent trait as well as the latent method factors in the model. According to Eid et al. (2008) different MTMM measurement designs require different types of MTMM-SEMs. Eid et al. (2008) proposed three different MTMM-SEMs for measurement designs with (a) structurally different methods, (b) interchangeable methods, and (c) a combination of both types of methods. In the present work, we extend this taxonomy to a multilevel correlated traits–correlated methods minus one [CTC(M − 1)] model for nested structurally different methods. The new model enables researchers to study method effects on both measurement levels (i.e., within and between clusters, classes, schools, etc.) and evaluate the convergent and discriminant validity of the measures. The statistical performance of the model is examined by a simulation study, and recommendations for the application of the model are given.

Suggested Citation

  • Tobias Koch & Martin Schultze & Jeremy Burrus & Richard D. Roberts & Michael Eid, 2015. "A Multilevel CFA-MTMM Model for Nested Structurally Different Methods," Journal of Educational and Behavioral Statistics, , vol. 40(5), pages 477-510, October.
    • Handle: RePEc:sae:jedbes:v:40:y:2015:i:5:p:477-510
    DOI: 10.3102/1076998615606109
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    References listed on IDEAS

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    1. Michael Eid, 2000. "A multitrait-multimethod model with minimal assumptions," Psychometrika, Springer;The Psychometric Society, vol. 65(2), pages 241-261, June.
    2. Steffi Pohl & Rolf Steyer & Katrin Kraus, 2008. "Modelling method effects as individual causal effects," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 41-63, January.
    3. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    4. Albert Satorra & Peter Bentler, 2001. "A scaled difference chi-square test statistic for moment structure analysis," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 507-514, December.
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    Cited by:

    1. Tobias Koch & Martin Schultze & Jana Holtmann & Christian Geiser & Michael Eid, 2017. "A Multimethod Latent State-Trait Model for Structurally Different And Interchangeable Methods," Psychometrika, Springer;The Psychometric Society, vol. 82(1), pages 17-47, March.

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