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Multitrait-multimethod change modelling. (English) Zbl 1443.62411

Summary: The first author [Multitrait-multimethod-multioccasion modeling. München: AVM – Akademische Verlagsgemeinschaft München (2009)] recently presented the Correlated State-Correlated (Methods-Minus-1) [CS-C(M\(-1\))] model for analysing longitudinal multitrait-multimethod (MTMM) data. In the present article, the authors discuss the extension of the CS-C(M\(-1\)) model to a model that includes latent difference variables, called CS-C(M\(-1\)) change model. The CS-C(M\(-1\)) change model allows investigators to study inter-individual differences in intra-individual change over time, to separate true change from random measurement error, and to analyse change simultaneously for different methods. Change in a reference method can be contrasted with change in other methods to analyse convergent validity of change.

MSC:

62P15 Applications of statistics to psychology

Software:

Mplus
Full Text: DOI

References:

[1] Akaike, H., A new look at the statistical model identification, IEEE Trans. Autom. Contr., 19, 716-723, (1974) · Zbl 0314.62039 · doi:10.1109/TAC.1974.1100705
[2] Arbuckle, J. L.; Marcoulides, G. A. (ed.); Schumacker, R. E. (ed.), Full information estimation in the presence of incomplete data, 243-277, (1996), Mahwah · Zbl 0923.62055
[3] Bentler, P. M., Comparative fit indexes in structural models, Psychol. Bull., 107, 238-246, (1990) · doi:10.1037/0033-2909.107.2.238
[4] Bollen, K.A.: Structural Equations with Latent Variables. Wiley, New York (1989) · Zbl 0731.62159
[5] Burns, G. L.; Haynes, S. N.; Eid, M. (ed.); Diener, E. (ed.), Clinical psychology: construct validation with multiple sources of information and multiple settings, 401-418, (2006), Washington · doi:10.1037/11383-027
[6] Burns, G. L.; Walsh, J. A.; Gomez, R., Convergent and discriminant validity of trait and source effects in ADHD-Inattention and Hyperactivity/Impulsivity measures across a 3-month interval, J. Abnorm. Child Psychol., 15, 529-541, (2003) · doi:10.1023/A:1025453132269
[7] Campbell, D. T.; Fiske, D. W., Convergent and discriminant validation by the multitrait-multimethod matrix, Psychol. Bull., 56, 81-105, (1959) · doi:10.1037/h0046016
[8] Cole, D. A.; Maxwell, S. E., Testing mediational models with longitudinal data: questions and tips in the use of structural equation modelling, J. Abnorm. Psychol., 112, 558-577, (2003) · doi:10.1037/0021-843X.112.4.558
[9] Cole, D. A.; Martin, J. M.; Peeke, L.; Henderson, A.; Harwell, J., Validation of depression and anxiety measures in white and black youths: multitrait-multimethod analyses, Psychol. Assess., 10, 261-276, (1998) · doi:10.1037/1040-3590.10.3.261
[10] Courvoisier, D.S.: Unfolding the constituents of psychological scores: development and application of mixture and multitrait-multimethod LST models. Unpublished doctoral dissertation, University of Geneva, Switzerland, 2006
[11] Courvoisier, D. S.; Nussbeck, F. W.; Eid, M.; Geiser, C.; Cole, D. A., Analysing the convergent validity of states and traits: development and application of multimethod latent state-trait models, Psychol. Assess., 20, 270-280, (2008) · doi:10.1037/a0012812
[12] Cudeck, R., Multiplicative models and MTMM matrices, J. Educ. Stat., 13, 131-147, (1988) · doi:10.2307/1164750
[13] Eid, M., A multitrait-multimethod model with minimal assumptions, Psychometrika, 65, 241-261, (2000) · Zbl 1291.62203 · doi:10.1007/BF02294377
[14] Eid, M., Diener, E.: Handbook of Multimethod Measurement in Psychology. American Psychological Association, Washington (2006) · doi:10.1037/11383-000
[15] Eid, M.; Schneider, C.; Schwenkmezger, P., Do you feel better or worse? The validity of perceived deviations of mood states from mood traits, Eur. J. Pers., 13, 283-306, (1999) · doi:10.1002/(SICI)1099-0984(199907/08)13:4<283::AID-PER341>3.0.CO;2-0
[16] Eid, M.; Lischetzke, T.; Nussbeck, F. W.; Trierweiler, L. I., Separating trait effects from trait-specific method effects in multitrait-multimethod models: a multiple indicator CT-C(M−1) model, Psychol. Methods, 8, 38-60, (2003) · doi:10.1037/1082-989X.8.1.38
[17] Eid, M.; Lischetzke, T.; Nussbeck, F. W.; Eid, M. (ed.); Diener, E. (ed.), Structural equation models for multitrait-multimethod data, 283-299, (2006), Washington · doi:10.1037/11383-020
[18] Eid, M.; Nussbeck, F. W.; Geiser, C.; Cole, D. A.; Gollwitzer, M.; Lischetzke, T., Structural equation modelling of multitrait-multimethod data: different models for different types of methods, Psychol. Methods, 13, 230-253, (2008) · doi:10.1037/a0013219
[19] Geiser, C.: Multitrait-Multimethod-Multioccasion Modeling. AVM, München (2009)
[20] Geiser, C.; Eid, M.; Nussbeck, F. W., On the meaning of the latent variables in the CT-C(M−1) model: a comment on Maydeu-Olivares & Coffman (2006), Psychol. Methods, 13, 49-57, (2008) · doi:10.1037/1082-989X.13.1.49
[21] Geiser, C.; Eid, M.; Nussbeck, F. W.; Courvoisier, D. S.; Cole, D. A., Analysing true change in longitudinal multitrait-multimethod studies: application of a multimethod change model to depression and anxiety in children, Dev. Psychol., 46, 29-45, (2010) · doi:10.1037/a0017888
[22] Grimm, K. J.; Pianta, R. C.; Konold, T., Longitudinal multitrait-multimethod models for developmental research, Multivar. Behav. Res., 44, 233-258, (2009) · doi:10.1080/00273170902794230
[23] Jöreskog, K. G.; Jöreskog, K. G. (ed.); Sörbom, D. (ed.), Statistical models and methods for analysis of longitudinal data, 129-169, (1979), Cambridge
[24] Julian, M. W., The consequences of ignoring multilevel data structures in nonhierarchical covariance modelling, Struct. Equ. Model., 8, 325-352, (2001) · doi:10.1207/S15328007SEM0803_1
[25] King-Kallimanis, B.L., Oort, F.J., Garst, G.J.A.: Using structural equation modelling to detect measurement bias and response shift in longitudinal data. Arch. Stat. Anal. (2010) · Zbl 1443.62413
[26] Kovacs, M., The Children’s Depression Inventory (CDI), Psychopharmacol. Bull., 21, 995-998, (1985)
[27] Lance, C. E.; Noble, C. L.; Scullen, S. E., A critique of the correlated trait-correlated method and correlated uniqueness models for multitrait-multimethod data, Psychol. Methods, 7, 228-244, (2002) · doi:10.1037/1082-989X.7.2.228
[28] Little, R.J.A., Rubin, D.B.: Statistical Analysis with Missing Data. Wiley, New York (2003)
[29] Marsh, H. W., Multitrait-multimethod analyses: inferring each trait/method combination with multiple indicators, Appl. Meas. Educ., 6, 49-81, (1993) · doi:10.1207/s15324818ame0601_4
[30] Marsh, H. W.; Hocevar, D., A new, more powerful approach to multitrait-multimethod analyses: application of second-order confirmatory factor analysis, J. Appl. Psychol., 73, 107-117, (1988) · doi:10.1037/0021-9010.73.1.107
[31] McArdle, J. J.; Cattell, R. B. (ed.); Nesselroade, J. (ed.), Dynamic but structural equation modelling of repeated measures data, 561-614, (1988), New York
[32] Muthén, L.K., Muthén, B.O.: Mplus User’s Guide, 5th edn. Muthén & Muthén, Los Angeles (1998-2007)
[33] Muthén, B. O.; Satorra, A.; Marsden, P. V. (ed.), Complex sample data in structural equation modelling, 267-316, (1995), Washington
[34] Oort, F. J., Three-mode models for multitrait-multimethod data, Methodology, 5, 78-87, (2009)
[35] Pohl, S.; Steyer, R., Modeling method effects as individual causal effects, J. R. Stat. Soc. A Stat., 171, 41-63, (2008)
[36] Raffalovich, L. E.; Bohrnstedt, G. W., Common, specific, and error variance components of factor models: estimation with longitudinal data, Sociol. Methods Res., 15, 385-405, (1987) · doi:10.1177/0049124187015004003
[37] Reynolds, C. R.; Richmond, B. O., What I think and feel: a revised measure of children’s manifest anxiety, J. Abnorm. Child Psychol., 6, 271-280, (1978) · doi:10.1007/BF00919131
[38] Satorra, A., Bentler, P.M.: A scaled difference chi-square test statistic for moment structure analysis. UCLA Department of Statistics. http://preprints.stat.ucla.edu/260/chisquare.pdf (1999). Accessed 8 January 2007
[39] Schafer, J. L.; Graham, J. W., Missing data: our view of the state of the art, Psychol. Methods, 7, 147-177, (2002) · doi:10.1037/1082-989X.7.2.147
[40] Schermelleh-Engel, K.; Moosbrugger, H.; Müller, H., Evaluating the fit of structural equation models: test of significance and descriptive goodness-of-fit measures, Methods Psychol. Res. Online, 8, 23-74, (2003)
[41] Scherpenzeel, A.; Saris, W. E.; Montfort, K. (ed.); Satorra, A. (ed.); Oud, H. (ed.), Multitrait-multimethod models for longitudinal research, 381-401, (2007), New York
[42] Sörbom, D., Detection of correlated errors in longitudinal data, Br. J. Math. Stat. Psychol., 28, 138-151, (1975) · Zbl 0324.62048
[43] Steiger, J. H., Structural model evaluation and modification: an interval estimation approach, Multivar. Behav. Res., 25, 173-180, (1990) · doi:10.1207/s15327906mbr2502_4
[44] Steyer, R.; Eid, M.; Schwenkmezger, P., Modeling true intraindividual change: true change as a latent variable, Methods Psychol. Res. Online, 2, 21-33, (1997)
[45] Steyer, R.; Partchev, I.; Shanahan, M.; Little, T. D. (ed.); Schnabel, K. U. (ed.); Baumert, J. (ed.), Modeling true intra-individual change in structural equation models: the case of poverty and children’s psychosocial adjustment, 109-126, (2000), Hillsdale
[46] Vautier, S., A longitudinal SEM approach to STAI data: two comprehensive multitrait-multistate models, J. Pers. Assess., 83, 167-179, (2004) · doi:10.1207/s15327752jpa8302_11
[47] Vautier, S.; Steyer, R.; Boomsma, A., The true-change model with individual method effects: reliability issues, Br. J. Math. Stat. Psychol., 61, 379-399, (2008) · doi:10.1348/000711007X206826
[48] Widaman, K. F.; Reise, S. P.; Bryant, K. J. (ed.); Windle, M. (ed.); West, S. G. (ed.), Exploring the measurement invariance of psychological instruments: applications in the substance use domain, 281-324, (1997), Washington · doi:10.1037/10222-009
[49] Wothke, W.; Little, T. D. (ed.); Schnabel, K. U. (ed.); Baumert, J. (ed.), Longitudinal and multi-group modelling with missing data, 219-240, (2000), Hillsdale
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