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Original Article

Specifying Measurement Error Correlations in Latent Growth Curve Models With Multiple Indicators

Published Online:January 01, 2014https://doi.org/10.1027/1614-2241/a000082

Abstract

In this tutorial paper we focus on a multi-item Latent Growth Curve model for modeling change across time of a latent variable measured by multiple items at different occasions: in the structural part the latent variable grows according to a random slope linear model, whereas in the measurement part the latent variable is measured at each occasion by a conventional factor model with time-invariant loadings. The specification of a multi-item Latent Growth Curve model involves several interrelated choices: indeed, the features of the structural part, such as the functional form of the growth, are linked to the features of the measurement part, such as the correlation structure across time of measurement errors. In the paper, we give guidelines on the specification of the variance-covariance structure of measurement errors. In particular, we investigate the empirical implications of different specification strategies through an analysis of student ratings collected in four academic years about courses of the University of Florence. In the application we compare three correlation structures (independence, lag-1, and compound symmetry), illustrating the differences in terms of substantive assumptions, model fit, and interpretability of the results.

References

  • Boker, S. M. , Neale, M. C. , Maes, H. H. , Wilde, M. J. , Spiegel, M. , Brick, T. R. , Spies, J. , Estabrook, R. , Kenny, S. , Bates, T. C. , Mehta, P. , Fox, J. (2011). OpenMx: An open source extended structural equation modeling framework. Psychometrika, 76, 306–317. First citation in articleCrossref, Google Scholar

  • Boker, S. M. , Neale, M. C. , Maes, H. H. , Wilde, M. J. , Spiegel, M. , Brick, T. R. , Estabrook, R. , Bates, T. C. , Mehta, P. , von Oertzen, T. , Gore, R. J. , Hunter, M. D. , Hackett, D. C. , Karch, J. , Brandmaier, A. (2012). OpenMx 1.2 User guide. Retrieved from openmx.psyc.virginia.edu First citation in articleGoogle Scholar

  • Bollen, K. A. , Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley. First citation in articleGoogle Scholar

  • Ferrer, E. , Balluerka, N. , Widaman, K. F. (2008). Factorial invariance and the specification of second-order latent growth models. Methodology, 4, 22–36. First citation in articleLink, Google Scholar

  • Giusti, C. , Varriale, R. (2008). Un modello multilivello per l’analisi longitudinale della valutazione della didattica [A multi level model for the longitudinal analysis of teacher evaluation] In A. Di Maio, M. Gallo, B. Simonetti (Eds.) Metodi, Modelli e Tecnonologie dell’informazione a Supporto delle Decisioni (parte seconda: applicazioni) (pp. 122–129). Milano, Italy: Franco Angeli. First citation in articleGoogle Scholar

  • Grimm, K. J. , Widaman, K. F. (2010). Residual structures in latent growth curve modeling. Structural Equation Modeling: A Multidisciplinary Journal, 17, 424–442. First citation in articleCrossref, Google Scholar

  • Hancock, G. R. , Kuo, W.-L. , Lawrence, F. R. (2001). Teacher’s corner: An illustration of second-order latent growth models. Structural Equation Modeling, 8, 470–489. First citation in articleCrossref, Google Scholar

  • McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In J. R. Nesselroade, R. B. Cattell (Eds.), Handbook of multivariate experimental psychology (2nd ed.). (pp. 561–614). New York, NY: Plenum. First citation in articleCrossref, Google Scholar

  • Meredith, W. , Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122. First citation in articleCrossref, Google Scholar

  • Muthén, B. (2004). Latent variable analysis: Growth mixture modeling and related techniques for longitudinal data. In D. Kaplan (Ed.), Handbook of quantitative methodology for the social sciences (pp. 345–368). Newbury Park, CA: Sage. First citation in articleCrossref, Google Scholar

  • Steele, F. (2008). Multilevel models for longitudinal data. Journal of the Royal Statistical Society A, 171, 5–19. First citation in articleGoogle Scholar

  • Vermunt, J. K. , Magidson, J. (2005). Technical guide for Latent GOLD 4.0: Basic and advanced. Belmont, MA: Statistical Innovations. First citation in articleGoogle Scholar

  • Vermunt, J. K. , Magidson, J. (2008). LG-Syntax user’s guide: Manual for Latent GOLD 4.5 syntax module. Belmont, MA: Statistical Innovations. First citation in articleGoogle Scholar

  • Wänström, L. (2009). Sample sizes for two-group second-order latent growth curve models. Multivariate Behavioral Research, 44, 588–619. First citation in articleCrossref, Google Scholar

  • Wolfinger, R. D. (1996). Heterogeneous variance: Covariance structures for repeated measures. Journal of Agricultural, Biological, and Environmental Statistics, 1, 205–230. First citation in articleCrossref, Google Scholar

  • Wu, A. D. , Liu, Y. , Gadermann, A. M. , Zumbo, B. D. (2010). Multiple-indicator multilevel growth model: A solution to multiple methodological challenges in longitudinal studies. Social Indicators Research, 97, 123–142. First citation in articleCrossref, Google Scholar