Latent Variable Growth Modeling with Multilevel Data
Growth modeling of multilevel data is presented within a latent variable framework that allows analysis with conventional structural equation modeling software. Latent variable modeling of growth considers a vector of observations over time for an individual, reducing the two-level problem to a one-level problem Analogous to this, three-level data on students, time points, and schools can be modeled by a two-level growth model. An interesting feature of this two-level model is that contrary to recent applications of multilevel latent variable modeling, a mean structure is imposed in addition to the covariance structure. An example using educational achievement data illustrates the methodology.
Unable to display preview. Download preview PDF.
- Bock, R. D. (1989). Multilevel analysis of educational data. San Diego, CA: Academic Press.Google Scholar
- Bryk, A. S. and Raudenbush, S. W. (1992). Hierarchical linear models: Applications and data analysis methods. Newbury Park, CA: Sage Publications.Google Scholar
- Goldstein, H. I. (1987). Multilevel models in educational and social research. London: Oxford University Press.Google Scholar
- Jöreskog, K. G. and Sörbom, D. (1977). Statistical models and methods for analysis of longitudinal data. In D. J. Aigner and A. S. Goldberger (eds.), Latent variables in socio-economic models (pp. 285–325. )Amsterdam. North-HollandGoogle Scholar
- Meredith, W. and Tisak, J. (1984). “Tuckerizing” curves. Paper presented at the Psychometric Society annual meetings, Santa Barbara, CA.Google Scholar
- Muthén, B. (1990). Mean and covariance structure analysis of hierarchical data. Paper presented at the Psychometric Society meeting in Princeton, New Jersey. UCLA Statistics Series #62, August 1990.Google Scholar
- Muthén, B. (1991). Analysis of longitudinal data using latent variable models with varying parameters. In L. Collins and J. Horn (eds.)Best Methods for the Analysis of Change. Recent Advances Unanswered Questions Future Directions(pp. 1–17). Washington D.C.: American Psychological Association.Google Scholar
- Muthén, B. (1993). Latent variable modeling of growth with missing data and multilevel data. In C.R. Rao and C. M. Cuadras (eds.)Multivariate Analysis: Future Directions 2(pp. 199–210). Amsterdam: North-Holland.Google Scholar
- Muthén, B. (1994a). Latent variable modeling of longitudinal and multilevel data. Invited paper for the annual meeting of the American Sociological Association, Section on Methodology, Showcase Session, Los Angeles, August 1994.Google Scholar
- Muthén, B. (1994b). Multilevel covariance structure analysis. In J. J Hox and I. G. Kreft (eds.), Multilevel analysis methods, (pp. 376–391). Thousand Oakes, CA: Sage Publications.Google Scholar
- Muthén, B. and Satorra, A. (1995). Complex sample data in structural equation modeling. Forthcoming inSociological Methodology1995.Google Scholar
- Wheaton, B., Muthén, B., Alwin, D., and Summers. G. (1977). Assessing reliability and stability in panel models. In D.R. Heise (ed.)Sociological Methodology1977 (pp. 84–136). San Francisco: Jossey-Bass.Google Scholar