Abstract
This study introduces three growth modeling techniques: latent growth modeling (LGM), hierarchical linear modeling (HLM), and longitudinal profile analysis via multidimensional scaling (LPAMS). It compares the multilevel growth parameter estimates and potential predictor effects obtained using LGM, HLM, and LPAMS. The purpose of this multilevel growth analysis is to alert applied researchers to selected analytical issues that are required for consideration in decisions to apply one of these three approaches to longitudinal academic achievement studies. The results indicated that there were no significant distinctions on either mean growth parameter estimates or on the effects of potential predictors to growth factors at both the student and school levels. However, the study also produced equivocal findings on the statistical testing of variance and covariance growth parameter estimates. Other practical issues pertaining to the three growth modeling methods are also discussed.
Similar content being viewed by others
References
Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis.Psychometrika, 49, 155–173.
Bentler, P. M., & Liang, J. (2003). Two-level mean and covariance structures: Maximum likelihood via an EM algorithm. In S. P. Reise & N. Duan (Eds.),Multilevel modeling: Methodological advances, issues, and applications (pp. 53–70). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
Biesanz, J. C., Deeb-Sossa, N., Papadakis, A., Bollen, K. A., & Curran, P. J. (2004). The role of coding time in estimation and interpreting growth curve models.Psychological Methods, 9, 30–52.
Bollen, K. A. (1989).Structural equations with latent variables. New York: John Wiley & Sons.
Boosma, A. (1985). Nonconvergence, improper solutions, and starting values in LISREL maximum likelihood estimation,Psychometrika, 50, 229–242.
Borg, I., & Groenen, P. (1997).Modern multidimensional scaling: Theory and applications, New York: Springer.
Brekke, J. S., Long, J. D., Nesbitt, N., & Sobel, E. (1997). The impact of service characteristics on functional outcomes from community support programs for persons with schizophrenia: a growth curve analysis.Journal of Consulting and Clinical Psychology, 65, 464–475.
Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In K. A. Bollen, & J. S. Long (Eds.),Testing Structural Equation Models (pp. 136–162). Beverly Hills, CA: Sage.
Bryk, A. S., & Raudenbush, S. W. (1987). Application of hierarchical linear models to assessing change.Psychological Bulletin, 101, 147 - 158.
Chou, C. P., Bentler, P. M., & Satorra, A. (1991). Scaled test statistics and robust standard for non-normal data in covariance structure analysis: A Monte Carlo study.British Journal of Mathematical and Statistical Psychology, 44, 359 - 368.
Cheung, M. W.-L., & Au, K. (2005). Applications of multilevel structural equation modeling to cross-culture research.Structural Equation Modeling, 12, 598 - 619.
Curran, P.J. (2003). Have multilevel models been structural equation models all along?Multivariate Behavioral Research, 38, 529–569.
Curran, P. J., & Hussong, A. M. (2002). Structural Equation Modeling of Repeated Measures data: Latent Curve Analysis. In D. S. Moskowitz & Scott L. Hershberger (Eds.),Modeling Intraindividual Variability with Repeated Measures Data: Methods and Application. New Jersey: Lawrence Erlbaum Association.
Davison, M. L. (1983).Multidimensional scaling. New York: Wiley.
Davison, M. L., Gasser, M., & Ding, S. (1996). Identifying major profile patterns in population: An exploratory study of WAIS and GATB patterns.Psychological Assessment, 8, 26 - 31.
Davison, M. L., Kang, H., & Kim, S. (1999). The structure of ability profile pattern: A multidimensional scaling perspective on the structure of intellect. In P. L. Ackerman, P. C. Kyllonen, & R. D. Roberts (Eds.),Learning and individual differences: Process, trait, and content determinant (pp. 187 - 204). Washington, D.C.: APA Books.
Ding, C. (2003). Exploratory longitudinal profile analysis via multidimensional scaling.Practical Assessment,Research & Evaluation, On-line serial 8.
Ding, C. S., Davison, M. L., & Petersen, A. C. (2005). Multidimensional scaling analysis of growth and change.Journal of Educational Measurement, 42, 171–191.
du Toit, S. H. C., & Cudeck, R. (2001). The analysis of nonlinear random coefficient regression models with LISREL using constraints. In R. Cudeck, S. H. C. du Toit, & D. Sorbom, (Eds.),Structural equation modeling: Present and future (pp. 259–278). Lincolnwood, IL: Scientific Software International.
Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models.Structural Equation Modeling, 8, 430 - 457.
Foorman, B., Francis, D., Novy, D., & Liberman, D. (1991). How letter-sound instruction mediates progress in first-grade reading and spelling.Journal of Educational Psychology, 83, 456–469.
Gold, M S., Bentler, P. M., & Kim, K. H. (2003). A comparison of maximum-likelihood and asymptotically distribution-free methods of treating incomplete nonnormal data.Structural Equation Modeling, 10, 47 - 79.
Grewal, R., Cote, J. A., & Baumgartner, H. (2004). Multicollinearity and Measurement Error in Structural Equation Models: Implications for Theory Testing,Marketing Science, 23, 519–529.
Huttenlocher, J. E., Haight, W., Bryk, A. S., & Seltzer, M. (1991). Early vocabulary growth: Relation to language input and gender.Developmental Psychology, 27, 236 - 249.
Jöreskog, K. G. (1969). A general approach to confirmatory maximum likelihood factor analysis.Psychometrika, 34, 183–202.
Kim, S., Frisby, C. L., & Davison, M. L. (2004). Estimating cognitive profiles using profile analysis via multidimensional scaling (PAMS).Multivariate Behavioral Research, 39(4), 595 - 624.
Kline, R. B. (1998).Principles and Practice of structural equation modeling. New York: The Guliford press.
Kmenta, J. (1971).Elements of econometrics. New York: MacMillan.
Kruskal, J. B. (1964). Nonmetric multidimensional scaling: A numerical method.Psychometrika, 29, 115 - 129.
Linda, N. Y., Lee, S.-Y., & Poon, W.-Y. (1993). Covariance structure analysis with three level data.Computational Statistics & Data Analysis, 15, 159–178.
Longford, N. T., & Muth’en, B. O. (1992). Factor analysis for clustered observations.Psychometrika, 57, 581–597.
MacCallum, R. (1986). Specification searches in covariance structure modeling.Psychological Bulletin, 100, 107–120.
Meredith, W., & Tisak, J. (1990). Latent curve analysis.Psychometrika, 55, 107–122.
Miccéri, T. (1989). The unicorn, the normal curve, and other improbable creatures.Psychological Bulletin, 105, 156–166.
Muthén, B. O. (1989). Latent variable modeling in heterogeneous populations.Psychometrika, 54, 557–585.
Muthén, B. O. (1991). Analysis of longitudinal data using latent variable models with varying parameters. In L. M. Collins, & J. L. Horn (Eds.),Best methods for the analysis of change: Recent advances, unanswered questions, future directions. Washington, D.C.:APA.
Muthén, B. O. (1994). Multilevel covariance structure analysis.Sociological Methods and Research, 22, 376–398.
Raudenbush, S. W., & Bryk, A. S. (2002).Hierarchical linear models: Applications and data analysis methods. California: Saga Publications, Inc.
Rogosa, D. R., & Willett, J. B. (1985). Understanding correlates of change by modeling individual differences in growth.Psychometrika, 50, 203–228
Rovine, M. J. & Molenaar P. M.(1998). A LISREL model for the analysis of repeated measures with a patterned covariance matrix.Structural Equation Modeling, 5, 318–343.
Smith, K. E., Landry, S. H., & Swank, P. R. (2000). Does the content of mothers’ verbal stimulation explain differences in the children’s development of verbal and nonverbal cognitive skills?Journal of School Psychology, 38, 27–49
Stoolmiller, M. (1995). Using latent growth models to sutyd developmental processes. In J. M. Gottman (Ed.), The analysis of change (pp. 103–138). Mahwah, NJ: Erlbaum.
Vasu, E. S., & Elmore, P. B. (1975).The effect of multicollinearity and the violation of the assumption of normality on the testing of hypotheses in regression analysis. Paper presented at the Annual Meeting of the American Educational Research Association. Washington, D.C.
Willett, J. B., & Sayer, A. G. (1994). Using covariance structure analysis to detect correlated and predictors of individual change over time.Psychological Bulletin, 116, 363–381.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shin, T. comparison of three growth modeling techniques in the multilevel analysis of longitudinal academic achievement scores: Latent growth modeling, hierarchical linear modeling, and longitudinal profile analysis via multidimensional scaling. Asia Pacific Educ. Rev. 8, 262–275 (2007). https://doi.org/10.1007/BF03029261
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF03029261