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12 - Modelling individual differences in change through latent variable growth and mixture growth modelling: basic principles and empirical examples

Published online by Cambridge University Press:  22 September 2009

Jan-eric Gustafsson
Affiliation:
Department of Education, Göteborg University, Sweden
Andreas Demetriou
Affiliation:
University of Cyprus
Athanassios Raftopoulos
Affiliation:
University of Cyprus
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Summary

Introduction

One of the most interesting and challenging tasks in the intersection of the fields of developmental psychology and differential psychology is the study of individual differences in development over time. To understand the nature of change during development, how change occurs, and what causes change it seems necessary not only to investigate general patterns, but also to take individual differences into account. There was, however, a time, not so long ago, when those with a focus on individual differences were reluctant to approach questions about change, because measurement of change was regarded as hopelessly difficult (e.g. Harris 1963). And those focusing on developmental problems have tended to neglect individual differences altogether.

During the last two decades the situation has changed dramatically for the better, however. One reason for this is the appearance of a new class of analytic techniques, namely growth curve models, or, for short, growth models. The basic idea of growth modelling is to describe developmental trajectories over time in terms of parsimonious models, the parameters of which may capture aspects such as initial level and rate of change. The analysis of growth curves was early identified as an important approach to research in developmental psychology (e.g. Bayley 1956). However, it was not until appropriate statistical techniques were developed in the 1980s that growth models were adopted on a wider scale in developmental psychology.

Type
Chapter
Information
Cognitive Developmental Change
Theories, Models and Measurement
, pp. 379 - 402
Publisher: Cambridge University Press
Print publication year: 2005

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References

Bayley, N. (1956). Individual patterns of development. Child Development, 27, 45–74Google ScholarPubMed
Dawson, T. L. (2002). New tools, new insights: Kohlberg's moral reasoning stages revisited. International Journal of Behaviour Development, 26, 154–66CrossRefGoogle Scholar
Demetriou, A., Christou, C., Spanoudis, G. and Platsidou, M. (2002). The development of mental processing: efficiency, working memory and thinking. Monographs of the Society for Research in Child Development, serial no. 268, 67(1)
Duncan, T. E., Duncan, S. C., Strycker, L. A. and Li, F. (1999). An introduction to latent variable growth curve modelling. Concepts, issues, and applications. Mahwah, NJ: Lawrence Erlbaum Associates
Fischer, K. W. and Dawson, T. L. (2002). A new kind of developmental science: using models to integrate theory and research. Commentary in Demetriou, A., Christou, C., Spanoudis, G. and Platsidou, M. (2002). The development of mental processing: efficiency, working memory and thinking. Monographs of the Society for Research in Child Development, serial no. 268, 67(1), 156–67CrossRefGoogle Scholar
Goldstein, H. (1995). Multilevel statistical models. London: Edward Arnold
Gustafsson, J. E. (2002). Measurement from a hierarchical point of view. In H. I. Braun, D. N. Jackson and D. E. Wiley (eds.) The role of constructs in psychological and educational measurement (pp. 73–95). Mahwah, NJ: Lawrence Erlbaum Associates
Gustafsson, J.-E. and Reuterberg, S.-E. (2000). Metodproblem vid studier av Högskoleprovets prognosförmåga – och deras lösning! (Methodological problems in studies of the prognostic power of the SweSAT – and their solution). Pedagogisk Forskning i Sverige, 5(4), 273–83Google Scholar
Gustafsson, J.-E. and Stahl, P. A. (2000). STREAMS User's Guide. Version 2.5. Molndal, Sweden: MultivariateWare
Gustafsson, J.-E. (2001). Using Mplus under STREAMS 2.5. Molndal, Sweden: MultivariateWare
Gustafsson, J.-E., Andersson, A. and Hansen, M. (2000). Prestationer och prestationsskillnader i 1990-talets skola. (Achievement and achievement differences in school during the 1990s). SOU 2000: 39, pp. 135–211
Gustafsson, J.-E., Wedman, I. and Westerlund, A. (1992). The dimensionality of the Swedish Scholastic Aptitude Test. Scandinavian Journal of Educational Research, 36, 21–39CrossRefGoogle Scholar
Harris, C. W. (1963). Problems in measuring change. Madison: University of Wisconsin Press
Heath, R. (1978). Personality and the development of students in higher education. In Parker, C. A. (ed.) Encouraging development in college students. Minneapolis: University of Minnesota Press
Humphreys, L. G. (1968). The fleeting nature of college academic success. Journal of Educational Psychology, 59, 375–80CrossRefGoogle ScholarPubMed
McArdle, J. J. (1988). Dynamic but structural equation modelling of repeated measures data. In R. B. Cattell and J. Nesselroade (eds.) Handbook of multivariate experimental psychology (2nd edn, pp. 561–614). New York: Plenum PressCrossRef
McArdle, J. J. and Epstein, D. (1987). Latent growth curves within developmental structural equation models. Child Development, 58, 110–33CrossRefGoogle ScholarPubMed
Meredith, W. and Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–22CrossRefGoogle Scholar
Muthén, B. (1989). Latent variable modelling in heterogeneous populations. Psychometrika, 54, 557–85CrossRefGoogle Scholar
Muthén, B, (1996). Growth modelling with binary responses. In A. V. Eye and C. Clogg (eds.) Categorical variables in developmental research: methods of analysis (pp. 37–54). San Diego, CA: Academic PressCrossRef
Muthén, B. (1997). Latent variable growth modelling with multilevel data. In M. Berkane (ed.) Latent variable modelling with application to causality (pp. 149–61). New York: Springer VerlagCrossRef
Muthén, B. (2000). Methodological issues in random coefficient growth modelling using a latent variable framework: applications to the development of heavy drinking. In J. Rose, L. Chassin, C. Presson and J. Sherman (eds.) Multivariate applications in substance use research (pp. 113–40). Hillsdale, NJ: Erlbaum
Muthén, B. (2001a). Second-generation structural equation modelling with a combination of categorical and continuous latent variables: new opportunities for latent class/latent growth modelling. In Collins, L. M. and Sayer, A. (eds.) New methods for the analysis of change (pp. 291–322). Washington, DC: APA
Muthén, B. (2001b). Latent variable mixture modelling. In G. A. Marcoulides and R. E. Schumacker (eds.) New developments and techniques in structural equation modelling (pp. 1–33). Lawrence Erlbaum Associates
Muthén, B., Kaplan, D. and Hollis, M. (1987). On structural equation modelling with data that are not missing completely at random. Psychometrika, 42, 431–62CrossRefGoogle Scholar
Muthén, B. and Khoo, S. T. (1998). Longitudinal studies of achievement growth using latent variable modelling. Learning and individual differences, special issue: latent growth curve analysis, 10, 73–101CrossRefGoogle Scholar
Muthén, B. and Muthén, L. (2000). Integrating person-centered and variable-centered analysis: growth mixture modelling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24, 882–91CrossRefGoogle Scholar
Muthén, L. K. and Muthén, B. O. (1998). Mplus User's Guide. Los Angeles, CA: Muthén and Muthén
Muthén, L. K. and Muthén, B. O. (2001). Mplus User's Guide (2nd edn). Los Angeles, CA: Muthén and Muthén
Perry, W. G. (1970). Forms of intellectual and ethical development in the college years: a scheme. New York: Holt, Rinehart and Winston
Raudenbush, S. W. and Chan, W. (1992). Growth curve analysis in accelerated longitudinal designs. Journal of Research in Crime and Delinquency, 29, 387–411CrossRefGoogle Scholar
Reuterberg, S.-E. (2002). Correcting validity coefficients for restriction of range and disjunctive selection rules with missing-data modelling: a simulation study. Manuscript
Rogosa, D. R., Brandt, D. and Zimowski, M. (1982). A growth curve approach to the measurement of change. Psychological Bulletin, 92, 726–48CrossRefGoogle Scholar
Rogosa, D. R. and Willett, J. B. (1985). Understanding correlates of change by modelling individual differences in growth. Psychometrika, 50, 203–28CrossRefGoogle Scholar
Rose, S. P. and Fischer, K. W. (1998). Models and rulers in dynamical development. British Journal of Developmental Psychology, 16, 123–31CrossRefGoogle Scholar
Svensson, A., Gustafsson, J.-E. and Reuterberg, S.-E. (2001). Högskoleprovets prognosvärde. Samband mellan provresultat och framgång första studieåret för civilingenjörs-, jurist-och lärarutbildningarna. (The prognostic power of the SweSAT. Relations between test performance and first year achievement for civil engineers, lawyers, and teachers). National Agency for Higher Education, Report 2001: 19R
Willett, J. B. and Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and predictors of individual change over time. Psychological Bulletin, 116, 363–81CrossRefGoogle Scholar

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