Growth curve modeling has become a mainstay in the study of development. In this article we review some of the flexibility provided by this technique for describing and testing hypotheses about: (1) intraindividual change across multiple occasions of measurement, and (2) interindividual differences in intraindividual change. Through empirical example we demonstrate how linear, quadratic, latent basis, exponential, and multiphase versions of the model can be specified using commonly available SEM/multilevel modeling software and illustrate and discuss how results are obtained and interpreted. Particularly, we underscore the “developmental theory” articulated by each model.
Baltes, P.B. (1997). On the incomplete architecture of human ontogeny: Selection, optimization, and compensation as foundation of developmental theory . American Psychologist, 52, 366—380.
2.
Baltes, P.B., & Nesselroade, J.R. (1979). History and rationales for longitudinal research. In J.R. Nesselroade & P.B. Baltes (Eds.), Longitudinal research in the study of behavior and development (pp. 1—39). New York: Academic Press.
3.
Baltes, P.B., Reese, H.W., & Nesselroade, J.R. (1977). Life-span developmental psychology: Introduction to research methods. Monterrey, CA: Brooks/Cole.
4.
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). Beverley Hills, CA: Sage.
5.
Browne, M.W., & du Toit, S.H.C. (1991). Models for learning data . In L. Collins & J.L. Horn (Eds.), Best methods for the analysis of change (pp. 47—68). Washington, DC: American Psychological Association.
6.
Bryk, A.S., & Raudenbush, S.W. (1992). Hierarchical linear models: Applications and data analysis methods. Newbury Park, CA : Sage.
7.
Cairns, R.B. (1986). Phenomena lost: Issues in the study of development . In J. Valsiner (Ed.), The individual subject and scientific psychology (pp. 97—112). New York: Plenum Press.
8.
Collins, L. (2006). Analysis of longitudinal data: The integration of theoretical model, temporal design, and statistical model. Annual Review ofPsychology, 57, 505—528.
9.
Collins, L.M., & Horn, J.L. (1991). Best methods for the analysis of change: Recent advances, unanswered questions, future directions. Washington, DC: American Psychological Association.
10.
Collins, L.M., & Sayer, A.G. (2001). New methods for the analysis of change. Washington, DC: American Psychological Association .
11.
Cudeck, R., & du Toit, S.H.C. (2002). A version of quadratic regression with interpretable parameters. Multivariate Behavioral Research, 37, 501—519.
12.
Cudeck, R., & Klebe, K.J. (2002). Multiphase mixed-effects models for repeated measures data. Psychological Methods, 7, 41—63.
13.
Estes, W. (1956). The problem of inference from curves based on group data. Psychological Bulletin, 53(2), 134—140.
14.
Ferrer, E., Hamagami, F., & McArdle, J.J. (2004). Modeling latent growth curves with incomplete data using different types of structural equation modeling and multilevel software. Structural Equation Modeling, 11, 452—483.
Ghisletta, P., & Lindenberger, U. (2004). Static and dynamic longitudinal structural analyses of cognitive changes in old age. Gerontology , 50, 12—16.
17.
Lerner, R.M. (2006). Handbook of child psychology. In W. Damon & R.M. Lerner (Eds.), Theoretical models of human development, Vol. 1 (6th ed.). New York: Wiley.
18.
Little, R., & Rubin, D. (1987). Statistical analysis with missing data. New York: Wiley.
19.
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 (Vol. 2, pp. 561—614). New York: Plenum Press.
McArdle, J.J., Ferrer, E., Hamagami, F., & Woodcock, R.W. (2002). Comparative longitudinal structural analyses of growth and decline of multiple intellectual abilities over the life span. Developmental Psychology, 38, 115—142.
22.
McArdle, J.J., & Hamagami, F. (1991). Modeling incomplete longitudinal data using latent growth structural equation models. In L. Collins & J.L. Horn (Eds.), Best methods for the analysis of change (pp. 276—304). Washington, DC: American Psychological Association.
23.
McArdle, J.J., & Hamagami, F. (2001). Latent difference score structural models for linear dynamic analyses with incomplete longitudinal data. In L. Collins & A. Sayer (Eds.), New methods for the analysis of change (pp. 139—175). Washington, DC: American Psychological Association .
24.
McArdle J.J., & Nesselroade, J.R. (2003). Growth curve analysis in contemporary psychological research. In J. Shinka & W. Velicer (Eds.), Comprehensive handbook of psychology, Volume two: Research methods in psychology (pp. 447—480). New York: Wiley .
25.
Meredith, W., & Tisak, J. (1990). Latent curve analysis. Psychometrika , 55, 107—122.
26.
Molenaar, P.C.M. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology, this time forever. Measurement: Interdisciplinary Research and Perspectives, 2, 201—218.
27.
Molenaar, P.C.M., Huizinga, H.M., & Nesselroade, J.R. (2003). The relationship between the structure of interindividual and intra-individual variability: A theoretical and empirical vindication of developmental systems theory. In U.M. Staudinger & U. Lindenberger (Eds.), Understanding human development (pp. 339—360). Boston: Kluwer Academic.
Rogosa, D.R., & Willett, J.B. (1985). Understanding correlates of change by modeling individual differences in growth. Psychometrika, 50, 203—228.
30.
Rovine, M.J., & Molenaar, P.C.M. (1998). The covariance between level and shape in the latent growth curve model with estimated basis coefficients. Methods inPsychological Research Online, 3, 95—107.
31.
Seeman, T.E., Berkman, L.F., Gulanski, B., Robbins, R., Greenspan, S., Charpentier, P., & Rowe, J. (1995). Self-esteem and neuroendocrine response to challenge: MacArthur successful aging studies. Psychosomatic Research , 39, 69—84.
32.
Seeman, T.E., Singer, B., & Charpentier, P. (1995). Gender differences in pattern of HPA axis response to challenge: MacArthur studies of successful aging. Psychoneuroendicrinology, 20, 711—725.
33.
Singer, J.D., & Willett, J.B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York: Oxford University Press.
34.
Verbeke, G., & Mollenberghs, G. (2000). Linear mixed models for longitudinal data. New York: Springer .
