Skip to main content

Methodological Issues in the Application of the Latent Growth Curve Model

  • Chapter

Part of the book series: Mathematical Modelling: Theory and Applications ((MMTA,volume 19))

Abstract

Latent growth curve analysis (McArdle, 1986, 1988; Meredith & Tisak, 1990; Willett & Sayer, 1994) is well suited to analyze systematic change in longitudinal data collected from a panel design. It represents outcome variables explicitly as a function of time and other measures. Specifically, latent growth curve analysis is a Statistical technique to estimate the Parameters that represent the growth curves that are assumed to have given rise to the structure of the repeatedly measured outcome variable over time. Growth curve analysis can be applied just to get a (unconditional) description of the mean growth over a certain period of time. However, the emphasis of this technique lies in explanation of differences between subjects in the parameters describing the growth curves; in other words, in the systematic inter-individual differences in intra-individual change.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature

  • Bandalos, D.L. (2002). The effects of item parceling on goodness-of-fit and Parameter estimate bias. Structural Equation Modeling, 9, 78–102.

    Article  Google Scholar 

  • Bechger, T.M. (1997). Methodological aspects ofcomparison of educational achievement: the case of reading literacy. Doctoral Dissertation, Amsterdam: TT-publications.

    Google Scholar 

  • Bock, R. D. (1979). Univariate and multivariate analysis of variance of timestructured data. In J. R. Nesselroade & P. B. Baltes (Eds.), Longitudinal research in the study of behavior and development (pp. 199–231). New York: Academic Press.

    Google Scholar 

  • Bollen, K. A. (1989). Structural equations with latent variables. New York: Wiley.

    Google Scholar 

  • Browne, M. W. (1982). Covariance structures. In D. M. Hawkins (Ed.), Topics in applied multivariate analysis (pp. 72–141). Cambridge: University Press.

    Chapter  Google Scholar 

  • Browne, M. & DuToit, S. (1991). Analysis of learning curves. In L. Collins & J.L. Hörn (Eds.), Best methodsfor the analysis ofchange. Washington, DC: American Psychological Association.

    Google Scholar 

  • Byrne, B. M., Shavelson, R. J., & Muthen, B. (1989). Testing for the equivalence of factor covariance and meanstructures: the issue of partial measurement invariance. Psychological Bulletin, 705,45–466.

    Google Scholar 

  • Chan, D. (1998). The conceptualization and analysis of change over time: An integrative approach incorporating longitudinal mean and covariance structures analysis (LMACS) and multiple indicator latent growth modeling (MLGM). Organizational Research Methods, 7, 421–483.

    Article  Google Scholar 

  • De Pijper, W. M., & Saris, W. E. (1982). The effect of identification restrictions on the test statistics in latent variable modeis. In K. G. Jöreskog & H. Wold (Eds.), Systems under indirect Observation, part 1. Amsterdam: North Holland.

    Google Scholar 

  • Dolan, C.V. & Molenaar, P.C.M. (1994). Testing specific hypotheses concerning latent group differences in multi-group covariance strueture analysis with struetured means. Multivariate Behavioral Research, 29, 203–222.

    Article  Google Scholar 

  • Drasgow, F. (1987).Study of the measurement bias of two standardized psychological tests. Journal of Applied Psychology, 72, 19–29.

    Article  Google Scholar 

  • Driessen, G., Langen, A. van & Vierke, H. (2000). Basisonderwijs: veldwerkverslag, leerlinggegevens enoudervragenlijst. Basisrapportage PRIMA-cohortonderzoek. Derdemeting 1998/99 [Primary education: research report, pupil’s data and parent’s questionary. Base report PRIMA cohort study. Third wave 1998/99]. Nijmegen: ITS, University of Nijmegen.

    Google Scholar 

  • Duncan, T. E., Duncan, S. C, Strycker, L. A., Li, F., & Alpert, A. (1999). An introduction to latent growth curve modeling: Concepts, issues, and applications Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Garst, H. (2000). Longitudinal research using structural equation modeling applied in studies of determinants of psychological well-being and personal initiave in East Germany öfter the unification. Unpublished doctoral dissertation, University of Amsterdam.

    Google Scholar 

  • Hall, R. J., Snell, A. F., & Foust, M. S. (1999). Item parceling strategies inSEM: Investigating the subtle effects of unmodeled secondary constructs. Organizational Research Methods, 2(3) , 233–256.

    Article  Google Scholar 

  • Hancock, G. R., Kuo, W. L., & Lawrence, F. R. (2001). An illustration of second-order latent growth modeis. Structural Equation Modeling, 8, 470–489.

    Article  Google Scholar 

  • Hörn, J.L. & McArdle, JJ.(1992). A practical and theoretical guide to measurement invariance in aging research. Experimental Aging Research, 18, 117– 144.

    Article  PubMed  Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1988). LISREL 7: A guide to the program and applications. Chicago, IL: SPSS Inc.

    Google Scholar 

  • Lubke, G.H. & Dolan, C.V. (2002). Can unequal residual variances across groups mask measurement invariance in the common factor model?. Manuscript accepted for publication.

    Google Scholar 

  • Lubke, G. H., Dolan, C. V., Kelderman, H., & Mellenbergh, G. J. (2001). Absence of measurement blas with respect to unmeasured variables: An implication od strict factorial invariance. Manuscript submitted for publication.

    Google Scholar 

  • MacCallum, R. C, Kim, C, Malarkey, W. B., & Kiecolt-Glaser, J. K. (1997). Studying multivariate change using multilevel modeis and latent growth curve modeis. Multivariate Behavioral Research, 32, 215–253.

    Article  Google Scholar 

  • McArdle, J. J. (1986). Latent variable growth within behavior genetic modeis. Behavior Genetics, 16(1) , 163–200.

    Article  PubMed  Google Scholar 

  • McArdle, J. J. (1988). Dynamic but structural equation modeling of repeated measures data. In R. B. Cattel, & J. Nesselroade (Eds.), Handbook of multivariate experimental psychology (2nd ed., pp. 561–614). New York: Plenum Press.

    Chapter  Google Scholar 

  • McArdle, JJ. (1989). Structural modeling experiments using multiple growth functions. In P. Ackerman, R. Kanfer & R. Cudeck (Eds.), Learning and individual differences: Abilities, Motivation and Methodology (pp. 71–117). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • McArdle, J. J. Anderson, E. (1990) . Latent variable growth modeis for research on aging. In Birren, J. E. Schaie, K. W., Handbook of the Psychology of Aging (pp.21–44). New York : Academic Press.

    Google Scholar 

  • Mcardle, J.J., & Bell, R. Q. (2000). An introduction to latent growth modeis for developmental data analysis. In T.D. Little, K.U. Schnabel, & J.Baumert (Eds.), Modeling longitudinal and multilevel data (pp. 69–108). Mahwah: Lawrence Erlbaum.

    Google Scholar 

  • McArdle, J. J. & Cattell, B. R. (1994). Structural equation modeis of factorial invariance in parallel proportional profiles and oblique confactor Problems. Multivariate Behavioral Research, 29, 63–113.

    Article  Google Scholar 

  • McArdle, J. J., & Epstein, D. (1987). Latent growth curves within developmental structural equation modeis. Child Development, 58, 110–133.

    Article  PubMed  Google Scholar 

  • McArdle, J. J. & Hamagami, F. (1992). Modeling incomplete longitudinal and cross-sectional data using latent growth structural modeis. Experimental Aging Research, 18, 145–166

    Article  PubMed  Google Scholar 

  • McArdle, J. J. & Hamagami, F. (1996). Modeling incomplete longitudinal and cross-sectional data using latent growth structural modeis. Experimental Aging Research, 18, 145–166.

    Article  Google Scholar 

  • Mehta, P. D., & West, S. G. (2000). Putting the individual back into growth curves. Psychological Methods, 5, 23–41.

    Article  PubMed  Google Scholar 

  • Mellenbergh, G.J., Kelderman, M., Stijlen, J.G. & Zondag, E. (1979). Linear modeis for the analysis and construction of instruments in a facet design.Psychological Bulletin, 86, 766–776.

    Article  Google Scholar 

  • Meredith, W. (1964). Notes on factorial invariance. Psychometrika, 29, 11–185

    Google Scholar 

  • Meredith, W. (1993). Measurement invariance, factor analysis, and factorial invariance. Psychometrika, 58, 525–543.

    Article  Google Scholar 

  • Meredith, W. M., & Tisak, J. (1990). Latent curve analysis. Psychometrika, 55, 107–122.

    Article  Google Scholar 

  • Muthen, B., & Khoo, S. (1998). Longitudinal studies of achievement growth using latent variable modeling. Learning and Individual Differences,10, 73–102.

    Article  Google Scholar 

  • Muthen, L. K. & Muthen, B. O. (1998). Mplus 1.04 [Computer Software]. Los Angeles: Muthen & Muthen.

    Google Scholar 

  • Oort, F. J. (2001). Three-mode modeis for multivariate longitudinal data British Journal of Mathematical and Statistical Psychology, 54, 49–78.

    Article  PubMed  Google Scholar 

  • Pentz, M. A., & Chou, Ch. P. (1994). Measurement invariance in longitudinal clinical research assuming change from development and Intervention. Journal of Consulting and Clinical Psychology, 62, 450–462

    Article  PubMed  Google Scholar 

  • Rao, C. R. (1958). Some Statistical methods for comparison of growth curves. Biometrics, 14,1–17.

    Article  Google Scholar 

  • Raykov, T. & Marcoulides, G.A. (2000). A First Course in Structural Equation Modeling. Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Rogosa, D., Brandt, D., & Zimowski, M. (1982). A growth curve approach to the measurement of change. Quantitative Methods in Psychology, 92, 726–748.

    Google Scholar 

  • Rogosa, D. & Willett, J. B. (1985). Understanding correlates of change by modeling individual differences in growth. Psychometrika, 50, 203–228.

    Article  Google Scholar 

  • Rovine, M.J., & Molenaar, P. C. M. (1998). A nonstandard method for estimating a linear growth model in LISREL.International Journal of Behavioral Development, 22, 453–473.

    Article  Google Scholar 

  • Saris, W.E. (1978). Introduction to the use of linear structural equation modeis in non-experimental research. Research Report, Amsterdam: Free University Amsterdam.

    Google Scholar 

  • Sayer, A. G., & Cumsille, P. E. (2001). Second-order latent growth modeis. In L. M. Collins & A. G. Sayer (Eds.),New methods for the analysis of change (pp. 179–200).

    Chapter  Google Scholar 

  • Stoel, R. D., & Van den Wittenboer, G. (2003). Time dependence of growth Parameters in latent growth curve modeis with time invariant covariates. Methods of Psychological Research, 8, 21–41.

    Google Scholar 

  • Stoolmiller, M. (1995). Using latent growth curve modeis to study developmental processes. In J. M. Gottman (Ed.), The analysis of change (pp. 103–138). New Jersey: Mahwah.

    Google Scholar 

  • Tucker, L. R. (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 19–23.

    Article  Google Scholar 

  • Vandenberg, R.J., & Lance, C.E. (2000). A Review and synthesis of the measurement invariance literature: Suggestions, practices and recommendations for organizational research. Organizational Research Methods, 3,4–70.

    Article  Google Scholar 

  • Willett, J. B., & Sayer, A. G. (1994). Using covariance structure analysis to detect correlates and predictors of individual change over time. Psychological Bulletin, 116, 363–381.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Stoel, R.D., van den Wittenboer, G., Hox, J. (2004). Methodological Issues in the Application of the Latent Growth Curve Model. In: van Montfort, K., Oud, J., Satorra, A. (eds) Recent Developments on Structural Equation Models. Mathematical Modelling: Theory and Applications, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-1958-6_13

Download citation

  • DOI: https://doi.org/10.1007/978-1-4020-1958-6_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-6549-0

  • Online ISBN: 978-1-4020-1958-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics