Skip to main content
SpringerLink
Log in

Five Steps in Latent Curve and Latent Change Score Modeling with Longitudinal Data

  • Chapter
  • First Online:
Longitudinal Research with Latent Variables

Abstract

This paper describes a set of applications of one class of longitudinal growth analysis - latent curve (LCM) and latent change score (LCS) analysis using structural equation modeling (SEM) techniques. These techniques are organized in five sections based on Baltes & Nesselroade (1979). (1) Describing the observed and unobserved longitudinal data. (2) Characterizing the developmental shape of both individuals and groups. (3) Examining the predictors of individual and group differences in developmental shapes. (4) Studying dynamic determinants among variables over time. (5) Studying group differences in dynamic determinants among variables over time. To illustrate all steps, we present SEM analyses of a relatively large set of data from the National Longitudinal Survey of Youth (NLSY). The inclusion of all five aspects of latent curve modeling is not often used in longitudinal analyses, so we discuss why more efforts to include all five are needed in developmental research.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Baltes, P. B., & Nesselroade, J. R. (1979). History and rationale of 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.

    Google Scholar 

  • Boker, S. M., & McArdle, J. J. (1995). Statistical vector field analysis applied to mixed cross-sectional and longitudinal data. Experimental Aging Research, 21, 77-93.

    Article  Google Scholar 

  • Browne, M., & 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: APA Press.

    Google Scholar 

  • Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear models: Applications and data analysis methods. Newbury Park, CA: Sage.

    Google Scholar 

  • Cattell, R. B. (1980). The separation and evaluation of personal and environmental contributions to behavior by the person-centered model (PCER). Multivariate Behavioral Research, 15, 371-402.

    Article  Google Scholar 

  • Cnaan, A., Laird, N. M., & Slasor, P. (1997). Using the general linear mixed model to analyze unbalanced repeated measures and longitudinal data. Statistics in Medicine, 16, 2349-2380.

    Article  Google Scholar 

  • Cook, T. D., & Campbell, D. T. (1979). Quasi-experimentation design and analysis issues for field settings. Skokie, IL: Rand-McNally.

    Google Scholar 

  • Cudeck, R., & Klebe, K. J. (2002). Multiphase mixed-effects models for repeated measures data. Psychological Methods, 7, 41-63.

    Article  Google Scholar 

  • Dunn, L. M., & Markwardt, F. C. (1970). Peabody Individual Achievement Test manual. Circle Pines, MN: American Guidance Service.

    Google Scholar 

  • Grimm, K. J. (2007). Multivariate longitudinal methods for studying developmental relationships between depression and academic achievement. International Journal of Behavioral Development, 31, 328-339.

    Article  Google Scholar 

  • Grimm, K. J., & McArdle, J. J. (2005). A note on the computer generation of structural expectations. In F. Dansereau & F. Yammarino (Eds.), Multi-level issues in strategy and research methods (Volume 4 of Research in multi-level issues) (pp. 335-372). Amsterdam: JAI Press/Elsevier.

    Google Scholar 

  • Hamagami, F., & McArdle, J. J. (2007). Dynamic extensions of latent difference score models. In S. M. Boker & M. J. Wenger, Data analytic techniques for dynamical systems. Notre Dame series on quantitative methodology (pp. 47-85). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Horn, J. L. (1973). On extension analysis and its relation to correlations between variables and factor scores. Multivariate Behavioral Research, 8, 477-489.

    Article  Google Scholar 

  • Jöreskog, K. G., & Sörbom, D. (1979). Advances in factor analysis and structural equation models. Cambridge, MA: Abt Books.

    MATH  Google Scholar 

  • Laird, N. M., & Ware, J. H. (1982). Random effects models for longitudinal data. Biometrics, 38, 963-974.

    Article  MATH  Google Scholar 

  • Littell, R. C., Miliken, G. A., Stoup, W. W., & Wolfinger, R. D. (1996). SAS system for mixed models. Cary, NC: SAS institute.

    Google Scholar 

  • Little, R. J. A. (1995). Modeling the dropout mechanism in repeated-measures studies. Journal of the American Statistical Association, 90, 1112-1121.

    Article  MATH  MathSciNet  Google Scholar 

  • Magnussen, D, (2003). Person-Centered methodology. In S. C. Peck & R. W. Roeser (Eds.), Person-centered approaches to studying development in context. San Francisco: Jossey-Bass.

    Google Scholar 

  • 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.

    Google Scholar 

  • McArdle, J. J. (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. (1994). Structural factor analysis experiments with incomplete data. Multivariate Behavioral Research, 29, 409-454.

    Article  Google Scholar 

  • McArdle, J. J. (2001). A latent difference score approach to longitudinal dynamic structural analyses. In R. Cudeck, S. du Toit & D. Sörbom (Eds.), Structural equation modeling: Present and future (pp. 342-380). Lincolnwood, IL: Scientific Software International.

    Google Scholar 

  • McArdle, J. J. (2005). The development of the RAM rules for latent variable structural equation modeling. In J. J. McArdle & A. Maydeu-Olivares (Eds.), Contemporary psychometrics: A festschrift for Roderick P. McDonald (pp. 225-273). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • McArdle, J. J. (2007). Dynamic structural equation modeling in longitudinal experimental studies. In K. van Montfort, J. Oud & A. Satorra (Eds.), Longitudinal models in the behavioral and related sciences (pp. 159-188). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • McArdle, J. J. (2009). Latent variable modeling of differences and changes. Annual Review of Psychology, 60, 577-605.

    Article  Google Scholar 

  • McArdle, J. J., & Bell, R. Q. (2000). An introduction to latent growth models for developmental data analysis. In T. D. Little, K. U. Schnabel & J. Baumert (Eds.), Modeling longitudinal and multilevel data: Practical issues, applied approaches, and specific examples (pp. 69-107). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • McArdle, J. J., Caja-Ferrer, E., Hamagami, F., & Woodcock, R. W. (2002). Comparative longitudinal structural analyses of the growth and decline of multiple intellectual abilities over the life span. Developmental Psychology, 38, 115-142.

    Article  Google Scholar 

  • McArdle, J. J., & Cattell, R. B. (1994). Structural equation models of factorial invariance in parallel proportional profiles and oblique confactor. Multivariate Behavioral Research, 20, 63-113.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • McArdle, J. J., & Hamagami, F. (2001). Linear dynamic analyses of incomplete longitudinal data. In L. Collins & A. Sayer (Eds.), New methods for the analysis of change. (pp. 137-176). Washington, DC: APA Press.

    Google Scholar 

  • McArdle, J. J., Hamagami, F., Meredith, W., & Bradway, K. P. (2001). Modeling the dynamic hypotheses of Gf-Gc theory using longitudinal life-span data. Learning and Individual Differences, 12, 53-79.

    Article  Google Scholar 

  • McArdle, J. J., & McDonald, R. P. (1984). Some algebraic properties of the Reticular Action Model for moment structures. The British Journal of Mathematical and Statistical Psychology, 37, 234-251.

    MATH  Google Scholar 

  • McArdle, J. J., & Nesselroade, J. R. (1994). Using multivariate data to structure developmental change. In S. H. Cohen & H. W. Reese (Eds.), Life-span developmental psychology: Methodological innovations (pp. 223-267). Hillsdale, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • McArdle, J. J., & Nesselroade, J. R. (2003). Growth curve analyses in contemporary psychological research. In J. Schinka & W. Velicer (Eds.), Comprehensive handbook of psychology: Vol. 2. Research methods in psychology (pp. 447-480). New York: Pergamon Press.

    Google Scholar 

  • McArdle, J. J., Small, B. J., Backman, L., & Fratiglioni, L. (2005). Longitudinal models of growth and survival applied to the early detection of Alzheimer’s Disease. Journal of Geriatric Psychiatry and Neurology, 18, 234-241.

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Muthén, B., & Muthén, L. (2000). Integrating person-centered and variable-centered analysis: Growth mixture modeling with latent trajectory classes. Alcoholism: Clinical and Experimental Research, 24, 882-891.

    Article  Google Scholar 

  • Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55, 463-469.

    Article  MATH  Google Scholar 

  • Miyazaki, Y., & Raudenbush, S. W. (2000). Tests for linkage of multiple cohorts in an accelerated longitudinal design. Psychological Methods, 5, 24-63.

    Article  Google Scholar 

  • Nagin, D. (1999). Analyzing developmental trajectories: Semi-parametric, group-based approach. Psychological Methods, 4, 139-177.

    Article  Google Scholar 

  • Nesselroade, J. R., & Baltes, P. B. (Eds.) (1979). Longitudinal research in the study of behavior and development. New York: Academic Press.

    Google Scholar 

  • Nesselroade, J. R., McArdle, J. J., Aggen, S. H., & Meyers, J. M. (2002). Dynamic factor analysis models for representing process in multivariate time-series. In D. S. Moskowitz & S. L. Hershberger (Eds.), Modeling intraindividual variability with repeated measures data: Methods and applications (pp. 235-265). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Oud, J. H. L., & Jansen, R. A. R. G. (2000). Continuous time state space modeling of panel data by means of SEM. Psychometrika, 65, 199-215.

    Article  MathSciNet  Google Scholar 

  • Ram, N., & Grimm, K. J. (2007). Using simple and complex growth models to articulate developmental change: Matching method to theory. International Journal of Behavioral Development, 31, 303-316.

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Rogosa, D. R. (1978). Some results for the Johnson-Neyman technique. Dissertation Abstracts International, 38(9-A).

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Singer, J. D. (1998). Using SAS PROC MIXED to fit multilevel models, hierarchical models, and individual growth models. Journal of Educational and Behavioral Statistics, 24, 323-355.

    Google Scholar 

  • Sliwinski, M., & Buschke, H. (1999). Cross-sectional and longitudinal relationships among age, cognition, and processing speed. Psychology and Aging, 14, 18-33.

    Article  Google Scholar 

  • Sullivan, E. V., Rosenbloom, M. J., Lim, K. O., & Pfefferman, A. (2000). Longitudinal changes in cognition, gait, balance in abstinent and relapsed alcoholic men: Relationships to changes in brain structure. Neuropsychology, 14, 178-188.

    Article  Google Scholar 

  • Verbeke, G., Molenberghs, G., Krickeberg, K., & Fienberg, S. (Eds.) (2000). Linear mixed models for longitudinal data. New York: Springer Verlag.

    MATH  Google Scholar 

  • Wedel, M., & DeSarbo, W. S. (1995). A mixture likelihood approach for generalized linear models. Journal of Classification, 12, 21-55.

    Article  MATH  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 

  • Wohlwill, J. F. (1973). The study of behavioral development. Oxford, England: Academic Press.

    Google Scholar 

  • Wohlwill, J. F. (1991). The merger of developmental theory and method. In P. Van Geert & L. P. Mos (Eds.), Annals of theoretical psychology: Vol. VII (pp. 129-138).

    Google Scholar 

  • Zeger, S. L., & Harlow, S. D. (1987). Mathematical models from laws of growth to tools for biologic analysis: Fifty years of growth. Growth, 51, 1-21.

    Google Scholar 

  • Zill. N. (1990). Behavior problem index based on parent report. In National Health Interview Survey. Child Health Supplement. Washington, DC: National Center for Health Statistics.

    Google Scholar 

Download references

Acknowledgements

The work described here has been supported since 1980 by the National Institute on Aging (Grant#AG-07137). Kevin Grimm was supported by a National Science Foundation REECE Program Grant (DRL-0815787) and the National Center for Research on Early Childhood Education, Institute of Education Sciences, U.S. Department of Education (R305A06021). We are especially grateful to the assistance of our close friend and colleague, John R. Nesselroade. This research was also influenced by discussions with many others, including Paul Baltes, Steven Boker, Emilio Ferrer, Paolo Ghisletta, Fumiaki Hamagami, John Horn, Bill Meredith, and Carol Prescott.

Author information

Authors and Affiliations

  1. Department of Psychology, University of Southern California, Los Angeles, USA

    John J. McArdle

  2. Department of Psychology, University of California, Davis, One Shields Avenue, Davis, CA, 95616, USA

    Kevin J. Grimm

Authors
  1. John J. McArdle
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kevin J. Grimm
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John J. McArdle .

Editor information

Editors and Affiliations

  1. Dept. Econometrics & Operations, Research, Vrije Universiteit Amsterdam, De Boelelaan 1105, Amsterdam, 1081 HV, Netherlands

    Kees van Montfort

  2. Behavioural Science Institute, Radboud University Nijmegen, Montessorilaan 3, Nijmegen, 6525 HR, Netherlands

    Johan H.L. Oud

  3. , Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, Barcelona, 08005, Spain

    Albert Satorra

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Berlin Heidelberg

About this chapter

Cite this chapter

McArdle, J.J., Grimm, K.J. (2010). Five Steps in Latent Curve and Latent Change Score Modeling with Longitudinal Data. In: van Montfort, K., Oud, J., Satorra, A. (eds) Longitudinal Research with Latent Variables. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11760-2_8

Download citation

Publish with us

Policies and ethics

Search

Navigation