Longitudinal Data Analysis

  • D. Betsy mccoach
  • John P. Madura
  • Karen E. Rambohernandez
  • Ann A. O’connell
  • Megan E. Welsh


Longitudinal data analysis is a very broad, general term for the analysis of data that are collected on the same units across time. Longitudinal data are sometimes referred to as repeated measures data or panel data (Hsiao, 2003; Frees, 2004). A variety of statistical models exist for analyzing longitudinal data.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Allen, M. J., & Yen, W. M. (1979). Introduction to measurement theory. Long Grove, IL: Waveland Press.Google Scholar
  2. Bast, J., & Reitsma, P. (1997). Matthew effects in reading: A comparison of latent growth curve models and simplex models with structured means. Multivariate Behavioral Research, 32, 135–167.CrossRefGoogle Scholar
  3. Bast, J., & Reitsma, P. (1998). Analyzing the development of individual differences in terms of Matthew effects in reading: Results from a Dutch longitudinal study. Developmental Psychology, 34, 1373–1399.CrossRefGoogle Scholar
  4. Bollen, K. A., & Curran, P. J. (2004). Autoregressive latent trajectory (ALT) models: A synthesis of two traditions. Sociological Methods Research, 32, 336–383.CrossRefGoogle Scholar
  5. Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley Interscience.Google Scholar
  6. Bryk, A. S., & Raudenbush, S. W. (1988). Toward a more appropriate conceptualization of research on school effects: A three-level hierarchical linear model. American Journal of Education, 97, 65–108.CrossRefGoogle Scholar
  7. Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods and Research, 33, 261–304.CrossRefGoogle Scholar
  8. Campbell, D. T., & Kenny, D. A. (1999). A primer of regression artifacts. New York: Guilford Press.Google Scholar
  9. Collins, L. M. (2006). Analysis of longitudinal data: The integration of theoretical model, temporal design, and statistical model. Annual Review of Psychology, 57, 505–28.CrossRefGoogle Scholar
  10. Cronbach, L. J., & Furby, L. (1970). How we should measure ‘change’: Or should we? Psychological Bulletin, 74, 68–80.CrossRefGoogle Scholar
  11. Curran, P. J. (2000). A latent curve framework for studying developmental trajectories of adolescent substance use. In J. Rose, L. Chassin, C.Presson, & J. Sherman (Eds.), Multivariate applications in substance use research. Hillsdale, NJ: Erlbaum.Google Scholar
  12. Duncan, T. E., Duncan, S. C., & Stryker, L. A. (2006). An introduction to latent variable growth curve modeling: Concepts, issues, and applications (2nd ed.). Mahwah, NJ: Lawrence Erlbaum and Associates.Google Scholar
  13. Enders, C. K. (2010). Applied missing data analysis. New York: Guilford Press.Google Scholar
  14. Ferrer-Caja, E., & McArdle, J. J. (2003). Alternative structural equation models for multivariate longitudinal data analysis. Structural Equation Modeling. 10, 493–524.CrossRefGoogle Scholar
  15. Forster, M. R. (2000). Key concepts in model selection: Performance and generalizability. Journal of Mathematical Psychology, 44, 205–231.CrossRefGoogle Scholar
  16. Frees, E. (2004). Longitudinal and panel data. Cambridge University Press.Google Scholar
  17. Gagné, F. (2005). From noncompetence to exceptional talent: Exploring the range of academic achievement within and between grade levels. Gifted Child Quarterly, 49, 139–153.CrossRefGoogle Scholar
  18. Hsiao, C. (2003). Analysis of panel data. Cambridge University Press.Google Scholar
  19. Howell, D. C. (2007). Statistical methods for psychology (6th ed.) Belmont, CA: Thompson-Wadsworth.Google Scholar
  20. Kenny, D. (1974). A quasi-experimental approach to assessing treatment effects in the nonequivalent control group design. Psychological Bulletin, 82, 342–362.Google Scholar
  21. Kenny, D. A., & Campbell, D. T. (1989). On the measurement of stability in over-time data. Journal of Personality, 57, 445–481.CrossRefGoogle Scholar
  22. Kline, R. B. (2005). Principles and practice of structural equation modeling (2nd ed.). New York, NY US: Guilford Press.Google Scholar
  23. Lo, Y., Mendell, N. R., & Rubin, D. B. (2001). Testing the number of components in a normal mixture. Biometrika, 88, 767–778.CrossRefGoogle Scholar
  24. Lohman, D. F., & Korb, K. A. (2006). Gifted today but not tomorrow? Longitudinal changes in ability and achievement during elementary school. Journal for the Education of the Gifted, 84.Google Scholar
  25. Marsh, H. W. (1993). Stability of individual differences in multiwave panel studies: Comparison of simplex models and one-factor models. Journal of Educational Measurement, 30,157–183.CrossRefGoogle Scholar
  26. Martineau, J. A. (2006). Distorting value added: The use of longitudinal, vertically scaled student achievement data for growth-based, value-added accountability. Journal of Educational and Behavioral Statistics, 31, 35–62.CrossRefGoogle Scholar
  27. McArdle, J. J. (2001). A latent difference score approach to longitudinal dynamic structural analyses. In R. Cudeck, S. du Toit, & D. Sorbom (Eds.). Structural equation modeling: Present and future. Lincolnwood, IL: SSI.Google Scholar
  28. McArdle, J. J. (2006). Dynamic structural equation modeling in longitudinal experimental studies. In K. van Montfort, H. Oud, & A. Satorra (Eds.). Longitudinal Models in the Behavioural and Related Sciences. Mahwah, NJ: Erlbaum.Google Scholar
  29. McCaffrey, D. F., Lockwood, J. R., Koretz, D. M., & Hamilton, L. S. (2003). Evaluating value-added models for teacher accountability. Santa Monica: The RAND Corporation.CrossRefGoogle Scholar
  30. McCoach, D. B., & Black, A. C. (2008). Assessing model adequacy. In A. A. O’Connell & D. B.Google Scholar
  31. McCoach (Eds.), Multilevel modeling of educational data (pp. 245–272). Charlotte, NC: Information Age Publishing.Google Scholar
  32. McCoach, D. B., & Kaniskan, B. (2010). Using time varying covariates in multilevel growth models. Frontiers in Quantitative Psychology and Measurement, 1(17). DOI:  10.3389/fpsyg.2010.00017
  33. McCoach, D. B., Rambo, K., & Welsh, M. (2012). Issues in the analysis of change. Handbook of measurement, assessment, and evaluation in higher education.Google Scholar
  34. McLachlan, G. J. (1987). On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Applied Statistics, 36, 318–324.CrossRefGoogle Scholar
  35. McLachlan, G. J., & Peel, D. (2000). Finite mixture models. New York: John Wiley.CrossRefGoogle Scholar
  36. Mehta, P. D., & Neale, M. C. (2005). People are variables too: Multilevel structural equations modeling. Psychological Methods, 10(3), 259–284.CrossRefGoogle Scholar
  37. Muthén, B., Brown, C., Masyn, K., Jo, B., Khoo, Yang C., Liao, J. (2002). General growth mixture modeling for randomized preventative interventions. Biostatistics, 3, 459–475.CrossRefGoogle Scholar
  38. O’Connell, A. A., Logan, J., Pentimonti, J, & McCoach, D. B. (in press). Linear and quadratic growth models for continuous and dichotomous outcomes.Google Scholar
  39. Popham, W. J. (1999). Classroom assessment: What teachers need to know (2nd Ed.) Boston: Allyn & Bacon.Google Scholar
  40. Ram, N., & Grimm, K. J. (2009). Growth mixture modeling: A method for identifying differences in longitudinal change among unobserved groups. International Journal of Behavioral Development, 33, 565–576.CrossRefGoogle Scholar
  41. Raudenbush, S. W. (2001). Toward a coherent framework for comparing trajectories of individual change. In A. G. Sayer (Ed.), New methods for the analysis of change. (pp. 35–64). Washington, DC US: American Psychological Association.CrossRefGoogle Scholar
  42. Raudenbush S., & Bryk, A (2002). Hierarchical linear models, 2nd Ed. London: Sage Publications.Google Scholar
  43. Raudenbush, S. W., & Xiao-Feng, L. (2001). Effect of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. Psychological Methods, 6, 387–401.CrossRefGoogle Scholar
  44. Rogosa, D., Brandt, D., & Zimowski, M. (1982). A growth curve approach to the measurement of change. Psychological Bulletin, 92, 726–748. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York, NY: OxfordGoogle Scholar
  45. University Press.Google Scholar
  46. Sclove, L. S. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika 52, 333–343.CrossRefGoogle Scholar
  47. Singer, J. D., & Willett, J. B. (2003). Applied longitudinal data analysis: Modeling change and event occurrence. New York, NY US: Oxford University Press.CrossRefGoogle Scholar
  48. Skrondal, A., & Rabe-Hesketh, S. (2008). Multilevel and related models for longitudinal data. In J. deLeeuw & E. Meijer (Eds.), Handbook of multilevel analysis, (pp. 275–300). New York: Springer Science+Business Media.CrossRefGoogle Scholar
  49. Stoel & Garre, 2011 Growth curve analysis using multilevel regression and structural equation modeling. (pp. 97–111). In J. J. Hox & J. K. Roberts (Eds.), Handbook of advanced multilevel analysis. New York, NY: Routledge.Google Scholar
  50. Thorndike, R. L. (1966). Intellectual status and intellectual growth. Journal of Educational Psychology, 57(3), 121–127.CrossRefGoogle Scholar
  51. Tofighi, D., & Enders, C. K. (2008). Identifying the correct number of classes in a growth mixture models. In G. R. Hancock & K. M. Samuelson (Eds.), Advances in latent variable mixture models. Charlotte, NC: Information Age.Google Scholar
  52. Wang, M., & Bodner, T. E. (2007). Growth mixture modeling: Identifying and predicting unobserved subpopulations with longitudinal data. Organizational Research Methods, 10, 635–656.CrossRefGoogle Scholar
  53. Willett, J. B. (1989). Questions and answers in the measurement of change. Review of Research in Education, 15, 345–422.Google Scholar

Copyright information

© Sense Publishers 2013

Authors and Affiliations

  • D. Betsy mccoach
  • John P. Madura
  • Karen E. Rambohernandez
  • Ann A. O’connell
  • Megan E. Welsh

There are no affiliations available

Personalised recommendations