, Volume 55, Issue 1, pp 107–122 | Cite as

Latent curve analysis

  • William Meredith
  • John Tisak


As a method for representing development, latent trait theory is presented in terms of a statistical model containing individual parameters and a structure on both the first and second moments of the random variables reflecting growth. Maximum likelihood parameter estimates and associated asymptotic tests follow directly. These procedures may be viewed as an alternative to standard repeated measures ANOVA and to first-order auto-regressive methods. As formulated, the model encompasses cohort sequential designs and allow for period or practice effects. A numerical illustration using data initially collected by Nesselroade and Baltes is presented.

Key words

longitudinal analysis individual growth curves structural equation modeling 


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  1. Anderson, T. W. (1963). The use of factor analysis in the statistical analysis of multiple time series,Psychometrika, 28, 1–25.Google Scholar
  2. Bentler, P. M. (1989).EQS structural equations program manual. Los Angeles: BMDP Statistical Software.Google Scholar
  3. Bock, R. D., & Thissen, D. (1980). Statistical problems of fitting individual growth curves. In F. E. Johnston, A. F. Roche & C. Susanne (Eds.),Human physical growth and maturation: Methodologies and factors (pp. 265–290). New York: Plenum Press.Google Scholar
  4. Graybill, F. A. (1969).Introduction to matrices with applications in statistics. Belmont, CA: Wadsworth.Google Scholar
  5. Jöreskog, K. G. (1970). Estimation and testing of simplex models.British Journal of Mathematical and Statistical Psychology, 23, 121–145.Google Scholar
  6. Jöreskog, K. G., & Sörbom, D. (1989).LISREL 7 user's reference guide. Mooresville, IN: Scientific Software.Google Scholar
  7. Jöreskog, K. G., & Sörbom, D. (1985). Simultaneous analysis of longitudinal data from several cohorts. In W. M. Mason & S. E. Fienberg (Eds.),Cohort analysis in social research (pp. 323–341). New York: Springer-Verlag.Google Scholar
  8. Lord, F. M., & Novick, M. R. (1968).Statistical theories of mental test scores. Menlo Park, CA: Addison-Wesley.Google Scholar
  9. Maritz, J. (1970).Empirical Bayes methods. London: Methuen.Google Scholar
  10. McDonald, R. P. (1978). A simple comprehensive model for the analysis of covariance structures.British Journal of Mathematical and Statistical Psychology, 31, 59–72.Google Scholar
  11. Nesselroade, J. R., & Baltes, P. B. (1974). Adolescent personality development and historical change: 1970–1972.Monographs of the Society for Research in Child Development, 39 (1, Serial No. 154).Google Scholar
  12. Ramsay, J. O. (1982). When the data are functions.Psychometrika, 47, 379–396.Google Scholar
  13. Rao, C. R. (1958). Some statistical methods for comparison of growth curves.Biometrics, 14, 1–17.Google Scholar
  14. Rogosa, D. R., Brandt, D., & Zimowski, M. (1982). A growth curve approach to the measurment of change.Psychological Bulletin, 90, 726–748.Google Scholar
  15. Rogosa, D. R., & Willett, J. B. (1985a). Understanding correlates of change by modeling individual differences in growth.Psychometrika, 50, 203–228.Google Scholar
  16. Rogosa, D. R., & Willett, J. B. (1985b). Satisfying a simplex structure is simpler than it should be.Journal of Educational Statistics, 10, 99–107.Google Scholar
  17. Schaie, K. W. (1965). A general model for the study of developmental problems.Psychological Bulletin, 64, 92–107.Google Scholar
  18. Scher, A. M., Young, A. C., & Meredith, W. M. (1960). Factor analysis of the electrocardiograph.Circulation Research, 8, 519–526.Google Scholar
  19. Schumaker, L. L. (1981).Spline functions: Basic theory. New York: John Wiley & Sons.Google Scholar
  20. Smith, P. L. (1979). Splines as a useful and convenient statistical tool.American Statistician, 33, 57–62.Google Scholar
  21. Thurstone, L. L., & Thurstone, T. G. (1962).SRA Primary Mental Abilities. Chicago: Science Research Associates.Google Scholar
  22. Tucker, L. R. (1958). Determination of parameters of a functional relation by factor analysis.Psychometrika, 23, 19–23.Google Scholar
  23. Tucker, L. R. (1966). Learning theory and multivariate experiment: Illustration of generalized learning curves. In R. B. Cattell (Ed.),Handbook of multivariate experimental psychology (pp. 476–501). Chicago: Rand McNally.Google Scholar
  24. Vinsonhaler, J. F., & Meredith, W. (1966). A stochastic model for repeated testing.Multivariate Behavioral Research, 1, 461–477.Google Scholar

Copyright information

© The Psychometric Society 1990

Authors and Affiliations

  • William Meredith
    • 1
  • John Tisak
    • 2
  1. 1.Department of PsychologyUniversity of CaliforniaBerkeley
  2. 2.Bowling Green State UniversityUSA

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