Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2025-01-05T13:35:28.906Z Has data issue: false hasContentIssue false

Latent Curve Analysis

Published online by Cambridge University Press:  01 January 2025

William Meredith*
Affiliation:
University of California, Berkeley
John Tisak
Affiliation:
Bowling Green State University
*
Requests for reprints should be sent to William Meredith, Department of Psychology, University of California, Berkeley, California 94720.

Abstract

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.

Type
Original Paper
Copyright
Copyright © 1990 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

The authors wish to thank John Nesselroade for providing us the data for our illustration and Karen Paul and Connie Tilse for assisting in the data analysis. This research was supported by a grant (No. AG03164) from the National Institute on Aging to the senior author.

References

Anderson, T. W. (1963). The use of factor analysis in the statistical analysis of multiple time series. Psychometrika, 28, 125.CrossRefGoogle Scholar
Bentler, P. M. (1989). EQS structural equations program manual, Los Angeles: BMDP Statistical Software.Google Scholar
Bock, R. D., Thissen, D. (1980). Statistical problems of fitting individual growth curves. In Johnston, F. E., Roche, A. F., Susanne, C. (Eds.), Human physical growth and maturation: Methodologies and factors (pp. 265290). New York: Plenum Press.CrossRefGoogle Scholar
Graybill, F. A. (1969). Introduction to matrices with applications in statistics, Belmont, CA: Wadsworth.Google Scholar
Jöreskog, K. G. (1970). Estimation and testing of simplex models. British Journal of Mathematical and Statistical Psychology, 23, 121145.CrossRefGoogle Scholar
Jöreskog, K. G., Sörbom, D. (1989). LISREL 7 user's reference guide, Mooresville, IN: Scientific Software.Google Scholar
Jöreskog, K. G., Sörbom, D. (1985). Simultaneous analysis of longitudinal data from several cohorts. In Mason, W. M., Fienberg, S. E. (Eds.), Cohort analysis in social research (pp. 323341). New York: Springer-Verlag.CrossRefGoogle Scholar
Lord, F. M., Novick, M. R. (1968). Statistical theories of mental test scores, Menlo Park, CA: Addison-Wesley.Google Scholar
Maritz, J. (1970). Empirical Bayes methods, London: Methuen.Google Scholar
McDonald, R. P. (1978). A simple comprehensive model for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 31, 5972.CrossRefGoogle Scholar
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).CrossRefGoogle ScholarPubMed
Ramsay, J. O. (1982). When the data are functions. Psychometrika, 47, 379396.CrossRefGoogle Scholar
Rao, C. R. (1958). Some statistical methods for comparison of growth curves. Biometrics, 14, 117.CrossRefGoogle Scholar
Rogosa, D. R., Brandt, D., Zimowski, M. (1982). A growth curve approach to the measurment of change. Psychological Bulletin, 90, 726748.CrossRefGoogle Scholar
Rogosa, D. R., Willett, J. B. (1985). Understanding correlates of change by modeling individual differences in growth. Psychometrika, 50, 203228.CrossRefGoogle Scholar
Rogosa, D. R., Willett, J. B. (1985). Satisfying a simplex structure is simpler than it should be. Journal of Educational Statistics, 10, 99107.CrossRefGoogle Scholar
Schaie, K. W. (1965). A general model for the study of developmental problems. Psychological Bulletin, 64, 92107.CrossRefGoogle Scholar
Scher, A. M., Young, A. C., Meredith, W. M. (1960). Factor analysis of the electrocardiograph. Circulation Research, 8, 519526.CrossRefGoogle Scholar
Schumaker, L. L. (1981). Spline functions: Basic theory, New York: John Wiley & Sons.Google Scholar
Smith, P. L. (1979). Splines as a useful and convenient statistical tool. American Statistician, 33, 5762.CrossRefGoogle Scholar
Thurstone, L. L., Thurstone, T. G. (1962). SRA Primary Mental Abilities, Chicago: Science Research Associates.Google Scholar
Tucker, L. R. (1958). Determination of parameters of a functional relation by factor analysis. Psychometrika, 23, 1923.CrossRefGoogle Scholar
Tucker, L. R. (1966). Learning theory and multivariate experiment: Illustration of generalized learning curves. In Cattell, R. B. (Eds.), Handbook of multivariate experimental psychology (pp. 476501). Chicago: Rand McNally.Google Scholar
Vinsonhaler, J. F., Meredith, W. (1966). A stochastic model for repeated testing. Multivariate Behavioral Research, 1, 461477.CrossRefGoogle ScholarPubMed