Statistical Problems of Fitting Individual Growth Curves

  • R. Darrell Bock
  • David Thissen
Part of the NATO Advanced Study Institutes Series book series (NSSA, volume 30)


A thorough-going longitudinal study of a child’s growth can produce upward of forty observations spaced over the years from birth to maturity. Such a data record is too long and inevitably too noisy (because of measurement error and short-run growth variation) to be interpreted without some sort of condensation and smoothing. The length of the record forces attention to certain critical regions or features of the curve, but the noisiness of the data makes it risky to characterize these regions or features by a few isolated measurements. The only safe approach to interpretation of individual growth data is via a statistical method capable of revealing the essential trend and concisely describing its main features.


Growth Parameter Common Standard Deviation Growth Velocity Curve Adrenal Functioning Longitudinal Growth Study 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bock, R.D., 1975, “Multivariate Statistical Methods in Behavioral Research,” McGraw Hill, New York.Google Scholar
  2. Bock, R.D., 1979, Univariate and multivariate analysis of variance of time-structured data, in: “Longitudinal Research in Human Development: Design and Analysis,” J.R. Nesselroade and P.B. Baltes, eds., Academic Press, New York (in press).Google Scholar
  3. Bock, R.D., and Thissen, D., 1976, Fitting multi-component models for growth in stature, Proceedings of the 9th International Biometric Conference, 1: 431–442.Google Scholar
  4. Box, G.E.P., and Jenkins, G.M., 1976, “Time Series Analysis: Forecasting and Control,” ( 2nd Ed. ), Holden-Day, San Francisco.Google Scholar
  5. Brillinger, D.K., 1975, “Time Series: Data Analysis and Theory,” Holt, Rinehart and Winston, New York.Google Scholar
  6. Burt, C., 1937, “The Backward Child,” Appleton-Century, New York.Google Scholar
  7. Chambers, J.M., 1977, “Computational Methods for Data Analysis,” Wiley, New York.Google Scholar
  8. Cochrane, D., and Orcutt, G.H., 1949, Applications of least-squares regression to relationships containing auto-correlated error terms, J. Am. Stat. Assoc., 44: 32–61.Google Scholar
  9. El Lozy, M., 1978, A critical analysis of the double and triple logistic growth curves, Ann. Human Biol., 5: 389–394.CrossRefGoogle Scholar
  10. Fearn, T., 1975, A Bayesian approach to growth curves, Biometrika, 62: 89–100.CrossRefGoogle Scholar
  11. Fuller, W.A., 1976, “Introduction to Statistical Time Series,” Wiley, New York.Google Scholar
  12. Gill, P.E., and Murray, W. (Eds.), 1974, “Numerical Methods for Constrained Optimization,” Academic Press, London.Google Scholar
  13. Glass, G.V., Willson, V.L., and Gottman, J.M., 1975, “Design and Analysis of Time-series Experiments,” Colorado Associated University Press, Boulder (Colorado).Google Scholar
  14. Jenkins, G.M., and Watts, D.G., 1968, “Spectral Analysis and its Applications,” Holden-Day, San Francisco.Google Scholar
  15. Jennerich, R.I., and Ralston, M.L., 1978, “Fitting Nonlinear Models to Data,” Technical Report #6, Health Sciences Computing Facility, University of California at Los Angeles.Google Scholar
  16. Jenss, R.M., and Bayley, N., 1937, A mathematical model for studying the growth of a child, Human Biol., 9: 556–563.Google Scholar
  17. Largo, R.H., Gasser, Th., Prader, A., Stuetzle, W., and Huber, P.J., 1978, Analysis of the adolescent growth spurt using smoothing spline functions, Ann. Human Biol., 5: 421–434.CrossRefGoogle Scholar
  18. Lindley, D.V., and Smith, A.F.M., 1972, Bayes estimates for the linear model, J. Royal Stat. Soc., Series B, 34: 1–41.Google Scholar
  19. Preece, M.A., and Baines, M.J., 1978, A new family of mathematical models describing the human growth curve, Ann. Human Biol., 5: 1–24.CrossRefGoogle Scholar
  20. Robertson, T.B., 1908, On the normal rate of growth of an individual, and its biochemical significance. Archiv für Entwicklungs Mechanik den Organismen, 25: 581–614.CrossRefGoogle Scholar
  21. Smith, A.F.M., 1973, A general Bayesian linear model. J. Royal Stat. Soc., Series B, 35: 67–75.Google Scholar
  22. Stützle, W., 1977, “Estimation and Parameterization of Growth Curves,” Juris, Zurich.Google Scholar
  23. Thissen, D., and Bock, R.D., 1979, Bayes estimation of individual growth parameters (in preparation).Google Scholar
  24. Tuddenham, R.D., and Snyder, M.M., 1954, Physical growth of California boys and girls from birth to eighteen years. University of California Publications in Child Development, 1: 183–364.Google Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • R. Darrell Bock
    • 1
  • David Thissen
    • 2
  1. 1.University of ChicagoChicagoUSA
  2. 2.University of KansasLawrenceUSA

Personalised recommendations