Abstract
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.
Supported in part by NSF Grant BNS 76-02849 to the University of Chicago and NSF Grant BNS 76-22943 A02 to the Center for Advanced Study in the Behavioral Sciences, Stanford, California.
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References
Bock, R.D., 1975, “Multivariate Statistical Methods in Behavioral Research,” McGraw Hill, New York.
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).
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.
Box, G.E.P., and Jenkins, G.M., 1976, “Time Series Analysis: Forecasting and Control,” ( 2nd Ed. ), Holden-Day, San Francisco.
Brillinger, D.K., 1975, “Time Series: Data Analysis and Theory,” Holt, Rinehart and Winston, New York.
Burt, C., 1937, “The Backward Child,” Appleton-Century, New York.
Chambers, J.M., 1977, “Computational Methods for Data Analysis,” Wiley, New York.
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.
El Lozy, M., 1978, A critical analysis of the double and triple logistic growth curves, Ann. Human Biol., 5: 389–394.
Fearn, T., 1975, A Bayesian approach to growth curves, Biometrika, 62: 89–100.
Fuller, W.A., 1976, “Introduction to Statistical Time Series,” Wiley, New York.
Gill, P.E., and Murray, W. (Eds.), 1974, “Numerical Methods for Constrained Optimization,” Academic Press, London.
Glass, G.V., Willson, V.L., and Gottman, J.M., 1975, “Design and Analysis of Time-series Experiments,” Colorado Associated University Press, Boulder (Colorado).
Jenkins, G.M., and Watts, D.G., 1968, “Spectral Analysis and its Applications,” Holden-Day, San Francisco.
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.
Jenss, R.M., and Bayley, N., 1937, A mathematical model for studying the growth of a child, Human Biol., 9: 556–563.
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.
Lindley, D.V., and Smith, A.F.M., 1972, Bayes estimates for the linear model, J. Royal Stat. Soc., Series B, 34: 1–41.
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.
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.
Smith, A.F.M., 1973, A general Bayesian linear model. J. Royal Stat. Soc., Series B, 35: 67–75.
Stützle, W., 1977, “Estimation and Parameterization of Growth Curves,” Juris, Zurich.
Thissen, D., and Bock, R.D., 1979, Bayes estimation of individual growth parameters (in preparation).
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.
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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. NATO Advanced Study Institutes Series, vol 30. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-6994-3_16
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