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9 - Parameter estimation in the context of non-linear longitudinal growth models

Published online by Cambridge University Press:  17 August 2009

R. Darrell Bock
Affiliation:
University of Chicago
Stephen H. C. du Toit
Affiliation:
Scientific Software International, Chicago
Roland C. Hauspie
Affiliation:
Vrije Universiteit, Amsterdam
Noël Cameron
Affiliation:
Loughborough University
Luciano Molinari
Affiliation:
Kinderspital Zürich
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Summary

Longitudinal measurements of human growth present special difficulties for statistical analysis, both in the fitting of parametric models for individual growth and when comparing growth in various populations. The main objective of parametric analysis is to describe or predict growth, or differences in growth, as a function of chronological age. Although it would be convenient in this connection to assume complete records of measurements at the same time points for all cases, that condition is almost impossible to fulfil even in carefully conducted longitudinal studies. For this reason, conventional multivariate statistical methods that assume measurement records of fixed dimensionality do not apply.

Further difficulties arise from the fact that growth is not a simple deterministic process that can be represented by a continuous function of time with a manageable number of parameters. Even well-fitting functional models will exhibit residual variation attributable to so-called ‘equation error’. To the extent that the residuals are unbiased (i.e. tend to sum to zero), the fitted growth curve will pass through the data points in such a way that the points in successive intervals will lie on one side of the curve and then on the other. This introduces autocorrelation among the residuals and violates the assumption of independent error required in most curve-fitting procedures – although it does not bias the shape of curves appreciably if the growth measurements are regularly spaced in time.

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Publisher: Cambridge University Press
Print publication year: 2004

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