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Goodness-of-fit testing in growth curve models: A general approach based on finite differences

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  • Mandal, A.
  • Huang, W.T.
  • Bhandari, S.K.
  • Basu, A.

Abstract

Growth curve models are routinely used in various fields such as biology, ecology, demography, population dynamics, finance, econometrics, etc. to study the growth pattern of different populations and the variables linked with them. Many different kinds of growth patterns have been used in the literature to model the different types of realistic growth mechanisms. It is generally a matter of substantial benefit to the data analyst to have a reasonable idea of the nature of the growth pattern under study. As a result, goodness-of-fit tests for standard growth models are often of considerable practical value. In this paper we develop some natural goodness-of-fit tests based on finite differences of the size variables under consideration. The method is general in that it is not limited to specific parametric forms underlying the hypothesized model so long as an appropriate finite difference of some function of the size variables can be made to vanish. In addition it allows the testing process to be carried out under a set up which manages to relax most of the assumptions made by Bhattacharya et al. (2009); these assumptions are generally reasonable but not guaranteed to hold universally. Thus our proposed method has a very wide scope of application. The performance of the theory developed is illustrated numerically through several sets of real data and through simulations.

Suggested Citation

  • Mandal, A. & Huang, W.T. & Bhandari, S.K. & Basu, A., 2011. "Goodness-of-fit testing in growth curve models: A general approach based on finite differences," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1086-1098, February.
  • Handle: RePEc:eee:csdana:v:55:y:2011:i:2:p:1086-1098
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    References listed on IDEAS

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    1. Nigel Meade & Towhidul Islam, 1998. "Technological Forecasting---Model Selection, Model Stability, and Combining Models," Management Science, INFORMS, vol. 44(8), pages 1115-1130, August.
    2. Zhiying Pan & D. Y. Lin, 2005. "Goodness-of-Fit Methods for Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 61(4), pages 1000-1009, December.
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    Cited by:

    1. Cronie, Ottmar & Särkkä, Aila, 2011. "Some edge correction methods for marked spatio-temporal point process models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2209-2220, July.

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