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    Semi-mechanistic modelling in nonlinear regression: a case study (with discussion)

    Domijan, Katarina and Jorgensen, Murray and Reid, Jeff (2006) Semi-mechanistic modelling in nonlinear regression: a case study (with discussion). Australian and New Zealand Journal of Statistics, 48 (3). pp. 373-391. ISSN 1369-1473

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    This paper discusses the use of highly parameterized semi‐mechanistic nonlinear models with particular reference to the PARJIB crop response model of Reid (2002)[Yield response to nutrient supply across a wide range of conditions 1. Model derivation. Field Crops Research77, 161–171]. Compared to empirical linear approaches, such models promise improved generality of application but present considerable challenges for estimation. Some success has been achieved with a fitting approach that uses a Levenberg–Marquardt algorithm starting from initial values determined by a genetic algorithm. Attention must be paid, however, to correlations between parameter estimates and an approach is described to identify these based on large simulated datasets. This work illustrates the value for the scientist in exploring the correlation structure in mechanistic or semi‐mechanistic models. Such information might be used to reappraise the structure of the model itself, especially if the experimental evidence is not strong enough to allow estimation of a parameter free of assumptions about the values of others. Thus statistical modelling and analysis can complement mechanistic studies, making more explicit what is known and what is not known about the processes being modelled and guiding further research.

    Item Type: Article
    Keywords: crop response to fertilizers; descriptive model; genetic algorithm; Levenberg-Marquardt algorithm; nutrients; parameter correlation; simulated data;
    Academic Unit: Faculty of Science and Engineering > Mathematics and Statistics
    Item ID: 10016
    Identification Number:
    Depositing User: Katarina Domijan
    Date Deposited: 27 Sep 2018 14:04
    Journal or Publication Title: Australian and New Zealand Journal of Statistics
    Publisher: Wiley
    Refereed: Yes
    Use Licence: This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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