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m →Nonparametric multiplicative regression: Organismal response to environment tend to be nonlinear => Organismal response to environment tends to be nonlinear |
m →Nonparametric multiplicative regression: the computer must search through huge number of potential models => the computer must search through a huge number of potential models |
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A key biological feature of an NPMR model is that failure of an organism to tolerate any single dimension of the predictor space results in overall failure of the organism. For example, assume that a plant needs a certain range of moisture in a particular temperature range. If either temperature or moisture fall outside the tolerance of the organism, then the organism dies. If it is too hot, then no amount of moisture can compensate to result in survival of the plant. Mathematically this works with NPMR because the product of the weights for the target point is zero or near zero if any of the weights for individual predictors (moisture or temperature) are zero or near zero. Note further that in this simple example, the second condition listed above is probably true: the response of the plant to moisture probably depends on temperature and vice-versa.
Optimizing the selection of predictors and their smoothing parameters in a multiplicative model is computationally intensive. With a large pool of predictors, the computer must search through a huge number of potential models in search for the best model. The best model has the best fit, subject to [[overfitting]] constraints or penalties (see below).<ref>{{cite journal |last=Grundel |first=R. |first2=N. B. |last2=Pavlovic |year=2007 |title=Response of bird species densities to habitat structure and fire history along a Midwestern open–forest Gradient |journal=[[The Condor (journal)|The Condor]] |volume=109 |issue=4 |pages=734–749 |doi=10.1650/0010-5422(2007)109[734:ROBSDT]2.0.CO;2 }}</ref><ref>{{cite journal |last=DeBano |first=S. J. |first2=P. B. |last2=Hamm |first3=A. |last3=Jensen |first4=S. I. |last4=Rondon |first5=P. J. |last5=Landolt |year=2010 |title=Spatial and temporal dynamics of potato tuberworm (''Lepidoptera: Gelechiidae'') in the Columbia Basin of the Pacific Northwest |journal=Environmental Entomology |volume=39 |issue=1 |pages=1–14 |doi=10.1603/EN08270 }}</ref>
;The local model
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