Abstract. Generalized additive models (GAMs) are a non‐parametric extension of generalized linear models (GLMs). They are introduced here as an exploratory tool in the analysis of species distributions with respect to climate. An important result is that the long‐debated question of whether a response curve, in one dimension, is actually symmetric and bell‐shaped or not, can be tested using GAMs. GAMs and GLMs are discussed and are illustrated by three examples using binary data. A grey‐scale plot of one of the fits is constructed to indicate which areas on a map seem climatically suitable for that species. This is useful for species introductions. Further applications are mentioned.
SUMMARY
Vector smoothing is used to extend the class of generalized additive models in a very natural way to include a class of multivariate regression models. The resulting models are called ‘vector generalized additive models‘. The class of models for which the methodology gives generalized additive extensions includes the multiple logistic regression model for nominal responses, the continuation ratio model and the proportional and non‐proportional odds models for ordinal responses, and the bivariate probit and bivariate logistic models for correlated binary responses. They may also be applied to generalized estimating equations.
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