Vector generalized additive models in plant ecology

Vector generalized additive models in plant ecology The class of vector generalized linear and additive models (VGLMs and VGAMs) are very large and encompasses many statistical distributions and models. In particular, the classical exponential family containing the normal, binomial and Poisson are a small subset of this family. VGLMs/VGAMs extend GLMs/GAMs by allowing more than one linear/additive predictor. VGLMs are primarily model-driven while its nonparametric counterpart, VGAMs, are more data-driven due to the use of vector smoothers. A very convenient vector smoother is the vector (smoothing) spline, which is a generalization of the cubic smoothing spline to correlat vector responses. In this paper, VGLMs and VGAMs are described and illustrated using examples that are of particular relevance to plant ecologists. It is attempted to show that VGAMs offer greater scope for additive modeling. Use of s-plus/r software written by the first author is illustrated on a few data sets using several statistical models, which include the negative binomial, beta distribution and the bivariate logistic model. Details of how the software can be obtained are provided. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Ecological Modelling Elsevier

Vector generalized additive models in plant ecology

Ecological Modelling, Volume 157 (2) – Nov 30, 2002

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Publisher
Elsevier
Copyright
Copyright © 2002 Elsevier Science B.V.
ISSN
0304-3800
eISSN
1872-7026
DOI
10.1016/S0304-3800(02)00192-8
Publisher site
See Article on Publisher Site

Abstract

The class of vector generalized linear and additive models (VGLMs and VGAMs) are very large and encompasses many statistical distributions and models. In particular, the classical exponential family containing the normal, binomial and Poisson are a small subset of this family. VGLMs/VGAMs extend GLMs/GAMs by allowing more than one linear/additive predictor. VGLMs are primarily model-driven while its nonparametric counterpart, VGAMs, are more data-driven due to the use of vector smoothers. A very convenient vector smoother is the vector (smoothing) spline, which is a generalization of the cubic smoothing spline to correlat vector responses. In this paper, VGLMs and VGAMs are described and illustrated using examples that are of particular relevance to plant ecologists. It is attempted to show that VGAMs offer greater scope for additive modeling. Use of s-plus/r software written by the first author is illustrated on a few data sets using several statistical models, which include the negative binomial, beta distribution and the bivariate logistic model. Details of how the software can be obtained are provided.

Journal

Ecological ModellingElsevier

Published: Nov 30, 2002

References

  • Smoothing reference centile curves: the LMS method and penalized likelihood
    Cole, T.J.; Green, P.J.
  • Alternative models for ordinal logistic regression
    Greenland, S.
  • Ordinal response regression models in ecology
    Guisan, A.; Harrell, F.E.
  • Predictive habitat distribution models in ecology
    Guisan, A.; Zimmermann, N.
  • Modelling and smoothing parameter estimation with multiple quadratic penalties
    Wood, S.N.
  • Comparison of statistical methods for age-related reference intervals
    Wright, E.M.; Royston, P.A.
  • On an alternative solution to the vector spline problem
    Yee, T.W.

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