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.