Constrained Additive Ordination

  • Thomas W. Yee
Part of the Springer Series in Statistics book series (SSS)


This chapter describes a nonparametric extension of RR-VGLMs and QRR-VGLMs, called RR-VGAMs, which enable constrained additive ordination (CAO) to be performed. RR-VGAMs are VGAMs fitted to a set of latent variables and some other explanatory variables \(\mbox{ $\boldsymbol{x}$}_{1}\). Unfortunately, only rank-1 models are currently implemented in VGAM, and to \(\mbox{ $\boldsymbol{x}$}_{1} = 1\), and to binary responses and Poisson counts only. Applied to multispecies data, one can see the ‘real’ shape of species’ response curves as a function of the dominant gradient—e.g., they are not constrained to be symmetric bell-shaped, as with QRR-VGLMs. A few practical suggestions are given to aid the use of the modelling function cao().


Component Function Site Score Approximate Standard Error Hunting Spider Nonlinear Degree 
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Copyright information

© Thomas Yee 2015

Authors and Affiliations

  • Thomas W. Yee
    • 1
  1. 1.Department of StatisticsUniversity of AucklandAucklandNew Zealand

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