Reduced-rank vector generalized linear models
by Thomas Yee
Abstract: The class of vector generalized linear and additive models (VGLMs/VGAMs) is very large and contains many statistical models, e.g., univariate and multivariate distributions, categorical data analysis, extreme value analysis, correlated binary data and nonlinear regression. Upon a quick overview of the framework and how to fit these using my VGAM package for R, we will focus on the reduced-rank VGLM (RR-VGLM) subclass. This contains the reduced-rank multinomial logit (aka stereotype) and Goodman's row-column association models for count data. Ecological ordination can, in theory, be partially performed too. Two-parameter RR-VGLMs hold surprisingly useful applications such as a negative-binomial distribution with a flexible data-driven variance function (aka NB-P) and the zero-inflated Poisson (aka COZIGAM). RR-VGLMs provide a technique for practical quasi-likelihood data analysis and there is untapped potential to be developed here.