VGAM FAMILY FUNCTIONS FOR CATEGORICAL AND GENETIC DATA(Categorical Data Analysis)

Vector generalized additive models (VGAMs) are a multivariate extension of generalized additive models (GAMs). VGAMs extend the GAM class mainly in two respects: they handle more than a single additive predictor, and consequently fit models outside the exponential family. VGAMs provide a large framework; they give maximum likelihood estimates for a wide range of data types and models such as univariate and multivariate distributions, categorical data analysis, time series, survival analysis, generalized estimating equations, correlated binary data, bioassay data and nonlinear least-squares problems. In this paper we briefly survey vector generalized linear models (VGLMs), VGAMs and an S-PLUS/R implementation called VGAM written by the author for general maximum likelihood estimation. Then we focus on specific family functions for categorical and genetic data, for example, the proportional odds, continuation ratio, adjacent categories and stereotype models for categorical data. The VGAM software library is freely available at http://www.stat.auckland.ac.nz/〜yee.