The VGAM package for R

The VGAM package for R fits vector generalized linear and additive models (VGLMs/VGAMs), as well as reduced-rank VGLMs (RR-VGLMs) and quadratic RR-VGLMs (QRR-VGLMs), and can be obtained below. It is a general program for maximum likelihood estimation, and centers on the six functions vglm(), vgam(), rrvglm(), cqo(), cao() and rcim().

VGAM can fit regression models to the following data types:

• Categorical response
  • Nominal
    • Multinomial logit model,
    • Stereotype model (reduced-rank multinomial logit model).
  • Ordinal
    • Proportional odds model (cumulative logit model),
    • Proportional hazards model (cumulative cloglog model),
    • Continuation ratio model (sequential logit model),
    • Stopping ratio model,
    • Adjacent categories model.
• Quantile and expectile regression
  • LMS method - e.g., for age-related reference intervals (Box-Cox to normal),
  • Asymmetric least squares (expectile regression), e.g., for normal, Poisson, binomial, exponential,
  • Gumbel, GEV, GPD models - for extreme value data.
• Reduced-rank VGLMs and Doubly constrained RR-VGLMs
  • e.g., RR-negative binomial (aka NB-P),
  • e.g., RR-multinomial (aka stereotype model), RR-Gaussian, etc. ,
  • Goodman's RC assocation model for two-way tables ,
  • Quadratic RR-VGLMs for constrained quadratic ordination (CQO; formerly called canonical Gaussian ordination or CGO)
  • Constrained additive ordination (CAO) ,
  • RR-AR for time series.
• Count regression models, e.g., a suite of negative binomial variants, or similar, including
  • NB-1,
  • NB-2,
  • NB-C,
  • NB-H,
  • NB-G,
  • NB-P (also known as the reduced-rank negative binomial),
  • COZIGAMs (also known as the reduced-rank zero-inflated Poisson),
  • VFL NB-Pois,
  • VFL GP-1-Pois,
  • VFL GP-2-Pois,
  • VFL EBB-Binom.
• Random-effects binomial models
  • Beta-binomial model - for teratological/toxicological data,
  • Extended beta-binomial model - for teratological/toxicological data,
  • Beta-geometric model - for offspring data.
• Bivariate binary responses
  • Bivariate logistic model (based on the odds ratio),
  • Bivariate probit model (based on the bivariate normal distribution).
• Linear and log-linear models
  • Varying-coefficient (linear) model,
  • Log-linear model for bi-/tri-variate binary responses.
• Generally altered, inflated, truncated and deflated (GAITD) regression
  • Poisson, logarithmic, zeta, negative binomial as parent distributions,
  • zero-inflated Poisson, binomial, negative binomial, geometric,
  • zero-altered Poisson, binomial, negative binomial, geometric,
  • positive Poisson, binomial, negative binomial, normal.
• Multivariate regression
  • Vector additive model,
  • Seemingly unrelated regressions (SUR).
• Nonlinear regression (via the Gauss-Newton algorithm)
  • Michaelis-Menten model,
  • Exponential regression (not distributed yet),
  • Multivariate nonlinear regression models (not working yet).
• Standard univariate and bivariate distributions (see also CRAN Task View: Probability Distributions)

  Cauchy (1- and 2-parameter)	exponential	geometric (and truncated geometric)
  normal	negative binomial	Weibull (and truncated Weibull)
  zeta	logarithmic series	inverse Gaussian
  Student t	chisquare	Pareto (and truncated Pareto)
  Haight's zeta	Erlang	Borel-Tanner
  log-gamma	generalized Poisson	inverse binomial
  hyperbolic secant	reciprocal inverse Gaussian	univariate simplex
  logistic (1- and 2-parameter)	gamma	beta (2 parameterizations)
  lognormal	skew normal	Leipnik
  Levy	Weibull	generalized beta II
  Singh-Maddala	Dagum	Fisk
  beta II	Lomax	inverse Lomax
  paralogistic	inverse paralogistic	Rayleigh
  Maxwell	Nakagami	beta-prime
  McKay's bivariate gamma	generalized gamma	Freund (1961) bivariate exponential
  F distribution	hypergeometric	McCullagh's (1989) distribution
  Frechet	4-parameter bilogistic	Frank's bivariate distribution
  von Mises	Birnbaum-Saunders	generalized beta (Libby and Novick, 1982)
  Zipf distribution	sequential binomial	double exponential binomial
  Plackett's bivariate distribution	Rice	Inverse binomial
  Kumaraswamy	Folded normal	Felix
  Lindley	Gompertz	Gumbel-II
  Makeham	Perks	Extended betabinomial (EBB; Prentice, 1986)
  Topp-Leone	Husler-Reiss angular surface	Generalized secant hyperbolic

• Bivariate distributions and copulas

  Bivariate normal	Bivariate Student-t	Bivariate Clayton copula
  Bivariate Frank copula	Ali-Mikhail-Haq	Farlie-Gumbel-Morgenstern

• Nonstandard distributions
  • Dirichlet, Dirichlet-multinomial
  • Genetic data, - e.g., A-B-AB-O, AB-Ab-aB-ab, blood groups,
  • Censored data, - e.g., normal, Tobit model, Gumbel, exponential,
  • Robust regression, - e.g., Huber,
  • Circular, - e.g., cardioid,
  • AR(1) for time series.
• Not done yet:
  • GEE1 for correlated binary data,
  • Circular data - e.g., wrapped-normal, wrapped-Cauchy (not distributed yet),
  • Spherical data (but none yet),
  • Binomial(n,p) - where p is known but n unknown,

  Here is the VGAM reference card.pdf (204 KB) (Last updated: 2024-09).

  For a summary of VGAM click here
  Here is a larger summary of VGAM: VGAM.pdf (2.8 MB).
  

  For the very latest (prerelease) version of VGAM click here
  

  Some data sets have now been placed into another package called VGAMdata. See here
  or CRAN. There is also another package on CRAN called VGAMextra.

  VGAMs are described in Yee and Wild (1996), JRSSB 58: 481-493 and Yee (2015), "Vector Generalized Linear and Additive Models: With an Implementation in R", Springer, NY:USA. If you use this software please quote from this BIBTEX file.

  The software, which is free, consists of R, FORTRAN 77 and ANSI C functions. Currently VGAM is available at CRAN. It runs under R 4.1.0 or higher. VGAM is written in Version 4 of the S language (Chambers, 1998), also known as S4.

  To download VGAM click here
  

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  Last modified: Thu 19 Sep 2024 11:37:57 NZST

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