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 S functions vglm(), vgam(), rrvglm(), cqo(), cao() and uqo(). VGAM can fit regression models to the following data types:

• Categorical response
  • Nominal
    • Multinomial logit model,
    • Stereotype model (reduced-rank multinomial logit model),
    • Adjacent categories model,
  • Ordinal
    • Proportional odds model (cumulative logit model),
    • Proportional hazards model (cumulative cloglog model),
    • Continuation ratio model (sequential logit model),
    • Stopping ratio model,
  • Others
    • Bradley Terry model (with and without ties; intercept only),
• Quantile and expectile regression
  • LMS method - e.g., for age-related reference intervals (Box-Cox to normal, Box-Cox to gamma, Yeo-Johnson to normal distributions),
  • Asymmetric least squares (expectile regression), e.g., for normal, Poisson, binomial, exponential,
  • Asymmetric Laplace distribution,
  • Gumbel, GEV, GPD models - for extreme value data,
• Reduced-rank VGLMs
  • 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)
  • Unconstrained quadratic ordination (UQO)
  • Constrained additive ordination (CAO)
  • RR-AR for time series
• Random-effects binomial models
  • 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)
• Generalized estimating equations
  • Log-linear model for bi-/tri-variate binary responses
• Zero-inflated, zero-altered (hurdle) and positive distributions
  • zero-inflated Poisson, binomial, negative binomial,
  • zero-altered Poisson, binomial, negative binomial,
  • 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

  Cauchy (1- and 2-parameter)	exponential	geometric
  normal	negative binomial	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 (2 and 3 parameter)	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
  Asymmetric Laplace

• 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,
• Not done yet:
  • GEE1 for correlated binary data,
  • Frank's models
  • Circular data - e.g., cardioid, von Mises, 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 (136K) (Last updated: 2009-06-18).

  For a summary of VGAM click here
  Here is a larger summary of VGAM: VGAM.pdf (3.2 Mb).
  

  Users can write their own VGAM family function to solve their own problems. New VGAM family functions are being written all the time.

  NOTE: At this stage, vglm(), vgam(), rrvglm() and cqo() are pretty well functioning. The functions cao() and uqo() have limited functionality. Many of its methods functions work too. There are only a limited number of help files! There are a number of improvements yet to be added. There are a number of bugs (especially to do with some family functions)---please send in bug reports.

  VGAMs are described in Yee and Wild (1996), JRSSB 58: 481-493. If you use this software please quote from this BIBTEX file.

  The software, which is free, consists of R, FORTRAN 77 and 90, and ANSI C functions. A limited amount of PDF documentation is available. Only a few data sets have been incorporated (R version only), and some of the above family functions aren't distributed yet. Currently VGAM is available at CRAN. It runs under R 2.5.x or higher. VGAM is written in Version 4 of the S language (Chambers, 1998).

  To download VGAM click here
  

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  Last modified: Thu Jun 18 18:01:40 EDT 2009

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