package for R
The VGAM package for
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
fit regression models to the following data types:
- Categorical response
- Multinomial logit model,
- Stereotype model (reduced-rank multinomial logit model).
- Proportional odds model (cumulative logit model),
- Proportional hazards model (cumulative cloglog model),
- Continuation ratio model (sequential logit model),
- Stopping ratio model,
- Adjacent categories model.
- 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-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
- Constrained additive ordination (CAO) ,
- RR-AR for time series.
- Count regression models,
e.g., a suite of negative binomial variants including
- NB-P (also known as the reduced-rank negative binomial),
- COZIGAMs (also known as the reduced-rank zero-inflated Poisson).
- 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).
- Linear and log-linear models
- Varying-coefficient (linear) model,
- Log-linear model for bi-/tri-variate binary responses.
- Zero-inflated, zero-altered (hurdle) and positive 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
CRAN Task View: Probability Distributions)
|Cauchy (1- and 2-parameter)
(and truncated geometric)
(and truncated Weibull)
(and truncated Pareto)
||reciprocal inverse Gaussian
|logistic (1- and 2-parameter)
||beta (2 parameterizations)
||generalized beta II
|McKay's bivariate gamma
||Freund (1961) bivariate exponential
||McCullagh's (1989) distribution
||Frank's bivariate distribution
||generalized beta (Libby and Novick, 1982)
||double exponential binomial
|Plackett's bivariate distribution
- Bivariate distributions and copulas
||Bivariate Clayton copula
|Bivariate Frank copula
- Nonstandard distributions
- 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
Here is the
VGAM reference card.pdf (192 KB)
(Last updated: 2020-10-24).
For a summary of VGAM
Here is a larger summary of VGAM:
VGAM.pdf (2.6 MB).
For the very latest (prerelease) version of VGAM
Some data sets have now been placed into another
package called VGAMdata.
There is also another
package called VGAMextra;
VGAMs are described in
Yee and Wild (1996), JRSSB 58: 481-493
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,
and ANSI C functions.
Currently VGAM is available at
It runs under R 3.4.0 or higher.
VGAM is written in Version 4 of the S language
(Chambers, 1998), also known as S4.
Mon Oct 26 10:08:27 NZDT 2020
Thomas Yee's personal home page