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VGAM (version 1.1-14)

Vector Generalized Linear and Additive Models

Description

An implementation of about 6 major classes of statistical regression models. The central algorithm is Fisher scoring and iterative reweighted least squares. At the heart of this package are the vector generalized linear and additive model (VGLM/VGAM) classes. VGLMs can be loosely thought of as multivariate GLMs. VGAMs are data-driven VGLMs that use smoothing. The book "Vector Generalized Linear and Additive Models: With an Implementation in R" (Yee, 2015) gives details of the statistical framework and the package. Currently only fixed-effects models are implemented. Many (100+) models and distributions are estimated by maximum likelihood estimation (MLE) or penalized MLE. The other classes are RR-VGLMs (reduced-rank VGLMs), quadratic RR-VGLMs, doubly constrained RR-VGLMs, quadratic RR-VGLMs, reduced-rank VGAMs, RCIMs (row-column interaction models)---these classes perform constrained and unconstrained quadratic ordination (CQO/UQO) models in ecology, as well as constrained additive ordination (CAO). Hauck-Donner effect detection is implemented. Note that these functions are subject to change; see the NEWS and ChangeLog files for latest changes.

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Version

Install

install.packages('VGAM')

Monthly Downloads

51,402

Version

1.1-14

License

GPL-3

Maintainer

Thomas Yee

Last Published

December 4th, 2025

Functions in VGAM (1.1-14)

The AB-Ab-aB-ab Blood Group System

Bayesian Information Criterion

Computation of the Exact EIM of an Order-1 Autoregressive Process

Autoregressive Process with Order-1 Family Function

The AR-1 Autoregressive Process

Akaike's Information Criterion

The A1A2A3 Blood Group System

The AA-Aa-aa Blood Group System

The ABO Blood Group System

Constraint Matrices for Symmetry, Order, Parallelism, etc.

Extract Model Coefficients for VLM Objects

Influence Function (S4 generic) of a Fitted Model

Returns Important Matrices etc. of a RR-VGLM Object

CommonVGAMffArguments

Common VGAM Family Function Arguments

Table 1 of Huggins (1989)

Coef.rrvglm-class

Class ``Coef.rrvglm''

Computes Model Coefficients and Quantities

Returns Important Matrices etc. of a QO Object

The Inverse Gaussian Distribution

Coef.qrrvglm-class

Class ``Coef.qrrvglm''

Linear Model and Poisson Mixed Data Type Distribution

The Pareto Distribution

Linear Model and Binomial Mixed Data Type Distribution

Link functions for VGLM/VGAM/etc. families

Linear Model and Poisson Mixed Data Type Family Function

Linear Model and Binomial Mixed Data Type Family Function

The MNSs Blood Group System

Kullback-Leibler Divergence

Quasi-variances Preprocessing Function

Mark the Baseline of Row and Column on a Matrix data

Create a Survival Object

R-squared for Latent Variable Models

Takeuchi's Information Criterion

Seemingly Unrelated Regressions Family Function

Select Variables for a Formula Response or the RHS of a Formula

V2 Missile Hits in London

Altered, Inflated, Truncated and Deflated Values in GAITD Regression

Truncated Values for the GT-Expansion Method

Exponential Regression by Asymmetric Maximum Likelihood Estimation

Utility Functions for the VGAM Package

Ordinal Regression with Adjacent Categories Probabilities

Binomial Logistic Regression by Asymmetric Maximum Likelihood Estimation

V1 Flying-Bombs Hits in London

Arcsine--Logit Link Mixtures

Vector Generalized Linear and Additive Models and Other Associated Models

Bacon and Eggs Data

Data on Back Pain Prognosis, from Anderson (1984)

Benford's Distribution

Asymmetric Least Squares Quantile Regression

The Bell Series of Integers

Poisson Regression by Asymmetric Maximum Likelihood Estimation

Arcsine Link Function

Auckland University Undergraduate Counts Data

Analysis of Deviance for Vector Generalized Linear Model Fits

aux.posbernoulli.t

Auxiliary Function for the Positive Bernoulli Family Function with Time Effects

The Beta-Geometric Distribution

The Benini Distribution

Benini Distribution Family Function

betabinomial.rho

Beta-binomial Distribution Family Function (with known rho)

The Two-parameter Beta Distribution Family Function

Beta Distribution of the Second Kind

Beta-binomial Distribution Family Function

The Beta-Binomial Distribution

The Two-parameter Beta Distribution Family Function

Beta-binomial Distribution Family Function

The Beta-Normal Distribution

Bivariate Farlie-Gumbel-Morgenstern Exponential Distribution Family Function

Farlie-Gumbel-Morgenstern's Bivariate Distribution

Clayton Copula (Bivariate) Distribution

The Beta-Prime Distribution

Farlie-Gumbel-Morgenstern's Bivariate Distribution Family Function

Clayton Copula (Bivariate) Family Function

Ali-Mikhail-Haq Bivariate Distribution

Beta-geometric Distribution Family Function

Ali-Mikhail-Haq Distribution Family Function

Gumbel's Type I Bivariate Distribution Family Function

Bivariate Logistic Distribution Family Function

Frank's Bivariate Distribution

Frank's Bivariate Distribution Family Function

Bivariate Binary Regression with an Odds Ratio (Family Function)

Bivariate Probit Regression

Bivariate Odds Ratio Model

Bivariate Logistic Distribution

Bivariate Probit Model

Trivariate Binary Regression with Three Odds Ratios (Family Function)

Binomial Family Function

Plackett's Bivariate Copula Family Function

Gaussian Copula (Bivariate) Family Function

Bivariate Normal Distribution

Gaussian Copula (Bivariate) Distribution

Trivariate Odds Ratio Model

Plackett's Bivariate Copula

Bivariate Normal Distribution Family Function

Biplot of Constrained Regression Models

Birnbaum-Saunders Regression Family Function

Bivariate Student-t Family Function

The Birnbaum-Saunders Distribution

Body Mass Index of New Zealand Adults Data

The Borel-Tanner Distribution

Western Spuce Budworm

Bivariate Student-t Distribution Density Function

Inputting Data to fit a Bradley Terry Model

Borel-Tanner Distribution Family Function

Bradley Terry Model With Ties

Bradley Terry Model

calibrate.rrvglm

Calibration for CLO models (RR-VGLMs)

Cardioid Distribution

Cardioid Distribution Family Function

Model Calibrations

calibrate.qrrvglm.control

Control Function for CQO/CAO Calibration

calibrate.rrvglm.control

Control Function for CLO (RR-VGLM) Calibration

calibrate.qrrvglm

Calibration for CQO and CAO models

Fitting Constrained Additive Ordination (CAO)

Control Function for RR-VGAMs (CAO)

calibrate-methods

Calibration for Constrained Regression Models

Chest Pain in NZ Adults Data

Cystic Fibrosis Data

Cauchy Distribution Family Function

Chinese Population in New Zealand 1867--2001 Data

Censored Gumbel Distribution

Censored Normal Distribution

Redirects the user to cqo

Cauchit Link Function

Censored Poisson Family Function

Cumulative Distribution Function for LMS Quantile Regression

Breathlessness and Wheeze Amongst Coalminers Data

concoef-methods

Constrained (Canonical) Coefficients

Redirects the User to rrvglm()

Extract Model Constrained/Canonical Coefficients

Extract Model Coefficients of a vgam() Object

Chi-squared and Chi Distributions

Extract Model Coefficients

Complementary Log-log Link Function

Constraint Matrices

Confidence Intervals for Parameters of VGLMs

Fitting Constrained Quadratic Ordination (CQO)

Crashes on New Zealand Roads in 2009

Corbet's Butterfly Data

Centre of the Parameter Space Distance for GLMs

Centre of the Parameter Space for GLMs

Centre of the Parameter Space Distance

Dagum Distribution Family Function

Centre of the Parameter Space

Differenced Zeta Distribution Family Function

Ordinal Regression with Continuation Ratios

Ordinal Regression with Cumulative Probabilities

Differenced Zeta Distribution

The Dagum Distribution

Captures of Peromyscus maniculatus (Also Known as Deer Mice).

Fitting a Dirichlet Distribution

Fitting a Dirichlet-Multinomial Distribution

Dependent (Response) Variable Extracted

Density Plot for LMS Quantile Regression

Plotting the GAITD Combo Density

Residual Degrees-of-Freedom

Error Function, and variants

Expectiles-Exponential

Expectiles of the Exponential Distribution

Expectiles-Normal

Expectiles of the Normal Distribution

Relative Frequencies of Serum Proteins in White Pekin Ducklings

Fitting a Dirichlet-Multinomial Distribution

double.expbinomial

Double Exponential Binomial Distribution Family Function

Empirical Cumulative Distribution Function

double.cens.normal

Univariate Normal Distribution with Double Censoring

Add or Drop All Possible Single Terms to/from a Model

Exponential Logarithmic Distribution Family Function

The Exponential Geometric Distribution

Erlang Distribution

Exponential Geometric Distribution Family Function

Exponentiated Exponential Distribution

The Exponential Logarithmic Distribution

Expectiles-Uniform

Expectiles of the Uniform Distribution

The Exponential Integral and Variants

Exponential Link Function

Exponentiated Exponential Distribution

Extended log-F Distribution

Mortality of Flour Beetles from Carbon Disulphide

Family Function Name

Exponential Distribution

Extended log-F Distribution Family Function

The Extended Beta-Binomial Distribution

The Exponential Poisson Distribution

Eye Disease Data: Diabetic Retinopathy

extbetabinomial

Extended Beta-binomial Distribution Family Function

Exponential Poisson Distribution Family Function

Fitted Values of a VLM object

The Felix Distribution

Toxicity trial for insects

Creates a Matrix of Appropriate Dimension

Fixing a Quantile Regression having Crossing

Fisk Distribution family function

Felix Distribution Family Function

The Fisk Distribution

F Distribution Family Function

Fisher's Z Link Function

Square Root and Folded Square Root Link Functions

The Frechet Distribution

Generally Altered, Inflated, Truncated and Deflated Logarithmic Regression

Model Formulae and Term Names for VGLMs

Folded Normal Distribution Family Function

Frechet Distribution Family Function

Freund's (1961) Bivariate Extension of the Exponential Distribution

The Folded-Normal Distribution

Generally Altered, Inflated, Truncated and Deflated Binomial Distribution

Generally Altered, Inflated, Truncated and Deflated Logarithmic Distribution

Generally Altered, Inflated, Truncated and Deflated Poisson Regression

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Distribution

1-parameter Gamma Regression Family Function

Multivariate Gamma Family Function: Mathai and Moschopoulos (1992)

2-parameter Gamma Regression Family Function

Generally Altered, Inflated, Truncated and Deflated Zeta Regression

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Regression

Generally Altered, Inflated and Truncated and Deflated Zeta Distribution

Generally Altered, Inflated, Truncated and Deflated Poisson Distribution

2-parameter Gamma Regression Family Function

GARMA (Generalized Autoregressive Moving-Average) Models

Gamma Hyperbola Bivariate Distribution

Generalized Poisson Distribution (Original Parameterization)

The Generalized Beta II Distribution

Generalized Gamma Distribution

Generalized Poisson Distribution (GP-1 and GP-2 Parameterizations of the Mean)

Generalized Beta Distribution of the Second Kind

Generalized Poisson Regression (Original Parameterization)

Generalized Gamma distribution family function

Generalized Poisson Regression (GP-1 Parameterization)

The Generalized Rayleigh Distribution

The Generalized Extreme Value Distribution

Generalized Poisson Regression (GP-2 Parameterization)

Retrieve One Component of ``.smart.prediction''

Generalized Rayleigh Distribution Family Function

Geometric (Truncated and Untruncated) Distributions

Generalized Secant Hyperbolic Distribution

Generalized Secant Hyperbolic Regression Family Function

Generalized Extreme Value Regression Family Function

get.smart.prediction

Retrieves ``.smart.prediction''

Grain Prices Data in USA

GAITD Offset for the GTE Method

Gompertz Regression Family Function

General Electric and Westinghouse Data

The Generalized Pareto Distribution

Gompertz Distribution

Gumbel-II Regression Family Function

Row-Column Interaction Models including Goodman's RC Association Model and Unconstrained Quadratic Ordination

Gumbel Regression Family Function

Generalized Pareto Distribution Regression Family Function

The Gumbel-II Distribution

Hunting Spider Data

Hormone Assay Data

The Gumbel Distribution

Hat Values and Regression Deletion Diagnostics

Hauck-Donner Effects: A Detection Test for Wald Tests

has.interceptvlm

Has a Fitted VGLM Got an Intercept Term?

Hauck-Donner Effect: Severity Measures

Hauck-Donner Effect: Severity Measures

Huber's Least Favourable Distribution Family Function

Husler-Reiss Angular Surface Distribution Family Function

Index from Array to Matrix

Haight's Zeta Distribution

Huber's Least Favourable Distribution

Hypergeometric Family Function

Hunua Ranges Data

The Husler-Reiss Angular Surface Distribution

Hyperbolic Secant Regression Family Function

Haight's Zeta Family Function

Identity Link Function

Inverse Gaussian Distribution Family Function

Inverse Binomial Distribution Family Function

Quantile Crossing Detection

Parallelism Constraint Matrices

Inverse Lomax Distribution Family Function

inv.paralogistic

Inverse Paralogistic Distribution Family Function

The Inverse Lomax Distribution

Inv.paralogistic

The Inverse Paralogistic Distribution

Does the Fitted Object Suffer from a Known Bug?

The Kumaraswamy Distribution

The Laplace Distribution

The Lambert W Function

Kumaraswamy Regression Family Function

Test For a Smart Object

Laplace Regression Family Function

Kendall's Tau Statistic

Annual catches on Lake Otamangakau from October 1974 to October 1989

Zero Constraint Matrices

Latent Variables

Acute Myelogenous Leukemia Survival Data

The Log-Gamma Distribution

Link Functions for VGLMs

Generalized Beta Distribution Family Function

Levy Distribution Family Function

The Lindley Distribution

Lerch Phi Function

Log-gamma Distribution Family Function

Logarithms with an Unit Offset and Exponential Term

1-parameter Lindley Distribution

Leipnik Regression Family Function

log F Distribution

The Generalized Beta Distribution (Libby and Novick, 1982)

LMS Quantile Regression with a Box-Cox Transformation to Normality

Extract Log-likelihood for VGLMs/VGAMs/etc.

Low-iron Rat Teratology Data

Natural Exponential Family Generalized Hyperbolic Secant Distribution Family Function

Logarithmic Distribution

LMS Quantile Regression with a Box-Cox transformation to a Gamma Distribution

LMS Quantile Regression with a Yeo-Johnson Transformation to Normality

logitoffsetlink

Logit-with-an-Offset Link Function

Loglinear Model for Four Binary Responses

Logarithmic Distribution

Log Link Function, and Variants

Loglinear Model for Two Binary Responses

Logistic Distribution Family Function

Complementary-log Link Function

Log-log and Log-log-log Link Functions

Logit Link Function

Loglinear Model for Three Binary Responses

Latent Variable Plot

Minimizing the L-q norm Family Function

Likelihood Ratio Test Statistics Evaluated at the Null Values

Lognormal Distribution

Lomax Distribution Family Function

Latent Variable Plot for QO models

Likelihood Ratio Test of Nested Models

Leadbeater's Possums

The Lomax Distribution

Log Link Function with an Offset

New Zealand Marital Data

Machinists Accidents

The Makeham Distribution

The Maxwell Distribution

Marginal Effects for Several Categorical Response Models

Latent Variable Plot for RR-VGLMs

McCullagh (1989) Distribution Family Function

Mean of the GAITD Combo Density

Makeham Regression Family Function

Maxwell Regression Family Function

Mean Excess Plot

model.matrixvlm

Construct the Design Matrix of a VLM Object

Melbourne Daily Maximum Temperatures

Mixture of Two Poisson Distributions

Michaelis-Menten Model

Mixture of Two Univariate Normal Distributions

Construct the Model Frame of a VLM Object

model.matrixqrrvglm

Construct the Model Matrix of a QRR-VGLM Object

Mixture of Two Exponential Distributions

Number of Iterations

Nakagami Distribution

Negative Binomial Canonical Link Function

negbinomial.size

Negative Binomial Distribution Family Function With Known Size

Negative Binomial Distribution Family Function

Nakagami Regression Family Function

Univariate Normal Distribution as a Varying-Coefficient Model

Multi-logit Link Function

Multinomial Logit Model

Ordinal Poisson Family Function

The Pareto(IV/III/II) Distributions

Oxford Temperature Data

The Paralogistic Distribution

Paralogistic Distribution Family Function

notdocumentedyet

Undocumented and Internally Used Functions and Classes

Ordinal Superiority Measures

Pareto(IV/III/II) Distribution Family Functions

2008 and 2012 Summer Olympic Final Medal Count Data

Number of Parameters

The Perks Distribution

Derivatives of the Incomplete Gamma Integral

plotdeplot.lmscreg

Density Plot for LMS Quantile Regression

Pareto and Truncated Pareto Distribution Family Functions

Model Diagnostic Plots for QRR-VGLMs

Perks Distribution Family Function

pgamma.deriv.unscaled

Derivatives of the Incomplete Gamma Integral (Unscaled Version)

Perspective plot for QRR-VGLMs

plotqtplot.lmscreg

Quantile Plot for LMS Quantile Regression

plotdgaitd.vglm

Plotting the GAITD Combo Density from a GAITD Regression Object

Poisson Points Distribution

The Poisson Lognormal Distribution

Poisson Regression

Default VGAM Plotting

Positive Bernoulli Sequence Model

Main Effects Plot for a Row-Column Interaction Model (RCIM)

Pneumoconiosis in Coalminers Data

plotvgam.control

Control Function for plotvgam()

Plots for VGLMs

Poisson-points-on-a-plane/volume Distances Distribution

posbernoulli.tb

Positive Bernoulli Family Function with Time and Behavioural Effects

Positive-Geometric Distribution

The Positive-Normal Distribution

Positive Poisson Distribution Family Function

Positive Negative Binomial Distribution Family Function

Positive Bernoulli Family Function with Time Effects

Positive Binomial Distribution Family Function

Power Link Function

Positive Normal Distribution Family Function

Positive Bernoulli Family Function with Behavioural Effects

Pregnant Rats Toxological Experiment Data

Method for Profiling vglm Objects

Yellow-bellied Prinia

Adds a List to the End of the List ``.smart.prediction''

Proportional Odds Model for Ordinal Regression

Predict Method for a CQO fit

Prentice (1974) Log-gamma Distribution

Probit Link Function

Predict Method for a VGLM fit

Probability Plots for Categorical Data Analysis

Quantile Plot for LMS Quantile Regression

Quasi-variances Extraction Function

The Dirichlet distribution

Rayleigh Distribution

Quantile Plot for Gumbel Regression

Upper Record Values from a Univariate Normal Distribution

Upper Record Values from a 1-parameter Exponential Distribution

qrrvglm.control

Control Function for QRR-VGLMs (CQO)

Rayleigh Regression Family Function

Constrained Quadratic Ordination

The Rice Distribution

Rootograms (S4 generic) for Assessing Goodness of Fit of Probability Models

Reciprocal Link Function

Reciprocal Inverse Gaussian distribution

Return Level Plot for GEV Fits

Rounding of Numbers to Base 2

Rice Distribution Family Function

Rhobit Link Function

Nested Reduced-rank Autoregressive Models for Multiple Time Series

Residuals for a VGLM fit

Defining Smooths in VGAM Formulas

Rutherford-Geiger Polonium Data

Expectiles-sc.t2

Expectiles/Quantiles of the Scaled Student t Distribution with 2 Df

rrvglm.optim.control

Control Function for rrvglm() Calling optim()

Scaled Student t Distribution with 2 df Family Function

Rao's Score Test Statistics Evaluated at the Null Values

Fitting Reduced-Rank Vector Generalized Linear Models (RR-VGLMs) and Doubly Constrained RR-VGLMs (DRR-VGLMs)

Control Function for rrvglm()

Class ``rrvglm''

Hauck-Donner Effects: Segmented Lines Plot

The Skellam Distribution

The Singh-Maddala Distribution

Skew-Normal Distribution

Simulate Responses for VGLMs and VGAMs

Skellam Distribution Family Function

Singh-Maddala Distribution Family Function

Smart Prediction Setup

The Two-stage Sequential Binomial Distribution Family Function

Simplex Distribution

Simplex Distribution Family Function

Square root--Log Link Mixtures

Slash Distribution

Determine What Mode the Smart Prediction is In

Defining Penalized Spline Smooths in VGAM Formulas

Slash Distribution Family Function

Univariate Skew-Normal Distribution Family Function

Smart Prediction

Special Values or Quantities in a Fitted Object

Defining O'Sullivan Spline Smooths in VGAM Formulas

smart.expression

S Expression for Smart Functions

Ordinal Regression with Stopping Ratios

The Tobit Distribution

Choose a model by AIC in a Stepwise Algorithm

Summarizing Vector Generalized Additive Model Fits

Summarizing Vector Generalized Linear Model Fits

Tobit Regression

summary.drrvglm

Summarizing Reduced Rank Vector Generalized Linear Model (RR-VGLM) and Doubly constrained RR-VGLM Fits

Summarizing Penalized Vector Generalized Additive Model Fits

Student t Distribution

Trivariate Normal Distribution Density and Random Variates

The Truncated Pareto Distribution

Toxoplasmosis Data

The Triangle Distribution

Trajectory plot for QRR-VGLMs

trim.constraints

Trimmed Constraint Matrices

Trajectory Plot

Trivariate Normal Distribution Family Function

The Topp-Leone Distribution

Topp-Leone Distribution Family Function

Truncated Weibull Distribution Family Function

Control Function for vgam()

Venice Maximum Sea Levels Data

University California Berkeley Graduate Admissions

Univariate Normal Distribution

undocumented-methods

Undocumented Methods Functions

Fitting Vector Generalized Additive Models

Waitakere Ranges Data

Plotting Functions for 'profile' Objects

Class ``vglmff''

Wald Test Statistics Evaluated at the Null Values

von Mises Distribution Family Function

Prior and Working Weights of a VGLM fit

Yeo-Johnson Transformation

Fitting Vector Generalized Linear Models

Weibull Distribution Family Function

Bitterness in Wine Data

The WSDM Function

The WSDM Function for GLMs

Weibull Distribution Family Function, Parameterized by the Mean

Zero-Altered Binomial Distribution

Calculate Variance-Covariance Matrix for a Fitted VLM or RR-VGLM or DRR-VGLM or QRR-VGLM Object

Control Function for vglm()

Vector Cubic Smoothing Spline

Zero-Altered Geometric Distribution

Zero-Altered Poisson Distribution

Yule-Simon Family Function

Zero-Altered Negative Binomial Distribution

Zero-Altered Binomial Distribution

Zero-Altered Poisson Distribution

Zero-Altered Negative Binomial Distribution

The Zeta Distribution

Zero-Altered Geometric Distribution

Cleans Up After Smart Prediction

The zero Argument in VGAM Family Functions

Yule-Simon Distribution

Wald Distribution Family Function

Zipf Distribution Family Function

Zeta Distribution Family Function

Riemann's (and the Hurwitz) Zeta Function, With Derivatives

Exchangeable Bivariate cloglog Odds-ratio Model From a Zero-inflated Poisson Distribution

Zero-Inflated Negative Binomial Distribution Family Function

Zero-Inflated Geometric Distribution

Zero-Inflated Binomial Distribution

Zero-Inflated Negative Binomial Distribution

Zero-Inflated Geometric Distribution Family Function

Zero-Inflated Binomial Distribution Family Function

Zero- and One-Inflated Beta Distribution Family Function

Zero-Inflated Poisson Distribution

The Zipf-Mandelbrot Distribution

The Zipf Distribution

Zero-Inflated Poisson Distribution Family Function

The Zero/One-Inflated Beta Distribution