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VGAM (version 1.1-13)

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

77,454

Version

1.1-13

License

GPL-3

Maintainer

Thomas Yee

Last Published

February 12th, 2025

Functions in VGAM (1.1-13)

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

Akaike's Information Criterion

The AR-1 Autoregressive Process

Autoregressive Process with Order-1 Family Function

The A1A2A3 Blood Group System

Computes Model Coefficients and Quantities

The AA-Aa-aa Blood Group System

Farlie-Gumbel-Morgenstern's Bivariate Distribution

Influence Function (S4 generic) of a Fitted Model

The Inverse Gaussian Distribution

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

Coef.qrrvglm-class

Class ``Coef.qrrvglm''

The AB-Ab-aB-ab Blood Group System

The ABO Blood Group System

Bivariate Farlie-Gumbel-Morgenstern Exponential Distribution Family Function

betabinomial.rho

Beta-binomial Distribution Family Function (with known rho)

Fitting Constrained Quadratic Ordination (CQO)

CommonVGAMffArguments

Common VGAM Family Function Arguments

The Pareto Distribution

Table 1 of Huggins (1989)

Linear Model and Binomial Mixed Data Type Distribution

Kullback-Leibler Divergence

Linear Model and Binomial Mixed Data Type Family Function

Link functions for VGLM/VGAM/etc. families

Create a Survival Object

Binomial Logistic Regression by Asymmetric Maximum Likelihood Estimation

Truncated Values for the GT-Expansion Method

Seemingly Unrelated Regressions Family Function

Exponential Regression by Asymmetric Maximum Likelihood Estimation

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

V1 Flying-Bombs Hits in London

V2 Missile Hits in London

The Bell Series of Integers

Utility Functions for the VGAM Package

Benford's Distribution

Analysis of Deviance for Vector Generalized Linear Model Fits

Returns Important Matrices etc. of a QO Object

Bayesian Information Criterion

Mark the Baseline of Row and Column on a Matrix data

The Beta-Binomial Distribution

Vector Generalized Linear and Additive Models and Other Associated Models

Arcsine Link Function

Beta-binomial Distribution Family Function

Benini Distribution Family Function

Ordinal Regression with Adjacent Categories Probabilities

Constraint Matrices for Symmetry, Order, Parallelism, etc.

Coef.rrvglm-class

Class ``Coef.rrvglm''

Auckland University Undergraduate Counts Data

aux.posbernoulli.t

Auxiliary Function for the Positive Bernoulli Family Function with Time Effects

The Benini Distribution

Clayton Copula (Bivariate) Distribution

The Two-parameter Beta Distribution Family Function

Farlie-Gumbel-Morgenstern's Bivariate Distribution Family Function

Returns Important Matrices etc. of a RR-VGLM Object

Extract Model Coefficients for VLM Objects

The Beta-Geometric Distribution

calibrate-methods

Calibration for Constrained Regression Models

Bivariate Odds Ratio Model

Model Calibrations

Linear Model and Poisson Mixed Data Type Distribution

The MNSs Blood Group System

Bivariate Probit Regression

Binomial Family Function

Ali-Mikhail-Haq Bivariate Distribution

Beta Distribution of the Second Kind

Linear Model and Poisson Mixed Data Type Family Function

Clayton Copula (Bivariate) Family Function

The Two-parameter Beta Distribution Family Function

Takeuchi's Information Criterion

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Distribution

The Beta-Normal Distribution

Data on Back Pain Prognosis, from Anderson (1984)

Bivariate Logistic Distribution Family Function

Beta-geometric Distribution Family Function

Quasi-variances Preprocessing Function

Bacon and Eggs Data

R-squared for Latent Variable Models

Fisher's Z Link Function

Gaussian Copula (Bivariate) Family Function

Gaussian Copula (Bivariate) Distribution

Arcsine--Logit Link Mixtures

Bivariate Binary Regression with an Odds Ratio (Family Function)

Lomax Distribution Family Function

Altered, Inflated, Truncated and Deflated Values in GAITD Regression

Beta-binomial Distribution Family Function

Cumulative Distribution Function for LMS Quantile Regression

Gumbel's Type I Bivariate Distribution Family Function

Asymmetric Least Squares Quantile Regression

Biplot of Constrained Regression Models

Poisson Regression by Asymmetric Maximum Likelihood Estimation

Plackett's Bivariate Copula Family Function

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

Bivariate Logistic Distribution

Inputting Data to fit a Bradley Terry Model

Birnbaum-Saunders Regression Family Function

Trivariate Odds Ratio Model

Chest Pain in NZ Adults Data

The Birnbaum-Saunders Distribution

Dagum Distribution Family Function

Bivariate Student-t Family Function

The Lindley Distribution

Exponential Link Function

Frank's Bivariate Distribution Family Function

Frank's Bivariate Distribution

The Exponential Logarithmic Distribution

Cauchy Distribution Family Function

The Beta-Prime Distribution

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

Crashes on New Zealand Roads in 2009

Plotting the GAITD Combo Density

The Lambert W Function

Expectiles-Normal

Expectiles of the Normal Distribution

Bradley Terry Model

Censored Normal Distribution

Topp-Leone Distribution Family Function

double.cens.normal

Univariate Normal Distribution with Double Censoring

Differenced Zeta Distribution

Ali-Mikhail-Haq Distribution Family Function

Generally Altered, Inflated, Truncated and Deflated Logarithmic Regression

calibrate.qrrvglm

Calibration for CQO and CAO models

Bivariate Student-t Distribution Density Function

Cardioid Distribution

Relative Frequencies of Serum Proteins in White Pekin Ducklings

Body Mass Index of New Zealand Adults Data

calibrate.qrrvglm.control

Control Function for CQO/CAO Calibration

Confidence Intervals for Parameters of VGLMs

Cardioid Distribution Family Function

Cystic Fibrosis Data

Generalized Poisson Regression (GP-2 Parameterization)

The Felix Distribution

Redirects the user to cqo

Fixing a Quantile Regression having Crossing

Borel-Tanner Distribution Family Function

Censored Gumbel Distribution

Generally Altered, Inflated, Truncated and Deflated Binomial Distribution

Fitting a Dirichlet-Multinomial Distribution

Ordinal Regression with Continuation Ratios

Complementary Log-log Link Function

Breathlessness and Wheeze Amongst Coalminers Data

Redirects the User to rrvglm()

Plackett's Bivariate Copula

Chinese Population in New Zealand 1867--2001 Data

Bivariate Probit Model

F Distribution Family Function

Trivariate Binary Regression with Three Odds Ratios (Family Function)

Residual Degrees-of-Freedom

Extract Model Coefficients

Corbet's Butterfly Data

Bivariate Normal Distribution Family Function

Quasi-variances Extraction Function

Kendall's Tau Statistic

Bivariate Normal Distribution Cumulative Distribution Function

The Dagum Distribution

Bradley Terry Model With Ties

Extract Model Coefficients of a vgam() Object

Hauck-Donner Effect: Severity Measures

Western Spuce Budworm

Laplace Regression Family Function

The Generalized Pareto Distribution

Gompertz Regression Family Function

New Zealand Marital Data

Fitting Constrained Additive Ordination (CAO)

Fitting a Dirichlet-Multinomial Distribution

Control Function for RR-VGAMs (CAO)

The Borel-Tanner Distribution

Mortality of Flour Beetles from Carbon Disulphide

Constraint Matrices

Cauchit Link Function

Hauck-Donner Effect: Severity Measures

Chi-squared and Chi Distributions

Response Variable Extracted

Fitting a Dirichlet Distribution

Husler-Reiss Angular Surface Distribution Family Function

Extract Model Constrained/Canonical Coefficients

double.expbinomial

Double Exponential Binomial Distribution Family Function

calibrate.rrvglm

Calibration for CLO models (RR-VGLMs)

extbetabinomial

Extended Beta-binomial Distribution Family Function

calibrate.rrvglm.control

Control Function for CLO (RR-VGLM) Calibration

Exponential Logarithmic Distribution Family Function

Censored Poisson Family Function

Gumbel-II Regression Family Function

Expectiles-Exponential

Expectiles of the Exponential Distribution

Constrained Quadratic Ordination

The Extended Beta-Binomial Distribution

Frechet Distribution Family Function

Exponentiated Exponential Distribution

LMS Quantile Regression with a Yeo-Johnson Transformation to Normality

Grain Prices Data in USA

Generalized Gamma Distribution

Exponential Distribution

Lognormal Distribution

Empirical Cumulative Distribution Function

Gamma Hyperbola Bivariate Distribution

Pareto and Truncated Pareto Distribution Family Functions

Univariate Skew-Normal Distribution Family Function

Minimizing the L-q norm Family Function

Inverse Lomax Distribution Family Function

Generally Altered, Inflated, Truncated and Deflated Logarithmic Distribution

Expectiles-Uniform

Expectiles of the Uniform Distribution

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

concoef-methods

Constrained (Canonical) Coefficients

Centre of the Parameter Space

Generalized Pareto Distribution Regression Family Function

The Exponential Geometric Distribution

Density Plot for LMS Quantile Regression

The Topp-Leone Distribution

The Fisk Distribution

Fisk Distribution family function

Huber's Least Favourable Distribution

Inverse Binomial Distribution Family Function

Toxicity trial for insects

Gompertz Distribution

Differenced Zeta Distribution Family Function

Exponentiated Exponential Distribution

The Generalized Extreme Value Distribution

Hunua Ranges Data

Hauck-Donner Effects: A Detection Test for Wald Tests

plotdgaitd.vglm

Plotting the GAITD Combo Density from a GAITD Regression Object

Extended log-F Distribution Family Function

Generally Altered, Inflated and Truncated and Deflated Zeta Distribution

The Frechet Distribution

The Log-Gamma Distribution

The Exponential Integral and Variants

Identity Link Function

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

Creates a Matrix of Appropriate Dimension

Parallelism Constraint Matrices

Perspective plot for QRR-VGLMs

The Folded-Normal Distribution

Generally Altered, Inflated, Truncated and Deflated Zeta Regression

GARMA (Generalized Autoregressive Moving-Average) Models

Generalized Secant Hyperbolic Regression Family Function

The Makeham Distribution

Folded Normal Distribution Family Function

Inv.paralogistic

The Inverse Paralogistic Distribution

Generalized Rayleigh Distribution Family Function

2-parameter Gamma Regression Family Function

Fitted Values of a VLM object

get.smart.prediction

Retrieves ``.smart.prediction''

Lerch Phi Function

Error Function, and variants

Erlang Distribution

Rounding of Numbers to Base 2

Generalized Extreme Value Regression Family Function

Mean of the GAITD Combo Density

Hunting Spider Data

Method for Profiling vglm Objects

Generalized Gamma distribution family function

Generally Altered, Inflated, Truncated and Deflated Poisson Distribution

Log-log and Log-log-log Link Functions

Loglinear Model for Three Binary Responses

Natural Exponential Family Generalized Hyperbolic Secant Distribution Family Function

Ordinal Regression with Cumulative Probabilities

Exponential Geometric Distribution Family Function

Family Function Name

1-parameter Gamma Regression Family Function

has.interceptvlm

Has a Fitted VGLM Got an Intercept Term?

Exponential Poisson Distribution Family Function

Low-iron Rat Teratology Data

The Exponential Poisson Distribution

Hat Values and Regression Deletion Diagnostics

model.matrixqrrvglm

Construct the Model Matrix of a QRR-VGLM Object

Extended log-F Distribution

The Generalized Rayleigh Distribution

Hyperbolic Secant Regression Family Function

Kumaraswamy Regression Family Function

Marginal Effects for Several Categorical Response Models

Generalized Beta Distribution of the Second Kind

The Husler-Reiss Angular Surface Distribution

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Regression

Square Root and Folded Square Root Link Functions

LMS Quantile Regression with a Box-Cox Transformation to Normality

Latent Variable Plot for QO models

The Generalized Beta Distribution (Libby and Novick, 1982)

Felix Distribution Family Function

log F Distribution

model.matrixvlm

Construct the Design Matrix of a VLM Object

Quantile Crossing Detection

Haight's Zeta Family Function

Does the Fitted Object Suffer from a Known Bug?

The Lomax Distribution

Generalized Poisson Distribution (Original Parameterization)

Construct the Model Frame of a VLM Object

Slash Distribution Family Function

The Kumaraswamy Distribution

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

notdocumentedyet

Undocumented and Internally Used Functions and Classes

Leipnik Regression Family Function

Trivariate Normal Distribution Family Function

The Pareto(IV/III/II) Distributions

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

Positive Bernoulli Family Function with Time Effects

Generalized Poisson Regression (Original Parameterization)

2-parameter Gamma Regression Family Function

The Perks Distribution

Multivariate Gamma Family Function: Mathai and Moschopoulos (1992)

General Electric and Westinghouse Data

Log-gamma Distribution Family Function

Generalized Secant Hyperbolic Distribution

negbinomial.size

Negative Binomial Distribution Family Function With Known Size

The Inverse Lomax Distribution

Model Formulae and Term Names for VGLMs

The Gumbel-II Distribution

Geometric (Truncated and Untruncated) Distributions

logitoffsetlink

Logit-with-an-Offset Link Function

Generally Altered, Inflated, Truncated and Deflated Poisson Regression

Logarithms with an Unit Offset and Exponential Term

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

Log Link Function, and Variants

Maxwell Regression Family Function

Multi-logit Link Function

Positive Binomial Distribution Family Function

Hypergeometric Family Function

Poisson Points Distribution

Latent Variable Plot for RR-VGLMs

Predict Method for a CQO fit

Multinomial Logit Model

Perks Distribution Family Function

The Gumbel Distribution

Huber's Least Favourable Distribution Family Function

The Maxwell Distribution

Leadbeater's Possums

Test For a Smart Object

Univariate Normal Distribution as a Varying-Coefficient Model

Positive Normal Distribution Family Function

Tobit Regression

Gumbel Regression Family Function

Slash Distribution

Likelihood Ratio Test of Nested Models

Model Diagnostic Plots for QRR-VGLMs

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

The Generalized Beta II Distribution

McCullagh (1989) Distribution Family Function

Derivatives of the Incomplete Gamma Integral

Summarizing Vector Generalized Linear Model Fits

Quantile Plot for Gumbel Regression

Hormone Assay Data

Log Link Function with an Offset

The Laplace Distribution

Inverse Gaussian Distribution Family Function

Generalized Poisson Regression (GP-1 Parameterization)

pgamma.deriv.unscaled

Derivatives of the Incomplete Gamma Integral (Unscaled Version)

Positive-Geometric Distribution

plotdeplot.lmscreg

Density Plot for LMS Quantile Regression

Quantile Plot for LMS Quantile Regression

The Paralogistic Distribution

Haight's Zeta Distribution

Rayleigh Distribution

Complementary-log Link Function

Rayleigh Regression Family Function

Oxford Temperature Data

Default VGAM Plotting

Number of Iterations

Scaled Student t Distribution with 2 df Family Function

inv.paralogistic

Inverse Paralogistic Distribution Family Function

Zero-Inflated Poisson Distribution Family Function

The Tobit Distribution

Link Functions for VGLMs

Negative Binomial Distribution Family Function

GAITD Offset for the GTE Method

Zero-Altered Binomial Distribution

1-parameter Lindley Distribution

Annual catches on Lake Otamangakau from October 1974 to October 1989

Machinists Accidents

Loglinear Model for Two Binary Responses

Pareto(IV/III/II) Distribution Family Functions

Generalized Beta Distribution Family Function

Weibull Distribution Family Function

Makeham Regression Family Function

Extract Log-likelihood for VGLMs/VGAMs/etc.

Reciprocal Inverse Gaussian distribution

Logarithmic Distribution

Index from Array to Matrix

Zero-Altered Geometric Distribution

Mixture of Two Univariate Normal Distributions

Mixture of Two Poisson Distributions

The Zero/One-Inflated Beta Distribution

Prentice (1974) Log-gamma Distribution

Latent Variable Plot

Ordinal Poisson Family Function

Zero Constraint Matrices

Return Level Plot for GEV Fits

Mixture of Two Exponential Distributions

Acute Myelogenous Leukemia Survival Data

Likelihood Ratio Test Statistics Evaluated at the Null Values

Hauck-Donner Effects: Segmented Lines Plot

Levy Distribution Family Function

Determine What Mode the Smart Prediction is In

Latent Variables

Nested Reduced-rank Autoregressive Models for Multiple Time Series

The zero Argument in VGAM Family Functions

Residuals for a VGLM fit

Plots for VGLMs

Predict Method for a VGLM fit

Logistic Distribution Family Function

Zero-Altered Poisson Distribution

Probit Link Function

Pneumoconiosis in Coalminers Data

Defining O'Sullivan Spline Smooths in VGAM Formulas

Zero-Inflated Geometric Distribution

Zero-Inflated Negative Binomial Distribution Family Function

Logarithmic Distribution

Trajectory Plot

posbernoulli.tb

Positive Bernoulli Family Function with Time and Behavioural Effects

The Dirichlet distribution

Ordinal Superiority Measures

The Positive-Normal Distribution

Positive Poisson Distribution Family Function

Mean Excess Plot

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

Ordinal Regression with Stopping Ratios

Logit Link Function

The Truncated Pareto Distribution

Upper Record Values from a 1-parameter Exponential Distribution

Number of Parameters

Trajectory plot for QRR-VGLMs

Fitting Vector Generalized Additive Models

plotvgam.control

Control Function for plotvgam()

Nakagami Distribution

Trivariate Normal Distribution Density and Random Variates

Fitting Vector Generalized Linear Models

Weibull Distribution Family Function, Parameterized by the Mean

Nakagami Regression Family Function

Melbourne Daily Maximum Temperatures

Square root--Log Link Mixtures

Paralogistic Distribution Family Function

Positive Negative Binomial Distribution Family Function

trim.constraints

Trimmed Constraint Matrices

Special Values or Quantities in a Fitted Object

rrvglm.optim.control

Control Function for rrvglm() Calling optim()

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

Negative Binomial Canonical Link Function

Defining Smooths in VGAM Formulas

The Two-stage Sequential Binomial Distribution Family Function

Control Function for vglm()

University California Berkeley Graduate Admissions

plotqtplot.lmscreg

Quantile Plot for LMS Quantile Regression

Michaelis-Menten Model

The Skellam Distribution

2008 and 2012 Summer Olympic Final Medal Count Data

Control Function for rrvglm()

The Triangle Distribution

undocumented-methods

Undocumented Methods Functions

The WSDM Function

Skellam Distribution Family Function

Smart Prediction

Yellow-bellied Prinia

Cleans Up After Smart Prediction

Zero-Altered Negative Binomial Distribution

Control Function for vgam()

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

Univariate Normal Distribution

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

Simplex Distribution

qrrvglm.control

Control Function for QRR-VGLMs (CQO)

Expectiles-sc.t2

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

Poisson Regression

Pregnant Rats Toxological Experiment Data

Proportional Odds Model for Ordinal Regression

The Rice Distribution

Simulate Responses for VGLMs and VGAMs

Vector Cubic Smoothing Spline

Zero-Altered Negative Binomial Distribution

Rhobit Link Function

The Poisson Lognormal Distribution

Waitakere Ranges Data

Power Link Function

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

Defining Penalized Spline Smooths in VGAM Formulas

Zero-Inflated Negative Binomial Distribution

Class ``vglmff''

Upper Record Values from a Univariate Normal Distribution

Zero- and One-Inflated Beta Distribution Family Function

Rutherford-Geiger Polonium Data

Skew-Normal Distribution

Positive Bernoulli Sequence Model

Probability Plots for Categorical Data Analysis

Wald Distribution Family Function

Zero-Altered Poisson Distribution

Reciprocal Link Function

Student t Distribution

Positive Bernoulli Family Function with Behavioural Effects

The Zeta Distribution

summary.drrvglm

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

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

Class ``rrvglm''

Zero-Inflated Geometric Distribution Family Function

Toxoplasmosis Data

Zero-Altered Binomial Distribution

Summarizing Penalized Vector Generalized Additive Model Fits

Rao's Score Test Statistics Evaluated at the Null Values

Rice Distribution Family Function

Wald Test Statistics Evaluated at the Null Values

smart.expression

S Expression for Smart Functions

Yule-Simon Distribution

The Zipf-Mandelbrot Distribution

Smart Prediction Setup

Zeta Distribution Family Function

Venice Maximum Sea Levels Data

Singh-Maddala Distribution Family Function

Zipf Distribution Family Function

Simplex Distribution Family Function

Zero-Inflated Binomial Distribution

The Singh-Maddala Distribution

The Zipf Distribution

Choose a model by AIC in a Stepwise Algorithm

Prior and Working Weights of a VGLM fit

Zero-Altered Geometric Distribution

Summarizing Vector Generalized Additive Model Fits

Bitterness in Wine Data

von Mises Distribution Family Function

Truncated Weibull Distribution Family Function

Plotting Functions for 'profile' Objects

Zero-Inflated Binomial Distribution Family Function

Yeo-Johnson Transformation

Zero-Inflated Poisson Distribution

Yule-Simon Family Function