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VGAM (version 1.1-12)

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

42,087

Version

1.1-12

License

GPL-3

Maintainer

Last Published

September 18th, 2024

Functions in VGAM (1.1-12)

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

Akaike's Information Criterion

Bayesian Information Criterion

The A1A2A3 Blood Group System

The AB-Ab-aB-ab Blood Group System

The AR-1 Autoregressive Process

Returns Important Matrices etc. of a RR-VGLM Object

Autoregressive Process with Order-1 Family Function

The AA-Aa-aa Blood Group System

Constraint Matrices for Symmetry, Order, Parallelism, etc.

Extract Model Coefficients for VLM Objects

Linear Model and Poisson Mixed Data Type Distribution

Returns Important Matrices etc. of a QO Object

Influence Function (S4 generic) of a Fitted Model

Coef.rrvglm-class

Class ``Coef.rrvglm''

Linear Model and Binomial Mixed Data Type Distribution

The ABO Blood Group System

Linear Model and Poisson Mixed Data Type Family Function

Coef.qrrvglm-class

Class ``Coef.qrrvglm''

Seemingly Unrelated Regressions Family Function

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

Computes Model Coefficients and Quantities

The Inverse Gaussian Distribution

Takeuchi's Information Criterion

Truncated Values for the GT-Expansion Method

Utility Functions for the VGAM Package

Exponential Regression by Asymmetric Maximum Likelihood Estimation

Arcsine--Logit Link Mixtures

The MNSs Blood Group System

Altered, Inflated, Truncated and Deflated Values in GAITD Regression

Auckland University Undergraduate Counts Data

Beta Distribution of the Second Kind

Binomial Logistic Regression by Asymmetric Maximum Likelihood Estimation

Create a Survival Object

Asymmetric Least Squares Quantile Regression

Linear Model and Binomial Mixed Data Type Family Function

Benini Distribution Family Function

Kullback-Leibler Divergence

Frank's Bivariate Distribution Family Function

The Benini Distribution

Link functions for VGLM/VGAM/etc. families

The Beta-Geometric Distribution

CommonVGAMffArguments

Common VGAM Family Function Arguments

aux.posbernoulli.t

Auxiliary Function for the Positive Bernoulli Family Function with Time Effects

Frank's Bivariate Distribution

Mark the Baseline of Row and Column on a Matrix data

Bivariate Probit Model

The Beta-Normal Distribution

Clayton Copula (Bivariate) Family Function

The Bell Series of Integers

The Beta-Prime Distribution

Bivariate Binary Regression with an Odds Ratio (Family Function)

Poisson Regression by Asymmetric Maximum Likelihood Estimation

Table 1 of Huggins (1989)

Bacon and Eggs Data

Gumbel's Type I Bivariate Distribution Family Function

Quasi-variances Preprocessing Function

Bivariate Farlie-Gumbel-Morgenstern Exponential Distribution Family Function

Bivariate Probit Regression

The Pareto Distribution

The Beta-Binomial Distribution

R-squared for Latent Variable Models

double.expbinomial

Double Exponential Binomial Distribution Family Function

Beta-geometric Distribution Family Function

Birnbaum-Saunders Regression Family Function

Bivariate Student-t Family Function

Complementary Log-log Link Function

calibrate.rrvglm.control

Control Function for CLO (RR-VGLM) Calibration

Benford's Distribution

The Birnbaum-Saunders Distribution

Bivariate Student-t Distribution Density Function

Gaussian Copula (Bivariate) Distribution

The Two-parameter Beta Distribution Family Function

Generalized Poisson Regression (Original Parameterization)

Ali-Mikhail-Haq Bivariate Distribution

V1 Flying-Bombs Hits in London

Body Mass Index of New Zealand Adults Data

Ordinal Regression with Cumulative Probabilities

Bivariate Logistic Distribution

Cystic Fibrosis Data

Plackett's Bivariate Copula Family Function

Constraint Matrices

Fitting Constrained Additive Ordination (CAO)

Clayton Copula (Bivariate) Distribution

Borel-Tanner Distribution Family Function

Response Variable Extracted

Generally Altered, Inflated, Truncated and Deflated Zeta Regression

Centre of the Parameter Space

Bivariate Logistic Distribution Family Function

Censored Poisson Family Function

Censored Normal Distribution

Censored Gumbel Distribution

Control Function for RR-VGAMs (CAO)

The Lindley Distribution

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

Biplot of Constrained Regression Models

V2 Missile Hits in London

Inputting Data to fit a Bradley Terry Model

Bivariate Normal Distribution Cumulative Distribution Function

Plotting the GAITD Combo Density

Gaussian Copula (Bivariate) Family Function

Breathlessness and Wheeze Amongst Coalminers Data

calibrate-methods

Calibration for Constrained Regression Models

Analysis of Deviance for Vector Generalized Linear Model Fits

Cardioid Distribution

Bradley Terry Model With Ties

The Borel-Tanner Distribution

Multi-logit Link Function

Redirects the User to rrvglm()

Arcsine Link Function

Huber's Least Favourable Distribution Family Function

Extract Model Coefficients

Binomial Family Function

Beta-binomial Distribution Family Function

Extract Model Coefficients of a vgam() Object

Negative Binomial Distribution Family Function

Vector Generalized Linear and Additive Models and Other Associated Models

Bradley Terry Model

Cardioid Distribution Family Function

Extended log-F Distribution Family Function

Ordinal Regression with Adjacent Categories Probabilities

Density Plot for LMS Quantile Regression

Residual Degrees-of-Freedom

Cauchit Link Function

concoef-methods

Constrained (Canonical) Coefficients

The Laplace Distribution

The Inverse Lomax Distribution

The Two-parameter Beta Distribution Family Function

The Dagum Distribution

Plackett's Bivariate Copula

Ali-Mikhail-Haq Distribution Family Function

Expectiles-Normal

Expectiles of the Normal Distribution

Expectiles-Exponential

Expectiles of the Exponential Distribution

Generally Altered, Inflated, Truncated and Deflated Poisson Regression

Exponential Link Function

calibrate.qrrvglm

Calibration for CQO and CAO models

The Exponential Geometric Distribution

Western Spuce Budworm

Exponential Geometric Distribution Family Function

Hat Values and Regression Deletion Diagnostics

Data on Back Pain Prognosis, from Anderson (1984)

Erlang Distribution

2-parameter Gamma Regression Family Function

Toxicity trial for insects

Corbet's Butterfly Data

Beta-binomial Distribution Family Function

Parallelism Constraint Matrices

Relative Frequencies of Serum Proteins in White Pekin Ducklings

Bivariate Normal Distribution Family Function

Felix Distribution Family Function

The Felix Distribution

Fitting a Dirichlet-Multinomial Distribution

Pneumoconiosis in Coalminers Data

Farlie-Gumbel-Morgenstern's Bivariate Distribution Family Function

Quantile Crossing Detection

Fitting Constrained Quadratic Ordination (CQO)

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

Model Formulae and Term Names for VGLMs

Farlie-Gumbel-Morgenstern's Bivariate Distribution

Fitting a Dirichlet Distribution

Frechet Distribution Family Function

Model Calibrations

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

Bivariate Odds Ratio Model

The Gumbel Distribution

Derivatives of the Incomplete Gamma Integral

Generalized Poisson Regression (GP-1 Parameterization)

Dagum Distribution Family Function

Cumulative Distribution Function for LMS Quantile Regression

calibrate.qrrvglm.control

Control Function for CQO/CAO Calibration

Folded Normal Distribution Family Function

extbetabinomial

Extended Beta-binomial Distribution Family Function

Empirical Cumulative Distribution Function

has.interceptvlm

Has a Fitted VGLM Got an Intercept Term?

Expectiles-Uniform

Expectiles of the Uniform Distribution

Fitting a Dirichlet-Multinomial Distribution

Ordinal Regression with Continuation Ratios

Exponential Distribution

Exponentiated Exponential Distribution

Positive Negative Binomial Distribution Family Function

The Beta-Binomial Distribution

Geometric (Truncated and Untruncated) Distributions

Hunting Spider Data

The Generalized Pareto Distribution

Extended log-F Distribution

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

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Regression

The Exponential Poisson Distribution

Exponentiated Exponential Distribution

Grain Prices Data in USA

Generally Altered, Inflated, Truncated and Deflated Binomial Distribution

The Generalized Beta II Distribution

Chest Pain in NZ Adults Data

Fitted Values of a VLM object

Redirects the user to cqo

Hypergeometric Family Function

calibrate.rrvglm

Calibration for CLO models (RR-VGLMs)

Confidence Intervals for Parameters of VGLMs

Differenced Zeta Distribution Family Function

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

Haight's Zeta Distribution

double.cens.normal

Univariate Normal Distribution with Double Censoring

Generalized Secant Hyperbolic Regression Family Function

The Husler-Reiss Angular Surface Distribution

Extract Model Constrained/Canonical Coefficients

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

Generalized Beta Distribution Family Function

Family Function Name

Exponential Poisson Distribution Family Function

Fisher's Z Link Function

Gompertz Regression Family Function

Mean Excess Plot

Index from Array to Matrix

Mortality of Flour Beetles from Carbon Disulphide

The Folded-Normal Distribution

Gumbel-II Regression Family Function

Logarithmic Distribution

Square Root and Folded Square Root Link Functions

Rayleigh Regression Family Function

F Distribution Family Function

Generalized Poisson Regression (GP-2 Parameterization)

The Fisk Distribution

Inv.paralogistic

The Inverse Paralogistic Distribution

Laplace Regression Family Function

Generally Altered, Inflated, Truncated and Deflated Logarithmic Distribution

Positive Bernoulli Family Function with Behavioural Effects

Generalized Gamma distribution family function

Hauck-Donner Effects: A Detection Test for Wald Tests

The Exponential Logarithmic Distribution

Complementary-log Link Function

Proportional Odds Model for Ordinal Regression

Fixing a Quantile Regression having Crossing

Cauchy Distribution Family Function

model.matrixqrrvglm

Construct the Model Matrix of a QRR-VGLM Object

The Generalized Beta Distribution (Libby and Novick, 1982)

Rice Distribution Family Function

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Distribution

Error Function, and variants

The Generalized Extreme Value Distribution

Chinese Population in New Zealand 1867--2001 Data

Generally Altered, Inflated, Truncated and Deflated Logarithmic Regression

GARMA (Generalized Autoregressive Moving-Average) Models

Generalized Rayleigh Distribution Family Function

2-parameter Gamma Regression Family Function

General Electric and Westinghouse Data

Generalized Beta Distribution of the Second Kind

The Lambert W Function

Log-log and Log-log-log Link Functions

Exponential Logarithmic Distribution Family Function

Chi-squared and Chi Distributions

Kendall's Tau Statistic

Latent Variables

New Zealand Marital Data

GAITD Offset for the GTE Method

Low-iron Rat Teratology Data

Generalized Gamma Distribution

Multivariate Gamma Family Function: Mathai and Moschopoulos (1992)

Maxwell Regression Family Function

Hauck-Donner Effect: Severity Measures

The Generalized Rayleigh Distribution

Zero-Altered Binomial Distribution

The Makeham Distribution

Creates a Matrix of Appropriate Dimension

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

Crashes on New Zealand Roads in 2009

Gompertz Distribution

notdocumentedyet

Undocumented and Internally Used Functions and Classes

Pareto(IV/III/II) Distribution Family Functions

inv.paralogistic

Inverse Paralogistic Distribution Family Function

Does the Fitted Object Suffer from a Known Bug?

Lomax Distribution Family Function

Generalized Pareto Distribution Regression Family Function

Method for Profiling vglm Objects

Kumaraswamy Regression Family Function

Lognormal Distribution

logitoffsetlink

Logit-with-an-Offset Link Function

get.smart.prediction

Retrieves ``.smart.prediction''

Hormone Assay Data

Univariate Normal Distribution as a Varying-Coefficient Model

Acute Myelogenous Leukemia Survival Data

LMS Quantile Regression with a Box-Cox Transformation to Normality

pgamma.deriv.unscaled

Derivatives of the Incomplete Gamma Integral (Unscaled Version)

Generalized Secant Hyperbolic Distribution

Construct the Model Frame of a VLM Object

The Exponential Integral and Variants

The Pareto(IV/III/II) Distributions

Levy Distribution Family Function

Generally Altered, Inflated, Truncated and Deflated Poisson Distribution

Class ``rrvglm''

The Positive-Normal Distribution

Probability Plots for Categorical Data Analysis

Loglinear Model for Three Binary Responses

Differenced Zeta Distribution

Log Link Function, and Variants

Extract Log-likelihood for VGLMs/VGAMs/etc.

Marginal Effects for Several Categorical Response Models

The Frechet Distribution

von Mises Distribution Family Function

Negative Binomial Canonical Link Function

Husler-Reiss Angular Surface Distribution Family Function

Zero-Altered Poisson Distribution

The Maxwell Distribution

1-parameter Lindley Distribution

Positive Binomial Distribution Family Function

Zero-Inflated Negative Binomial Distribution Family Function

Michaelis-Menten Model

Inverse Gaussian Distribution Family Function

Positive-Geometric Distribution

Hyperbolic Secant Regression Family Function

Multinomial Logit Model

Poisson Points Distribution

Generalized Poisson Distribution (Original Parameterization)

Fisk Distribution family function

The Gumbel-II Distribution

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

LMS Quantile Regression with a Yeo-Johnson Transformation to Normality

Log Link Function with an Offset

Huber's Least Favourable Distribution

The Perks Distribution

Gumbel Regression Family Function

Lerch Phi Function

Identity Link Function

Logarithmic Distribution

Poisson Regression

Hunua Ranges Data

qrrvglm.control

Control Function for QRR-VGLMs (CQO)

Logit Link Function

Generally Altered, Inflated and Truncated and Deflated Zeta Distribution

Inverse Binomial Distribution Family Function

Scaled Student t Distribution with 2 df Family Function

Pareto and Truncated Pareto Distribution Family Functions

Ordinal Superiority Measures

Logistic Distribution Family Function

Model Diagnostic Plots for QRR-VGLMs

Trivariate Normal Distribution Family Function

Test For a Smart Object

The Kumaraswamy Distribution

Leipnik Regression Family Function

Number of Parameters

Cleans Up After Smart Prediction

The Poisson Lognormal Distribution

Machinists Accidents

Trivariate Normal Distribution Density and Random Variates

Logarithms with an Unit Offset and Exponential Term

plotqtplot.lmscreg

Quantile Plot for LMS Quantile Regression

1-parameter Gamma Regression Family Function

Ordinal Regression with Stopping Ratios

Haight's Zeta Family Function

Gamma Hyperbola Bivariate Distribution

Tobit Regression

smart.expression

S Expression for Smart Functions

Mixture of Two Poisson Distributions

Mean of the GAITD Combo Density

Paralogistic Distribution Family Function

Fitting Vector Generalized Linear Models

Latent Variable Plot for QO models

Positive Bernoulli Sequence Model

Zero-Altered Negative Binomial Distribution

Expectiles-sc.t2

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

Yule-Simon Distribution

Generalized Extreme Value Regression Family Function

The Lomax Distribution

Annual catches on Lake Otamangakau from October 1974 to October 1989

Log-gamma Distribution Family Function

plotdeplot.lmscreg

Density Plot for LMS Quantile Regression

Link Functions for VGLMs

Natural Exponential Family Generalized Hyperbolic Secant Distribution Family Function

Leadbeater's Possums

Summarizing Penalized Vector Generalized Additive Model Fits

negbinomial.size

Negative Binomial Distribution Family Function With Known Size

Mixture of Two Univariate Normal Distributions

model.matrixvlm

Construct the Design Matrix of a VLM Object

Rounding of Numbers to Base 2

Latent Variable Plot for RR-VGLMs

Loglinear Model for Two Binary Responses

plotdgaitd.vglm

Plotting the GAITD Combo Density from a GAITD Regression Object

Zero Constraint Matrices

Makeham Regression Family Function

Melbourne Daily Maximum Temperatures

2008 and 2012 Summer Olympic Final Medal Count Data

Oxford Temperature Data

Minimizing the L-q norm Family Function

The Log-Gamma Distribution

Pregnant Rats Toxological Experiment Data

Likelihood Ratio Test Statistics Evaluated at the Null Values

Constrained Quadratic Ordination

Weibull Distribution Family Function

The Tobit Distribution

The Singh-Maddala Distribution

Quantile Plot for Gumbel Regression

Reciprocal Inverse Gaussian distribution

Upper Record Values from a 1-parameter Exponential Distribution

Trajectory Plot

Smart Prediction

Inverse Lomax Distribution Family Function

plotvgam.control

Control Function for plotvgam()

The Topp-Leone Distribution

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

Singh-Maddala Distribution Family Function

Nakagami Distribution

posbernoulli.tb

Positive Bernoulli Family Function with Time and Behavioural Effects

Predict Method for a VGLM fit

Perks Distribution Family Function

Ordinal Poisson Family Function

The Paralogistic Distribution

Fitting Vector Generalized Additive Models

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

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

Perspective plot for QRR-VGLMs

Simulate Responses for VGLMs and VGAMs

Return Level Plot for GEV Fits

log F Distribution

Wald Distribution Family Function

Zipf Distribution Family Function

Positive Normal Distribution Family Function

Nested Reduced-rank Autoregressive Models for Multiple Time Series

Plots for VGLMs

Prior and Working Weights of a VGLM fit

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

Likelihood Ratio Test of Nested Models

summary.drrvglm

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

The Zeta Distribution

Zeta Distribution Family Function

The Dirichlet distribution

Latent Variable Plot

Toxoplasmosis Data

Rhobit Link Function

Univariate Skew-Normal Distribution Family Function

Residuals for a VGLM fit

Slash Distribution Family Function

McCullagh (1989) Distribution Family Function

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

Yellow-bellied Prinia

Default VGAM Plotting

Control Function for rrvglm()

The Rice Distribution

Power Link Function

Predict Method for a CQO fit

Probit Link Function

Mixture of Two Exponential Distributions

Nakagami Regression Family Function

Square root--Log Link Mixtures

Topp-Leone Distribution Family Function

Rao's Score Test Statistics Evaluated at the Null Values

Positive Bernoulli Family Function with Time Effects

The Two-stage Sequential Binomial Distribution Family Function

Slash Distribution

Upper Record Values from a Univariate Normal Distribution

Defining Penalized Spline Smooths in VGAM Formulas

Reciprocal Link Function

Hauck-Donner Effects: Segmented Lines Plot

Rayleigh Distribution

Summarizing Vector Generalized Additive Model Fits

Positive Poisson Distribution Family Function

Trajectory plot for QRR-VGLMs

Simplex Distribution Family Function

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

Skew-Normal Distribution

The Skellam Distribution

Quantile Plot for LMS Quantile Regression

trim.constraints

Trimmed Constraint Matrices

Control Function for vglm()

Zero-Inflated Poisson Distribution Family Function

Smart Prediction Setup

Control Function for vgam()

Skellam Distribution Family Function

rrvglm.optim.control

Control Function for rrvglm() Calling optim()

Defining O'Sullivan Spline Smooths in VGAM Formulas

undocumented-methods

Undocumented Methods Functions

Truncated Weibull Distribution Family Function

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

Weibull Distribution Family Function, Parameterized by the Mean

Bitterness in Wine Data

Special Values or Quantities in a Fitted Object

The Zipf-Mandelbrot Distribution

The Triangle Distribution

The Truncated Pareto Distribution

Rutherford-Geiger Polonium Data

Quasi-variances Extraction Function

Prentice (1974) Log-gamma Distribution

The Zipf Distribution

Zero-Altered Geometric Distribution

The Zero/One-Inflated Beta Distribution

University California Berkeley Graduate Admissions

Zero- and One-Inflated Beta Distribution Family Function

Zero-Inflated Geometric Distribution Family Function

Zero-Inflated Binomial Distribution Family Function

Univariate Normal Distribution

Waitakere Ranges Data

Wald Test Statistics Evaluated at the Null Values

Zero-Inflated Negative Binomial Distribution

Zero-Altered Binomial Distribution

Zero-Altered Negative Binomial Distribution

Defining Smooths in VGAM Formulas

Determine What Mode the Smart Prediction is In

Simplex Distribution

Choose a model by AIC in a Stepwise Algorithm

Student t Distribution

Plotting Functions for 'profile' Objects

Zero-Altered Poisson Distribution

Zero-Altered Geometric Distribution

Vector Cubic Smoothing Spline

Summarizing Vector Generalized Linear Model Fits

Zero-Inflated Poisson Distribution

Venice Maximum Sea Levels Data

Class ``vglmff''

Yeo-Johnson Transformation

Yule-Simon Family Function

Zero-Inflated Binomial Distribution

The zero Argument in VGAM Family Functions

Zero-Inflated Geometric Distribution