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VGAM (version 1.1-11)

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

28,696

Version

1.1-11

License

GPL-3

Maintainer

Last Published

May 15th, 2024

Functions in VGAM (1.1-11)

The AR-1 Autoregressive Process

Akaike's Information Criterion

The ABO Blood Group System

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

Bayesian Information Criterion

The AA-Aa-aa Blood Group System

The AB-Ab-aB-ab Blood Group System

The A1A2A3 Blood Group System

Autoregressive Process with Order-1 Family Function

Constraint Matrices for Symmetry, Order, Parallelism, etc.

Extract Model Coefficients for VLM Objects

Coef.rrvglm-class

Class ``Coef.rrvglm''

Computes Model Coefficients and Quantities

The Inverse Gaussian Distribution

CommonVGAMffArguments

Common VGAM Family Function Arguments

Table 1 of Huggins (1989)

Returns Important Matrices etc. of a RR-VGLM Object

Influence Function (S4 generic) of a Fitted Model

Returns Important Matrices etc. of a QO Object

Coef.qrrvglm-class

Class ``Coef.qrrvglm''

The MNSs Blood Group System

Linear Model and Binomial Mixed Data Type Distribution

Linear Model and Poisson Mixed Data Type Distribution

Linear Model and Poisson Mixed Data Type Family Function

The Pareto Distribution

Linear Model and Binomial Mixed Data Type Family Function

Takeuchi's Information Criterion

Quasi-variances Preprocessing Function

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

Seemingly Unrelated Regressions Family Function

R-squared for Latent Variable Models

Mark the Baseline of Row and Column on a Matrix data

V1 Flying-Bombs Hits in London

Create a Survival Object

Link functions for VGLM/VGAM/etc. families

Kullback-Leibler Divergence

V2 Missile Hits in London

Truncated Values for the GT-Expansion Method

Utility Functions for the VGAM Package

The Laplace Distribution

Arcsine--Logit Link Mixtures

Vector Generalized Linear and Additive Models and Other Associated Models

Asymmetric Laplace Distribution Family Functions

Altered, Inflated, Truncated and Deflated Values in GAITD Regression

Ordinal Regression with Adjacent Categories Probabilities

Data on Back Pain Prognosis, from Anderson (1984)

Bacon and Eggs Data

Asymmetric Least Squares Quantile Regression

Poisson Regression by Asymmetric Maximum Likelihood Estimation

Binomial Logistic Regression by Asymmetric Maximum Likelihood Estimation

The Benini Distribution

Benini Distribution Family Function

Analysis of Deviance for Vector Generalized Linear Model Fits

Arcsine Link Function

Beta-binomial Distribution Family Function

The Bell Series of Integers

Exponential Regression by Asymmetric Maximum Likelihood Estimation

The Two-parameter Beta Distribution Family Function

Auckland University Undergraduate Counts Data

Farlie-Gumbel-Morgenstern's Bivariate Distribution Family Function

Beta Distribution of the Second Kind

The Two-parameter Beta Distribution Family Function

Farlie-Gumbel-Morgenstern's Bivariate Distribution

aux.posbernoulli.t

Auxiliary Function for the Positive Bernoulli Family Function with Time Effects

Clayton Copula (Bivariate) Family Function

Ali-Mikhail-Haq Distribution Family Function

Benford's Distribution

The Beta-Normal Distribution

The Beta-Geometric Distribution

Beta-geometric Distribution Family Function

The Beta-Prime Distribution

Ali-Mikhail-Haq Bivariate Distribution

Bivariate Farlie-Gumbel-Morgenstern Exponential Distribution Family Function

Bivariate Binary Regression with an Odds Ratio (Family Function)

Bivariate Normal Distribution Cumulative Distribution Function

Bivariate Odds Ratio Model

Frank's Bivariate Distribution Family Function

The Beta-Binomial Distribution

Birnbaum-Saunders Regression Family Function

The Birnbaum-Saunders Distribution

Beta-binomial Distribution Family Function

Gaussian Copula (Bivariate) Distribution

Bivariate Logistic Distribution

Gaussian Copula (Bivariate) Family Function

Inputting Data to fit a Bradley Terry Model

Bradley Terry Model With Ties

Clayton Copula (Bivariate) Distribution

Bivariate Logistic Distribution Family Function

Plackett's Bivariate Copula Family Function

Frank's Bivariate Distribution

Body Mass Index of New Zealand Adults Data

Model Calibrations

Bivariate Student-t Family Function

Bivariate Student-t Distribution Density Function

The Borel-Tanner Distribution

Bivariate Probit Regression

Bradley Terry Model

Borel-Tanner Distribution Family Function

Cardioid Distribution Family Function

calibrate.qrrvglm

Calibration for CQO and CAO models

Gumbel's Type I Bivariate Distribution Family Function

Cauchit Link Function

Bivariate Probit Model

Constraint Matrices

Chinese Population in New Zealand 1867--2001 Data

Binomial Family Function

calibrate.rrvglm.control

Control Function for CLO (RR-VGLM) Calibration

Bivariate Normal Distribution Family Function

Plackett's Bivariate Copula

Centre of the Parameter Space

Censored Gumbel Distribution

Fitting Constrained Additive Ordination (CAO)

Biplot of Constrained Regression Models

Western Spuce Budworm

Chi-squared and Chi Distributions

Censored Normal Distribution

Control Function for RR-VGAMs (CAO)

calibrate-methods

Calibration for Constrained Regression Models

Ordinal Regression with Cumulative Probabilities

Dagum Distribution Family Function

Redirects the User to rrvglm()

calibrate.qrrvglm.control

Control Function for CQO/CAO Calibration

calibrate.rrvglm

Calibration for CLO models (RR-VGLMs)

Cauchy Distribution Family Function

Differenced Zeta Distribution Family Function

Cumulative Distribution Function for LMS Quantile Regression

Differenced Zeta Distribution

Censored Poisson Family Function

Cardioid Distribution

Redirects the user to cqo

Cystic Fibrosis Data

Corbet's Butterfly Data

Complementary Log-log Link Function

Fitting Constrained Quadratic Ordination (CQO)

Extract Model Coefficients

Breathlessness and Wheeze Amongst Coalminers Data

Chest Pain in NZ Adults Data

Error Function, and variants

Residual Degrees-of-Freedom

Crashes on New Zealand Roads in 2009

Extract Model Coefficients of a vgam() Object

The Dagum Distribution

concoef-methods

Constrained (Canonical) Coefficients

Plotting the GAITD Combo Density

Density Plot for LMS Quantile Regression

Response Variable Extracted

The Exponential Logarithmic Distribution

Extract Model Constrained/Canonical Coefficients

Exponential Logarithmic Distribution Family Function

extbetabinomial

Extended Beta-binomial Distribution Family Function

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

Confidence Intervals for Parameters of VGLMs

Erlang Distribution

Ordinal Regression with Continuation Ratios

double.expbinomial

Double Exponential Binomial Distribution Family Function

Expectiles-Exponential

Expectiles of the Exponential Distribution

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

Fitting a Dirichlet-Multinomial Distribution

double.cens.normal

Univariate Normal Distribution with Double Censoring

Expectiles-Normal

Expectiles of the Normal Distribution

Relative Frequencies of Serum Proteins in White Pekin Ducklings

Model Formulae and Term Names for VGLMs

Empirical Cumulative Distribution Function

Fitting a Dirichlet Distribution

Fitting a Dirichlet-Multinomial Distribution

The Exponential Integral and Variants

Frechet Distribution Family Function

Extended log-F Distribution

2-parameter Gamma Regression Family Function

Expectiles-Uniform

Expectiles of the Uniform Distribution

Exponential Link Function

Exponentiated Exponential Distribution

2-parameter Gamma Regression Family Function

Generally Altered, Inflated, Truncated and Deflated Poisson Regression

Extended log-F Distribution Family Function

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

Generalized Poisson Regression (Original Parameterization)

Generally Altered, Inflated, Truncated and Deflated Zeta Regression

Family Function Name

Exponential Geometric Distribution Family Function

GARMA (Generalized Autoregressive Moving-Average) Models

Folded Normal Distribution Family Function

Square Root and Folded Square Root Link Functions

The Frechet Distribution

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

Exponentiated Exponential Distribution

The Exponential Geometric Distribution

Exponential Distribution

Exponential Poisson Distribution Family Function

Felix Distribution Family Function

Generalized Gamma Distribution

Generalized Poisson Distribution (Original Parameterization)

The Exponential Poisson Distribution

The Generalized Extreme Value Distribution

Generalized Beta Distribution of the Second Kind

GAITD Offset for the GTE Method

Generalized Rayleigh Distribution Family Function

The Felix Distribution

The Beta-Binomial Distribution

Fitted Values of a VLM object

The Generalized Rayleigh Distribution

get.smart.prediction

Retrieves ``.smart.prediction''

Generalized Extreme Value Regression Family Function

Toxicity trial for insects

Fisher's Z Link Function

Fixing a Quantile Regression having Crossing

The Generalized Pareto Distribution

General Electric and Westinghouse Data

Grain Prices Data in USA

Mortality of Flour Beetles from Carbon Disulphide

F Distribution Family Function

Gompertz Regression Family Function

Creates a Matrix of Appropriate Dimension

Generally Altered, Inflated, Truncated and Deflated Binomial Distribution

has.interceptvlm

Has a Fitted VGLM Got an Intercept Term?

The Gumbel Distribution

Hat Values and Regression Deletion Diagnostics

The Folded-Normal Distribution

Huber's Least Favourable Distribution Family Function

The Husler-Reiss Angular Surface Distribution

Huber's Least Favourable Distribution

Quantile Crossing Detection

Fisk Distribution family function

The Fisk Distribution

Generally Altered, Inflated, Truncated and Deflated Logarithmic Distribution

Hauck-Donner Effects: A Detection Test for Wald Tests

Hauck-Donner Effects: Severity Measures

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Distribution

Hypergeometric Family Function

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Regression

Generally Altered, Inflated, Truncated and Deflated Logarithmic Regression

Generally Altered, Inflated, Truncated and Deflated Poisson Distribution

Generally Altered, Inflated and Truncated and Deflated Zeta Distribution

Multivariate Gamma Family Function: Mathai and Moschopoulos (1992)

Inverse Gaussian Distribution Family Function

1-parameter Gamma Regression Family Function

The Inverse Lomax Distribution

Inverse Lomax Distribution Family Function

Parallelism Constraint Matrices

The Generalized Beta II Distribution

Acute Myelogenous Leukemia Survival Data

The Laplace Distribution

inv.paralogistic

Inverse Paralogistic Distribution Family Function

Levy Distribution Family Function

The Generalized Beta Distribution (Libby and Novick, 1982)

Latent Variables

Link Functions for VGLMs

Generalized Beta Distribution Family Function

Logistic Distribution Family Function

Logit Link Function

Generalized Gamma distribution family function

Inv.paralogistic

The Inverse Paralogistic Distribution

Does the Fitted Object Suffer from a Known Bug?

Gamma Hyperbola Bivariate Distribution

Generalized Secant Hyperbolic Regression Family Function

Generalized Secant Hyperbolic Distribution

Gompertz Distribution

Generalized Poisson Regression (GP-1 Parameterization)

Low-iron Rat Teratology Data

Complementary-log Link Function

Log-Laplace and Logit-Laplace Distribution Family Functions

Generalized Poisson Regression (GP-2 Parameterization)

Gumbel-II Regression Family Function

Generalized Pareto Distribution Regression Family Function

Hormone Assay Data

Geometric (Truncated and Untruncated) Distributions

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

The Lambert W Function

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

Hunting Spider Data

Hyperbolic Secant Regression Family Function

The Gumbel-II Distribution

Identity Link Function

Gumbel Regression Family Function

Logarithmic Distribution

Haight's Zeta Family Function

Laplace Regression Family Function

Hunua Ranges Data

Inverse Binomial Distribution Family Function

Latent Variable Plot for QO models

Kendall's Tau Statistic

Husler-Reiss Angular Surface Distribution Family Function

The Kumaraswamy Distribution

Loglinear Model for Two Binary Responses

Annual catches on Lake Otamangakau from October 1974 to October 1989

The Makeham Distribution

Haight's Zeta Distribution

The Log-Gamma Distribution

Latent Variable Plot for RR-VGLMs

The Lindley Distribution

Kumaraswamy Regression Family Function

Log-gamma Distribution Family Function

Index from Array to Matrix

1-parameter Gamma Distribution

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

Marginal Effects for Several Categorical Response Models

Natural Exponential Family Generalized Hyperbolic Secant Distribution Family Function

logitoffsetlink

Logit-with-an-Offset Link Function

The Log-Laplace Distribution

Log-log and Log-log-log Link Functions

LMS Quantile Regression with a Box-Cox Transformation to Normality

Lognormal Distribution

log F Distribution

Test For a Smart Object

The Lomax Distribution

Mean Excess Plot

Michaelis-Menten Model

Likelihood Ratio Test of Nested Models

Negative Binomial Canonical Link Function

Zero Constraint Matrices

Extract Log-likelihood for VGLMs/VGAMs/etc.

Latent Variable Plot

Leadbeater's Possums

Negative Binomial Distribution Family Function

Paralogistic Distribution Family Function

Logarithmic Distribution

Leipnik Regression Family Function

Lerch Phi Function

New Zealand Marital Data

The Paralogistic Distribution

Maxwell Regression Family Function

Mixture of Two Exponential Distributions

LMS Quantile Regression with a Yeo-Johnson Transformation to Normality

Logarithms with an Unit Offset and Exponential Term

model.matrixvlm

Construct the Design Matrix of a VLM Object

Loglinear Model for Three Binary Responses

Machinists Accidents

Makeham Regression Family Function

Log Link Function with an Offset

Mixture of Two Univariate Normal Distributions

Lomax Distribution Family Function

Log Link Function, and Variants

The Maxwell Distribution

Construct the Model Frame of a VLM Object

Pneumoconiosis in Coalminers Data

Minimizing the L-q norm Family Function

Mixture of Two Poisson Distributions

Likelihood Ratio Test Statistics Evaluated at the Null Values

model.matrixqrrvglm

Construct the Model Matrix of a QRR-VGLM Object

Mean of the GAITD Combo Density

Ordinal Superiority Measures

Melbourne Daily Maximum Temperatures

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

negbinomial.size

Negative Binomial Distribution Family Function With Known Size

Multi-logit Link Function

Univariate Normal Distribution as a Varying-Coefficient Model

McCullagh (1989) Distribution Family Function

Pareto(IV/III/II) Distribution Family Functions

Nakagami Regression Family Function

Positive-Geometric Distribution

Derivatives of the Incomplete Gamma Integral

Oxford Temperature Data

pgamma.deriv.unscaled

Derivatives of the Incomplete Gamma Integral (Unscaled Version)

Nakagami Distribution

Multinomial Logit Model

The Perks Distribution

notdocumentedyet

Undocumented and Internally Used Functions and Classes

Model Diagnostic Plots for QRR-VGLMs

Positive Negative Binomial Distribution Family Function

plotqtplot.lmscreg

Quantile Plot for LMS Quantile Regression

The Pareto(IV/III/II) Distributions

plotdeplot.lmscreg

Density Plot for LMS Quantile Regression

posbernoulli.tb

Positive Bernoulli Family Function with Time and Behavioural Effects

plotdgaitd.vglm

Plotting the GAITD Combo Density from a GAITD Regression Object

Number of Parameters

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

Default VGAM Plotting

Positive Bernoulli Family Function with Behavioural Effects

Positive Poisson Distribution Family Function

Perspective plot for QRR-VGLMs

plotvgam.control

Control Function for plotvgam()

Power Link Function

Plots for VGLMs

2008 and 2012 Summer Olympic Final Medal Count Data

Positive Bernoulli Family Function with Time Effects

Poisson Points Distribution

Yellow-bellied Prinia

Quantile Plot for LMS Quantile Regression

The Poisson Lognormal Distribution

Quasi-variances Extraction Function

Positive Bernoulli Sequence Model

Probit Link Function

Poisson Regression

Reciprocal Link Function

Method for Profiling vglm Objects

Pregnant Rats Toxological Experiment Data

qrrvglm.control

Control Function for QRR-VGLMs (CQO)

Proportional Odds Model for Ordinal Regression

Predict Method for a CQO fit

Residuals for a VGLM fit

Constrained Quadratic Ordination

Ordinal Poisson Family Function

Rutherford-Geiger Polonium Data

Positive Binomial Distribution Family Function

The Positive-Normal Distribution

Control Function for rrvglm()

Quantile Plot for Gumbel Regression

Rice Distribution Family Function

rrvglm.optim.control

Control Function for rrvglm() Calling optim()

Positive Normal Distribution Family Function

Defining Smooths in VGAM Formulas

Simulate Responses for VGLMs and VGAMs

The Dirichlet distribution

Reciprocal Inverse Gaussian distribution

Pareto and Truncated Pareto Distribution Family Functions

Rounding of Numbers to Base 2

Class ``rrvglm''

Singh-Maddala Distribution Family Function

Perks Distribution Family Function

Rao's Score Test Statistics Evaluated at the Null Values

Hauck-Donner Effects: Segmented Lines Plot

Ordinal Regression with Stopping Ratios

Predict Method for a VGLM fit

Rayleigh Regression Family Function

Nested Reduced-rank Autoregressive Models for Multiple Time Series

The Singh-Maddala Distribution

Prentice (1974) Log-gamma Distribution

Topp-Leone Distribution Family Function

Probability Plots for Categorical Data Analysis

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

Rayleigh Distribution

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

Defining O'Sullivan Spline Smooths in VGAM Formulas

Skellam Distribution Family Function

Rhobit Link Function

Simplex Distribution Family Function

Tobit Regression

Defining Penalized Spline Smooths in VGAM Formulas

Choose a model by AIC in a Stepwise Algorithm

The Tobit Distribution

Trajectory Plot

The Topp-Leone Distribution

Simplex Distribution

Student t Distribution

Trivariate Normal Distribution Family Function

Univariate Skew-Normal Distribution Family Function

Trivariate Normal Distribution Density and Random Variates

Slash Distribution Family Function

Toxoplasmosis Data

smart.expression

S Expression for Smart Functions

Trajectory plot for QRR-VGLMs

The Rice Distribution

Triangle Distribution Family Function

Scaled Student t Distribution with 2 df Family Function

Expectiles-sc.t2

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

Determine What Mode the Smart Prediction is In

Summarizing Vector Generalized Additive Model Fits

Upper Record Values from a 1-parameter Exponential Distribution

Summarizing Vector Generalized Linear Model Fits

Fitting Vector Generalized Linear Models

The Truncated Pareto Distribution

Truncated Weibull Distribution Family Function

University California Berkeley Graduate Admissions

undocumented-methods

Undocumented Methods Functions

Slash Distribution

Square root--Log Link Mixtures

Fitting Vector Generalized Additive Models

Control Function for vgam()

Vector Cubic Smoothing Spline

Upper Record Values from a Univariate Normal Distribution

Waitakere Ranges Data

von Mises Distribution Family Function

Wald Test Statistics Evaluated at the Null Values

Plotting Functions for 'profile' Objects

summary.drrvglm

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

Wald Distribution Family Function

Summarizing Penalized Vector Generalized Additive Model Fits

Return Level Plot for GEV Fits

The Triangle Distribution

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

Yule-Simon Family Function

Yule-Simon Distribution

The Zipf Distribution

The Zipf-Mandelbrot Distribution

The Two-stage Sequential Binomial Distribution Family Function

Zero-Altered Poisson Distribution

The zero Argument in VGAM Family Functions

Smart Prediction Setup

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

The Skellam Distribution

Zero-Altered Poisson Distribution

Skew-Normal Distribution

Zero-Inflated Geometric Distribution

Venice Maximum Sea Levels Data

trim.constraints

Trimmed Constraint Matrices

Zero-Inflated Geometric Distribution Family Function

Cleans Up After Smart Prediction

Yeo-Johnson Transformation

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

Weibull Distribution Family Function, Parameterized by the Mean

Weibull Distribution Family Function

Zipf Distribution Family Function

Zero-Altered Binomial Distribution

Zero-Altered Geometric Distribution

Zero-Altered Geometric Distribution

Smart Prediction

Zero-Inflated Binomial Distribution

Zero-Inflated Binomial Distribution Family Function

Zero- and One-Inflated Beta Distribution Family Function

Zero-Altered Binomial Distribution

Special Values or Quantities in a Fitted Object

The Zeta Distribution

The Zero/One-Inflated Beta Distribution

Zeta Distribution Family Function

Univariate Normal Distribution

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

Control Function for vglm()

Class ``vglmff''

Prior and Working Weights of a VGLM fit

Bitterness in Wine Data

Zero-Altered Negative Binomial Distribution

Zero-Altered Negative Binomial Distribution

Zero-Inflated Negative Binomial Distribution

Zero-Inflated Poisson Distribution

Zero-Inflated Negative Binomial Distribution Family Function

Zero-Inflated Poisson Distribution Family Function