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VGAM (version 1.1-9)

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, 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

39,215

Version

1.1-9

License

GPL-3

Maintainer

Last Published

September 19th, 2023

Functions in VGAM (1.1-9)

The ABO Blood Group System

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

The AA-Aa-aa Blood Group System

The AR-1 Autoregressive Process

The AB-Ab-aB-ab Blood Group System

Bayesian Information Criterion

Akaike's Information Criterion

The A1A2A3 Blood Group System

Computes Model Coefficients and Quantities

Autoregressive Process with Order-1 Family Function

Coef.qrrvglm-class

Class ``Coef.qrrvglm''

The Inverse Gaussian Distribution

Coef.rrvglm-class

Class ``Coef.rrvglm''

Extract Model Coefficients for VLM Objects

Influence Function (S4 generic) of a Fitted Model

CommonVGAMffArguments

Common VGAM Family Function Arguments

Returns Important Matrices etc. of a RR-VGLM Object

Table 1 of Huggins (1989)

Kullback-Leibler Divergence

Returns Important Matrices etc. of a QO Object

The Pareto Distribution

Mark the Baseline of Row and Column on a Matrix data

The MNSs Blood Group System

R-squared for Latent Variable Models

Link functions for VGLM/VGAM/etc. families

Quasi-variances Preprocessing Function

Seemingly Unrelated Regressions Family Function

Create a Survival Object

V1 Flying-Bombs Hits in London

V2 Missile Hits in London

Truncated Values for the GT-Expansion Method

Takeuchi's Information Criterion

Vector Generalized Linear and Additive Models and Associated Models

Utility Functions for the VGAM Package

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

Altered, Inflated, Truncated and Deflated Values in GAITD Regression

Analysis of Deviance for Vector Generalized Linear Model Fits

Poisson Regression by Asymmetric Maximum Likelihood Estimation

The Laplace Distribution

Ordinal Regression with Adjacent Categories Probabilities

Asymmetric Least Squares Quantile Regression

Auckland University Undergraduate Counts Data

Exponential Regression by Asymmetric Maximum Likelihood Estimation

Binomial Logistic Regression by Asymmetric Maximum Likelihood Estimation

Asymmetric Laplace Distribution Family Functions

Beta Distribution of the Second Kind

The Benini Distribution

Bacon and Eggs Data

aux.posbernoulli.t

Auxiliary Function for the Positive Bernoulli Family Function with Time Effects

Data on Back Pain Prognosis, from Anderson (1984)

The Bell Series of Integers

The Beta-Binomial Distribution

The Two-parameter Beta Distribution Family Function

Benford's Distribution

Benini Distribution Family Function

Beta-binomial Distribution Family Function

Ali-Mikhail-Haq Bivariate Distribution

Clayton Copula (Bivariate) Family Function

The Two-parameter Beta Distribution Family Function

Beta-binomial Distribution Family Function

Ali-Mikhail-Haq Distribution Family Function

The Beta-Normal Distribution

Beta-geometric Distribution Family Function

The Beta-Prime Distribution

The Beta-Geometric Distribution

Clayton Copula (Bivariate) Distribution

Frank's Bivariate Distribution Family Function

Bivariate Logistic Distribution Family Function

Bivariate Binary Regression with an Odds Ratio (Family Function)

Frank's Bivariate Distribution

Farlie-Gumbel-Morgenstern's Bivariate Distribution Family Function

Farlie-Gumbel-Morgenstern's Bivariate Distribution

Bivariate Farlie-Gumbel-Morgenstern Exponential Distribution Family Function

Gumbel's Type I Bivariate Distribution Family Function

Bivariate Logistic Distribution

Gaussian Copula (Bivariate) Family Function

Gaussian Copula (Bivariate) Distribution

Bivariate Probit Model

Plackett's Bivariate Copula Family Function

Bivariate Odds Ratio Model

Bivariate Probit Regression

Plackett's Bivariate Copula

Bivariate Normal Distribution Family Function

Bivariate Normal Distribution Cumulative Distribution Function

The Birnbaum-Saunders Distribution

Biplot of Constrained Regression Models

Bradley Terry Model

Birnbaum-Saunders Regression Family Function

Bivariate Student-t Family Function

Inputting Data to fit a Bradley Terry Model

Borel-Tanner Distribution Family Function

The Borel-Tanner Distribution

Binomial Family Function

calibrate.rrvglm

Calibration for CLO models (RR-VGLMs)

calibrate.rrvglm.control

Control Function for CLO (RR-VGLM) Calibration

calibrate-methods

Calibration for Constrained Regression Models

Model Calibrations

Bradley Terry Model With Ties

Fitting Constrained Additive Ordination (CAO)

Western Spuce Budworm

Bivariate Student-t Distribution Density Function

Control Function for RR-VGAMs (CAO)

Cystic Fibrosis Data

Redirects the user to cqo

Cardioid Distribution

Cauchit Link Function

Cardioid Distribution Family Function

Cauchy Distribution Family Function

Extract Model Coefficients of a vgam() Object

Extract Model Coefficients

Cumulative Distribution Function for LMS Quantile Regression

Censored Gumbel Distribution

Complementary Log-log Link Function

Breathlessness and Wheeze Amongst Coalminers Data

Chi-squared Distribution

Body Mass Index of New Zealand Adults Data

calibrate.qrrvglm

Calibration for CQO and CAO models

Chest Pain in NZ Adults Data

Redirects the User to rrvglm()

Ordinal Regression with Continuation Ratios

calibrate.qrrvglm.control

Control Function for CQO/CAO Calibration

Chinese Population in New Zealand 1867--2001 Data

Dagum Distribution Family Function

Centre of the Parameter Space

Confidence Intervals for Parameters of VGLMs

Constraint Matrices

The Dagum Distribution

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

Ordinal Regression with Cumulative Probabilities

Density Plot for LMS Quantile Regression

Empirical Cumulative Distribution Function

Differenced Zeta Distribution

Censored Normal Distribution

Fitting a Dirichlet Distribution

Censored Poisson Family Function

Fitting Constrained Quadratic Ordination (CQO)

Crashes on New Zealand Roads in 2009

Response Variable Extracted

Expectiles-Exponential

Expectiles of the Exponential Distribution

Residual Degrees-of-Freedom

double.cens.normal

Univariate Normal Distribution with Double Censoring

concoef-methods

Constrained (Canonical) Coefficients

The Exponential Geometric Distribution

Extract Model Constrained/Canonical Coefficients

Corbet's Butterfly Data

Exponential Link Function

The Exponential Integral and Variants

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

Plotting the GAITD Combo Density

Extended log-F Distribution

double.expbinomial

Double Exponential Binomial Distribution Family Function

Fitting a Dirichlet-Multinomial Distribution

The Exponential Logarithmic Distribution

Differenced Zeta Distribution Family Function

Fitting a Dirichlet-Multinomial Distribution

Relative Frequencies of Serum Proteins in White Pekin Ducklings

Error Function, and variants

Erlang Distribution

Exponentiated Exponential Distribution

Expectiles-Uniform

Expectiles of the Uniform Distribution

Extended log-F Distribution Family Function

Exponential Geometric Distribution Family Function

Expectiles-Normal

Expectiles of the Normal Distribution

The Folded-Normal Distribution

Exponentiated Exponential Distribution

Creates a Matrix of Appropriate Dimension

Toxicity trial for insects

The Felix Distribution

Exponential Logarithmic Distribution Family Function

Exponential Distribution

Folded Normal Distribution Family Function

The Exponential Poisson Distribution

Exponential Poisson Distribution Family Function

Fixing a Quantile Regression having Crossing

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Distribution

Mortality of Flour Beetles from Carbon Disulphide

Fisher's Z Link Function

Generalized Gamma distribution family function

Family Function Name

Generally Altered, Inflated, Truncated and Deflated Negative Binomial Regression

Fisk Distribution family function

Gamma Hyperbola Bivariate Distribution

Generalized Gamma Distribution

GARMA (Generalized Autoregressive Moving-Average) Models

Generally Altered, Inflated, Truncated and Deflated Logarithmic Regression

F Distribution Family Function

Folded Square Root Link Function

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

Model Formulae and Term Names for VGLMs

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

Felix Distribution Family Function

get.smart.prediction

Retrieves ``.smart.prediction''

The Fisk Distribution

Generalized Poisson Regression (Original Parameterization)

Generalized Poisson Regression (GP-1 Parameterization)

Generally Altered, Inflated, Truncated and Deflated Binomial Distribution

Frechet Distribution Family Function

Generally Altered, Inflated, Truncated and Deflated Zeta Regression

Generally Altered, Inflated and Truncated and Deflated Zeta Distribution

Generalized Poisson Regression (GP-2 Parameterization)

Generally Altered, Inflated, Truncated and Deflated Logarithmic Distribution

The Gumbel Distribution

Fitted Values of a VLM object

1-parameter Gamma Regression Family Function

Generally Altered, Inflated, Truncated and Deflated Poisson Distribution

Generalized Rayleigh Distribution Family Function

Inverse Gaussian Distribution Family Function

The Frechet Distribution

2-parameter Gamma Regression Family Function

Inverse Lomax Distribution Family Function

The Generalized Rayleigh Distribution

General Electric and Westinghouse Data

Generalized Beta Distribution of the Second Kind

Leipnik Regression Family Function

The Generalized Beta II Distribution

The Husler-Reiss Angular Surface Distribution

Generally Altered, Inflated, Truncated and Deflated Poisson Regression

2-parameter Gamma Regression Family Function

Generalized Poisson Distribution (Original Parameterization)

Multivariate Gamma Family Function: Mathai and Moschopoulos (1992)

Gamma-Ordinal Link Function

Geometric (Truncated and Untruncated) Distributions

GAITD Offset for the GTE Method

Generalized Extreme Value Regression Family Function

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

has.interceptvlm

Has a Fitted VGLM Got an Intercept Term?

Gompertz Regression Family Function

Hat Values and Regression Deletion Diagnostics

Lerch Phi Function

Gompertz Distribution

Hunua Ranges Data

Generalized Pareto Distribution Regression Family Function

Husler-Reiss Angular Surface Distribution Family Function

The Generalized Extreme Value Distribution

Hyperbolic Secant Regression Family Function

Hypergeometric Family Function

Gumbel-II Regression Family Function

Haight's Zeta Distribution

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

Index from Array to Matrix

The Gumbel-II Distribution

The Generalized Pareto Distribution

Kendall's Tau Statistic

Gumbel Regression Family Function

Hormone Assay Data

Haight's Zeta Family Function

Kumaraswamy Regression Family Function

Hauck-Donner Effects: A Detection Test for Wald Tests

Link Functions for VGLMs

Hauck-Donner Effects: Severity Measures

The Kumaraswamy Distribution

Generalized Beta Distribution Family Function

Complementary-log Link Function

Grain Prices Data in USA

Huber's Least Favourable Distribution Family Function

Logarithmic Distribution

Annual catches on Lake Otamangakau from October 1974 to October 1989

The Laplace Distribution

Huber's Least Favourable Distribution

Loglinear Model for Three Binary Responses

Identity Link Function

Hunting Spider Data

The Inverse Lomax Distribution

Latent Variables

inv.paralogistic

Inverse Paralogistic Distribution Family Function

Test For a Smart Object

The Generalized Beta Distribution (Libby and Novick, 1982)

Zero Constraint Matrices

LMS Quantile Regression with a Yeo-Johnson Transformation to Normality

Inverse Binomial Distribution Family Function

Low-iron Rat Teratology Data

Inv.paralogistic

The Inverse Paralogistic Distribution

logitoffsetlink

Logit-with-an-Offset Link Function

Quantile Crossing Detection

The Lambert W Function

Laplace Regression Family Function

Extract Log-likelihood for VGLMs/VGAMs/etc.

Logarithms with an Unit Offset and Exponential Term

Natural Exponential Family Generalized Hyperbolic Secant Distribution Family Function

Log Link Function, and Variants

The Log-Laplace Distribution

Minimizing the L-q norm Family Function

Does the Fitted Object Suffer from a Known Bug?

Logarithmic Distribution

Likelihood Ratio Test Statistics Evaluated at the Null Values

Log-log and Log-log-log Link Functions

The Log-Gamma Distribution

Log-gamma Distribution Family Function

Parallelism Constraint Matrices

log F Distribution

Ordinal Poisson Family Function

Ordinal Superiority Measures

Acute Myelogenous Leukemia Survival Data

Log Link Function with an Offset

Lognormal Distribution

Lomax Distribution Family Function

Likelihood Ratio Test of Nested Models

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

Levy Distribution Family Function

plotdgaitd.vglm

Plotting the GAITD Combo Density from a GAITD Regression Object

Model Diagnostic Plots for QRR-VGLMs

Machinists Accidents

Latent Variable Plot

Makeham Regression Family Function

Log-Laplace and Logit-Laplace Distribution Family Functions

Loglinear Model for Two Binary Responses

Mean Excess Plot

The Positive-Normal Distribution

Michaelis-Menten Model

LMS Quantile Regression with a Box-Cox Transformation to Normality

Positive Normal Distribution Family Function

The Makeham Distribution

Method for Profiling vglm Objects

Mixture of Two Univariate Normal Distributions

New Zealand Marital Data

Mixture of Two Poisson Distributions

Marginal Effects for Several Categorical Response Models

Negative Binomial Distribution Family Function

Proportional Odds Model for Ordinal Regression

Maxwell Regression Family Function

negbinomial.size

Negative Binomial Distribution Family Function With Known Size

Oxford Temperature Data

Paralogistic Distribution Family Function

Rhobit Link Function

Mixture of Two Exponential Distributions

The Lindley Distribution

Nakagami Regression Family Function

model.matrixvlm

Construct the Design Matrix of a VLM Object

The Rice Distribution

Default VGAM Plotting

plotvgam.control

Control Function for plotvgam()

1-parameter Gamma Distribution

The Maxwell Distribution

Number of Parameters

Nakagami Distribution

Poisson Regression

McCullagh (1989) Distribution Family Function

Univariate Normal Distribution as a Varying-Coefficient Model

The Poisson Lognormal Distribution

2008 and 2012 Summer Olympic Final Medal Count Data

Logistic Distribution Family Function

Control Function for rrvglm()

notdocumentedyet

Undocumented and Internally Used Functions and Classes

Perspective plot for QRR-VGLMs

Positive Poisson Distribution Family Function

Multi-logit Link Function

rrvglm.optim.control

Control Function for rrvglm() Calling optim()

Logit Link Function

Scaled Student t Distribution with 2 df Family Function

Multinomial Logit Model

Derivatives of the Incomplete Gamma Integral

Poisson-Ordinal Link Function

The Paralogistic Distribution

Pareto(IV/III/II) Distribution Family Functions

Plots for VGLMs

Positive Bernoulli Sequence Model

Expectiles-sc.t2

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

The Lomax Distribution

Positive-Geometric Distribution

Pneumoconiosis in Coalminers Data

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

Leadbeater's Possums

Perks Distribution Family Function

The Perks Distribution

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

plotqtplot.lmscreg

Quantile Plot for LMS Quantile Regression

Poisson Points Distribution

Simulate Responses for VGLMs and VGAMs

Singh-Maddala Distribution Family Function

Positive Bernoulli Family Function with Behavioural Effects

Latent Variable Plot for QO models

Positive Bernoulli Family Function with Time Effects

Latent Variable Plot for RR-VGLMs

Power Link Function

Predict Method for a VGLM fit

Positive Negative Binomial Distribution Family Function

Mean of the GAITD Combo Density

Yellow-bellied Prinia

Melbourne Daily Maximum Temperatures

Probit Link Function

Upper Record Values from a 1-parameter Exponential Distribution

Prentice (1974) Log-gamma Distribution

Upper Record Values from a Univariate Normal Distribution

Probability Plots for Categorical Data Analysis

qrrvglm.control

Control Function for QRR-VGLMs (CQO)

Quantile Plot for LMS Quantile Regression

Construct the Model Frame of a VLM Object

Class ``rrvglm''

Toxoplasmosis Data

Quasi-variances Extraction Function

Triangle Distribution Family Function

model.matrixqrrvglm

Construct the Model Matrix of a QRR-VGLM Object

Fitting Reduced-Rank Vector Generalized Linear Models (RR-VGLMs)

Univariate Normal Distribution

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

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

Univariate Skew-Normal Distribution Family Function

Quantile Plot for Gumbel Regression

Negative Binomial Canonical Link Function

Slash Distribution Family Function

Rice Distribution Family Function

Reciprocal Inverse Gaussian distribution

Constrained Quadratic Ordination

Control Function for vglm()

Class ``vglmff''

Reciprocal Link Function

Residuals for a VGLM fit

The Two-stage Sequential Binomial Distribution Family Function

Wald Test Statistics Evaluated at the Null Values

The Dirichlet distribution

Smart Prediction Setup

Student t Distribution

Wald Distribution Family Function

Summarizing Penalized Vector Generalized Additive Model Fits

Topp-Leone Distribution Family Function

Rounding of Numbers to Base 2

Return Level Plot for GEV Fits

Yule-Simon Family Function

Nested Reduced-rank Autoregressive Models for Multiple Time Series

Yule-Simon Distribution

Negative Binomial-Ordinal Link Function

The Topp-Leone Distribution

The Truncated Pareto Distribution

The Zeta Distribution

The Pareto(IV/III/II) Distributions

Zeta Distribution Family Function

Pareto and Truncated Pareto Distribution Family Functions

The Zipf Distribution

The Zipf-Mandelbrot Distribution

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

Special Values or Quantities in a Fitted Object

Simplex Distribution Family Function

Truncated Weibull Distribution Family Function

pgamma.deriv.unscaled

Derivatives of the Incomplete Gamma Integral (Unscaled Version)

Fitting Vector Generalized Linear Models

Rao's Score Test Statistics Evaluated at the Null Values

Simplex Distribution

The Singh-Maddala Distribution

Prior and Working Weights of a VGLM fit

plotdeplot.lmscreg

Density Plot for LMS Quantile Regression

Hauck-Donner Effects: Segmented Lines Plot

Summarizing Vector Generalized Additive Model Fits

Bitterness in Wine Data

Skellam Distribution Family Function

posbernoulli.tb

Positive Bernoulli Family Function with Time and Behavioural Effects

Zero-Altered Binomial Distribution

Summarizing Vector Generalized Linear Model Fits

Zero-Altered Binomial Distribution

Defining Penalized Spline Smooths in VGAM Formulas

The Skellam Distribution

Skew-Normal Distribution

smart.expression

S Expression for Smart Functions

Venice Maximum Sea Levels Data

Determine What Mode the Smart Prediction is In

Smart Prediction

Tobit Regression

Zero-Inflated Binomial Distribution

Positive Binomial Distribution Family Function

Cleans Up After Smart Prediction

The Tobit Distribution

The Triangle Distribution

trim.constraints

Trimmed Constraint Matrices

Trivariate Normal Distribution Family Function

Pregnant Rats Toxological Experiment Data

University California Berkeley Graduate Admissions

Yeo-Johnson Transformation

Zero-Inflated Binomial Distribution Family Function

Trivariate Normal Distribution Density and Random Variates

Weibull Distribution Family Function, Parameterized by the Mean

Predict Method for a CQO fit

undocumented-methods

Undocumented Methods Functions

Weibull Distribution Family Function

Zero-Altered Geometric Distribution

Zero-Altered Geometric Distribution

Zero-Altered Poisson Distribution

von Mises Distribution Family Function

The zero Argument in VGAM Family Functions

Plotting Functions for 'profile' Objects

Zero-Altered Poisson Distribution

Vector Cubic Smoothing Spline

Waitakere Ranges Data

Zero-Altered Negative Binomial Distribution

Rayleigh Regression Family Function

Zero-Inflated Geometric Distribution

Zero-Altered Negative Binomial Distribution

Riemann's Zeta Function

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

Rayleigh Distribution

Rutherford-Geiger Polonium Data

Zero-Inflated Geometric Distribution Family Function

Zipf Distribution Family Function

Zero- and One-Inflated Beta Distribution Family Function

Defining Smooths in VGAM Formulas

The Zero/One-Inflated Beta Distribution

Slash Distribution

Defining O'Sullivan Spline Smooths in VGAM Formulas

Ordinal Regression with Stopping Ratios

Choose a model by AIC in a Stepwise Algorithm

Trajectory Plot

Trajectory plot for QRR-VGLMs

Fitting Vector Generalized Additive Models

Control Function for vgam()

Zero-Inflated Negative Binomial Distribution

Zero-Inflated Negative Binomial Distribution Family Function

Zero-Inflated Poisson Distribution

Zero-Inflated Poisson Distribution Family Function