glm {base}R Documentation

Fitting Generalized Linear Models

Description

glm is used to fit generalized linear models.

Models for glm are specified by giving a symbolic description of the linear predictor and a description of the error distribution.

Usage

glm(formula, family = gaussian, data, weights = NULL, subset = NULL,
    na.action, start = NULL, offset = NULL,
    control = glm.control(epsilon=0.0001, maxit=10, trace=FALSE),
    model = TRUE, method = "glm.fit", x = FALSE, y = TRUE,
    contrasts = NULL, ...)
glm.control(epsilon = 0.0001, maxit = 10, trace = FALSE)
glm.fit(x, y, weights = rep(1, nrow(x)),
        start = NULL, etastart  =  NULL, mustart = NULL,
        offset = rep(0, nrow(x)),
        family = gaussian(), control = glm.control(),
        intercept = TRUE)

Arguments

formula a symbolic description of the model to be fit. The details of model specification are given below.
family a description of the error distribution and link function to be used in the model. See family for details.
data an optional data frame containing the variables in the model. By default the variables are taken from the environment ffrom which glm is called.
weights an optional vector of weights to be used in the fitting process.
subset an optional vector specifying a subset of observations to be used in the fitting process.
na.action a function which indicates what should happen when the data contain NAs. The default is set by the na.action setting of options, and is na.fail if that is unset. The ``factory-fresh'' default is na.omit.
start starting values for the parameters in the linear predictor.
etastart starting values for the linear predictor.
mustart starting values for the vector of means.
offset this can be used to specify an a priori known component to be included in the linear predictor during fitting.
control a list of parameters for controlling the fitting process. See the documentation for glm.control for details.
model a logical value indicating whether model frame should be included as a component of the returned value.
method the method to be used in fitting the model. The default (and presently only) method glm.fit uses iteratively reweighted least squares.
x, y logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value.
contrasts an optional list. See the contrasts.arg of model.matrix.default.

Details

A typical predictor has the form response ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. For binomial models the response can also be specified as a factor (when the first level denotes failure and all others success) or as a two-column matrix with the columns giving the numbers of successes and failures. A terms specification of the form first+second indicates all the terms in first together with all the terms in second with duplicates removed.

A specification of the form first:second indicates the the set of terms obtained by taking the interactions of all terms in first with all terms in second. The specification first*second indicates the cross of first and second. This is the same as first+second+first:second.

Value

glm returns an object of class glm which inherits from the class lm. The function summary (i.e., summary.glm) can be used to obtain or print a summary of the results and the function anova (i.e., anova.glm) to produce an analysis of variance table.

The generic accessor functions coefficients, effects, fitted.values and residuals can be used to extract various useful features of the value returned by glm.

Note

Offsets specified by offset will not be included in predictions by predict.glm, whereas those specified by an offset term in the formula will be.

See Also

anova.glm, summary.glm, etc. for glm methods, and the generic functions anova, summary, effects, fitted.values, and residuals. Further, lm for non-generalized linear models.

Examples

## Annette Dobson (1990) "An Introduction to Generalized Linear Models".
## Page 93: Randomized Controlled Trial :
counts <- c(18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,9)
treatment <- gl(3,3)
print(d.AD <- data.frame(treatment, outcome, counts))
glm.D93 <- glm(counts ~ outcome + treatment, family=poisson())
anova(glm.D93)
summary(glm.D93)

## an example with offsets from Venables & Ripley (1999, pp.217-8)


 ## Need the anorexia data from a 1999 version of the package MASS:
 library(MASS)
 data(anorexia)

anorex.1 <- glm(Postwt ~ Prewt + Treat + offset(Prewt),
            family = gaussian, data = anorexia)
summary(anorex.1)
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