glm {stats}  R Documentation 
glm
is used to fit generalized linear models, specified by
giving a symbolic description of the linear predictor and a
description of the error distribution.
glm(formula, family = gaussian, data, weights, subset, na.action, start = NULL, etastart, mustart, offset, control = glm.control(...), model = TRUE, method = "glm.fit", x = FALSE, y = TRUE, contrasts = NULL, ...) glm.fit(x, y, weights = rep(1, nobs), start = NULL, etastart = NULL, mustart = NULL, offset = rep(0, nobs), family = gaussian(), control = glm.control(), intercept = TRUE) ## S3 method for class 'glm': weights(object, type = c("prior", "working"), ...)
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. This can be a character string
naming a family function, a family function or the result of a call
to a family function. (See family for details of
family functions.) 
data 
an optional data frame containing the variables
in the model. If not found in data , the variables are taken
from environment(formula) , typically the environment from
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 NA s. The default is set by
the na.action setting of options , and is
na.fail if that is unset. The “factoryfresh”
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 method "glm.fit" uses iteratively reweighted
least squares (IWLS). The only current alternative is
"model.frame" which returns the model frame and does no fitting. 
x, y 
For glm :
logical values indicating whether the response
vector and model matrix used in the fitting process
should be returned as components of the returned value.
For glm.fit : x is a design matrix of dimension n
* p , and y is a vector of observations of length n .

contrasts 
an optional list. See the contrasts.arg
of model.matrix.default . 
object 
an object inheriting from class "glm" . 
type 
character, partial matching allowed. Type of weights to extract from the fitted model object. 
intercept 
logical. Should an intercept be included? 
... 
further arguments passed to or from other methods. 
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 twocolumn 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. The terms in
the formula will be reordered so that main effects come first,
followed by the interactions, all secondorder, all thirdorder and so
on: to avoid this pass a terms
object as the formula.
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
.
glm.fit
and glm.fit.null
are the workhorse functions:
the former calls the latter for a null model (with no intercept).
If more than one of etastart
, start
and mustart
is specified, the first in the list will be used.
All of weights
, subset
, offset
, etastart
and mustart
are evaluated in the same way as variables in
formula
, that is first in data
and then in the
environment of formula
.
glm
returns an object of class inheriting from "glm"
which inherits from the class "lm"
. See later in this section.
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
.
weights
extracts a vector of weights, one for each case in the
fit (after subsetting and na.action
).
An object of class "glm"
is a list containing at least the
following components:
coefficients 
a named vector of coefficients 
residuals 
the working residuals, that is the residuals in the final iteration of the IWLS fit. 
fitted.values 
the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function. 
rank 
the numeric rank of the fitted linear model. 
family 
the family object used. 
linear.predictors 
the linear fit on link scale. 
deviance 
up to a constant, minus twice the maximized loglikelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero. 
aic 
Akaike's An Information Criterion, minus twice the maximized loglikelihood plus twice the number of coefficients (so assuming that the dispersion is known. 
null.deviance 
The deviance for the null model, comparable with
deviance . The null model will include the offset, and an
intercept if there is one in the model 
iter 
the number of iterations of IWLS used. 
weights 
the working weights, that is the weights in the final iteration of the IWLS fit. 
prior.weights 
the case weights initially supplied. 
df.residual 
the residual degrees of freedom. 
df.null 
the residual degrees of freedom for the null model. 
y 
the y vector used. (It is a vector even for a binomial
model.) 
converged 
logical. Was the IWLS algorithm judged to have converged? 
boundary 
logical. Is the fitted value on the boundary of the attainable values? 
call 
the matched call. 
formula 
the formula supplied. 
terms 
the terms object used. 
data 
the data argument . 
offset 
the offset vector used. 
control 
the value of the control argument used. 
method 
the name of the fitter function used, in R always
"glm.fit" . 
contrasts 
(where relevant) the contrasts used. 
xlevels 
(where relevant) a record of the levels of the factors used in fitting. 
In addition, nonempty fits will have components qr
, R
and effects
relating to the final weighted linear fit.
Objects of class "glm"
are normally of class c("glm",
"lm")
, that is inherit from class "lm"
, and welldesigned
methods for class "lm"
will be applied to the weighted linear
model at the final iteration of IWLS. However, care is needed, as
extractor functions for class "glm"
such as
residuals
and weights
do not just pick out
the component of the fit with the same name.
If a binomial
glm
model is specified by giving a
twocolumn response, the weights returned by prior.weights
are
the total numbers of cases (factored by the supplied case weights) and
the component y
of the result is the proportion of successes.
The original R implementation of glm
was written by Simon
Davies working for Ross Ihaka at the University of Auckland, but has
since been extensively rewritten by members of the R Core team.
The design was inspired by the S function of the same name described in Hastie & Pregibon (1992).
Dobson, A. J. (1990) An Introduction to Generalized Linear Models. London: Chapman and Hall.
Hastie, T. J. and Pregibon, D. (1992) Generalized linear models. Chapter 6 of Statistical Models in S eds J. M. Chambers and T. J. Hastie, Wadsworth & Brooks/Cole.
McCullagh P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. New York: Springer.
anova.glm
, summary.glm
, etc. for
glm
methods,
and the generic functions anova
, summary
,
effects
, fitted.values
,
and residuals
. Further, lm
for
nongeneralized linear models.
esoph
, infert
and
predict.glm
have examples of fitting binomial glms.
## Dobson (1990) 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 (2002, p.189) ## Not run: ## Need the anorexia data from a recent version of the package 'MASS': library(MASS) data(anorexia) ## End(Not run) anorex.1 < glm(Postwt ~ Prewt + Treat + offset(Prewt), family = gaussian, data = anorexia) summary(anorex.1) # A Gamma example, from McCullagh & Nelder (1989, pp. 3002) clotting < data.frame( u = c(5,10,15,20,30,40,60,80,100), lot1 = c(118,58,42,35,27,25,21,19,18), lot2 = c(69,35,26,21,18,16,13,12,12)) summary(glm(lot1 ~ log(u), data=clotting, family=Gamma)) summary(glm(lot2 ~ log(u), data=clotting, family=Gamma)) ## Not run: ## for an example of the use of a terms object as a formula demo(glm.vr) ## End(Not run)