glm(formula, family=gaussian, data, weights=NULL, subset=NULL, na.action=na.fail, start=NULL, offset=NULL, control=glm.control(epsilon=0.0001, maxit=10, trace=FALSE), model = TRUE, method = "glm.fit", x = FALSE, y = TRUE) glm.control(epsilon=0.0001, maxit=10, trace=FALSE) glm.fit(x, y, weights=rep(1, nrow(x)), start=NULL, etastart = NULL, offset=rep(0, nrow(x)), family=gaussian(), control=glm.control(), intercept=TRUE)
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 which lm is called from.
|
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 action (na.omit )
is to omit any incomplete observations.
The alternative action na.fail causes lm to
print an error message and terminate if there are any incomplete
observations.
|
start
| starting values for the parameters in the linear predictor. |
etastart
| starting values for the linear predictor. |
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 design matrix used in the fitting process should be returned as components of the returned value. |
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.
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
.
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
.
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.## Annette Dobson (1990) "An Introduction to Statistical Modelling". ## 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) ## Annette Dobson (1990) "An Introduction to Statistical Modelling". ## 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) ## Annette Dobson (1990) "An Introduction to Statistical Modelling". ## 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) ## Annette Dobson (1990) "An Introduction to Statistical Modelling". ## 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)