| glm {base} | 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 = NULL, subset = NULL,
na.action, start = NULL, offset = NULL,
control = glm.control(...), model = TRUE, method = "glm.fit",
x = FALSE, y = TRUE, contrasts = NULL, ...)
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)
glm.fit.null(x, y, weights = rep(1, nrow(x)),
start = NULL, etastart = NULL, mustart = NULL,
offset = rep(0, nrow(x)),
family = gaussian(), control = glm.control(),
intercept = FALSE)
## 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.
See |
data |
an optional data frame containing the variables
in the model. By default the variables are taken 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 |
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 |
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 |
x, y |
For For |
contrasts |
an optional list. See the |
object |
an object inheriting from class |
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 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.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.
glm returns an object of class 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 |
linear.predictors |
the linear fit on link scale. |
deviance |
up to a constant, minus twice the maximized log-likelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero. |
aic |
Akaike's An Information Criterion, minus twice the maximized log-likelihood plus twice the number of coefficients (so assuming that the dispersion is known. |
null.deviance |
The deviance for the null model, comparable with
|
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 |
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 |
data |
the |
offset |
the offset vector used. |
control |
the value of the |
method |
the name of the fitter function used, in R always
|
contrasts |
(where relevant) the contrasts used. |
xlevels |
(where relevant) a record of the levels of the factors used in fitting. |
In addition, non-null 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 well-designed
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
two-column 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.
McCullagh P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
Dobson, A. J. (1990) An Introduction to Generalized Linear Models. London: Chapman and Hall.
Venables, W. N. and Ripley, B. D. (1999) Modern Applied Statistics with S-PLUS. 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
non-generalized 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 (1999, pp.217-8)
## 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. 300-2)
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))