glm function - RDocumentation (original) (raw)
glm: Fitting Generalized Linear Models
Description
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.
Usage
glm(formula, family = gaussian, data, weights, subset, na.action, start = NULL, etastart, mustart, offset, control = list(…), model = TRUE, method = "glm.fit", x = FALSE, y = TRUE, singular.ok = TRUE, contrasts = NULL, …)
glm.fit(x, y, weights = rep(1, nobs), start = NULL, etastart = NULL, mustart = NULL, offset = rep(0, nobs), family = gaussian(), control = list(), intercept = TRUE, singular.ok = TRUE)
S3 method for glm
weights(object, type = c("prior", "working"), …)
Arguments
formula
an object of class "[formula](/link/formula?package=stats&version=3.6.2)"
(or one that can be coerced to that class): a symbolic description of the model to be fitted. The details of model specification are given under ‘Details’.
family
a description of the error distribution and link function to be used in the model. For glm
this can be a character string naming a family function, a family function or the result of a call to a family function. For glm.fit
only the third option is supported. (See [family](/link/family?package=stats&version=3.6.2)
for details of family functions.)
data
an optional data frame, list or environment (or object coercible by [as.data.frame](/link/as.data.frame?package=stats&version=3.6.2)
to a 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 ‘prior weights’ to be used in the fitting process. Should be NULL
or a numeric vector.
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](/link/options?package=stats&version=3.6.2)
, and is[na.fail](/link/na.fail?package=stats&version=3.6.2)
if that is unset. The ‘factory-fresh’ default is [na.omit](/link/na.omit?package=stats&version=3.6.2)
. Another possible value isNULL
, no action. Value [na.exclude](/link/na.exclude?package=stats&version=3.6.2)
can be useful.
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. This should be NULL
or a numeric vector of length equal to the number of cases. One or more [offset](/link/offset?package=stats&version=3.6.2)
terms can be included in the formula instead or as well, and if more than one is specified their sum is used. See [model.offset](/link/model.offset?package=stats&version=3.6.2)
.
control
a list of parameters for controlling the fitting process. For glm.fit
this is passed to[glm.control](/link/glm.control?package=stats&version=3.6.2)
.
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 alternative "model.frame"
returns the model frame and does no fitting.
User-supplied fitting functions can be supplied either as a function or a character string naming a function, with a function which takes the same arguments as glm.fit
. If specified as a character string it is looked up from within the stats namespace.
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 dimensionn * p
, and y
is a vector of observations of lengthn
.
singular.ok
logical; if FALSE
a singular fit is an error.
contrasts
an optional list. See the contrasts.arg
of model.matrix.default
.
intercept
logical. Should an intercept be included in the_null_ model?
object
an object inheriting from class "glm"
.
type
character, partial matching allowed. Type of weights to extract from the fitted model object. Can be abbreviated.
…
For glm
: arguments to be used to form the defaultcontrol
argument if it is not supplied directly.
For weights
: further arguments passed to or from other methods.
Value
glm
returns an object of class inheriting from "glm"
which inherits from the class "lm"
. See later in this section. If a non-standard method
is used, the object will also inherit from the class (if any) returned by that function.
The function [summary](/link/summary?package=stats&version=3.6.2)
(i.e., [summary.glm](/link/summary.glm?package=stats&version=3.6.2)
) can be used to obtain or print a summary of the results and the function[anova](/link/anova?package=stats&version=3.6.2)
(i.e., [anova.glm](/link/anova.glm?package=stats&version=3.6.2)
) to produce an analysis of variance table.
The generic accessor functions [coefficients](/link/coefficients?package=stats&version=3.6.2)
,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. Since cases with zero weights are omitted, their working residuals are NA
.
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](/link/family?package=stats&version=3.6.2)
object used.
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
A version of Akaike's An Information Criterion, minus twice the maximized log-likelihood plus twice the number of parameters, computed via the aic
component of the family. For binomial and Poison families the dispersion is fixed at one and the number of parameters is the number of coefficients. For gaussian, Gamma and inverse gaussian families the dispersion is estimated from the residual deviance, and the number of parameters is the number of coefficients plus one. For a gaussian family the MLE of the dispersion is used so this is a valid value of AIC, but for Gamma and inverse gaussian families it is not. For families fitted by quasi-likelihood the value is NA
.
null.deviance
The deviance for the null model, comparable withdeviance
. The null model will include the offset, and an intercept if there is one in the model. Note that this will be incorrect if the link function depends on the data other than through the fitted mean: specify a zero offset to force a correct calculation.
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 weights initially supplied, a vector of1
s if none were.
df.residual
the residual degrees of freedom.
df.null
the residual degrees of freedom for the null model.
y
if requested (the default) the y
vector used. (It is a vector even for a binomial model.)
x
if requested, the model matrix.
model
if requested (the default), the model frame.
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](/link/terms?package=stats&version=3.6.2)
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 (when provided as a[character](/link/character?package=stats&version=3.6.2)
string to glm()
) or the fitter[function](/link/function?package=stats&version=3.6.2)
(when provided as that).
contrasts
(where relevant) the contrasts used.
xlevels
(where relevant) a record of the levels of the factors used in fitting.
na.action
(where relevant) information returned by[model.frame](/link/model.frame?package=stats&version=3.6.2)
on the special handling of NA
s.
In addition, non-empty 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 asresiduals and weights do not just pick out the component of the fit with the same name.
If a binomial glm model was 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.
Fitting functions
The argument method
serves two purposes. One is to allow the model frame to be recreated with no fitting. The other is to allow the default fitting function glm.fit
to be replaced by a function which takes the same arguments and uses a different fitting algorithm. If glm.fit
is supplied as a character string it is used to search for a function of that name, starting in thestats namespace.
The class of the object return by the fitter (if any) will be prepended to the class returned by glm
.
Details
A typical predictor has the form response ~ terms
whereresponse
is the (numeric) response vector and terms
is a series of terms which specifies a linear predictor forresponse
. For binomial
and quasibinomial
families the response can also be specified as a [factor](/link/factor?package=stats&version=3.6.2)
(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 insecond
with any duplicates removed.
A specification of the form first:second
indicates the set of terms obtained by taking the interactions of all terms infirst
with all terms in second
. The specificationfirst*second
indicates the cross of first
andsecond
. This is the same as first + second + first:second
.
The terms in the formula will be re-ordered so that main effects come first, followed by the interactions, all second-order, all third-order and so on: to avoid this pass a terms
object as the formula.
Non-NULL
weights
can be used to indicate that different observations have different dispersions (with the values inweights
being inversely proportional to the dispersions); or equivalently, when the elements of weights
are positive integers \(w_i\), that each response \(y_i\) is the mean of \(w_i\) unit-weight observations. For a binomial GLM prior weights are used to give the number of trials when the response is the proportion of successes: they would rarely be used for a Poisson GLM.
glm.fit
is the workhorse function: it is not normally called directly but can be more efficient where the response vector, design matrix and family have already been calculated.
If more than one of etastart
, start
and mustart
is specified, the first in the list will be used. It is often advisable to supply starting values for a [quasi](/link/quasi?package=stats&version=3.6.2)
family, and also for families with unusual links such as gaussian("log")
.
All of weights
, subset
, offset
, etastart
and mustart
are evaluated in the same way as variables informula
, that is first in data
and then in the environment of formula
.
For the background to warning messages about ‘fitted probabilities numerically 0 or 1 occurred’ for binomial GLMs, see Venables & Ripley (2002, pp.197--8).
References
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.
See Also
[anova.glm](/link/anova.glm?package=stats&version=3.6.2)
, [summary.glm](/link/summary.glm?package=stats&version=3.6.2)
, etc. forglm
methods, and the generic functions [anova](/link/anova?package=stats&version=3.6.2)
, [summary](/link/summary?package=stats&version=3.6.2)
,[effects](/link/effects?package=stats&version=3.6.2)
, [fitted.values](/link/fitted.values?package=stats&version=3.6.2)
, and [residuals](/link/residuals?package=stats&version=3.6.2)
.
[lm](/link/lm?package=stats&version=3.6.2)
for non-generalized linear models (which SAS calls GLMs, for ‘general’ linear models).
[loglin](/link/loglin?package=stats&version=3.6.2)
and [loglm](/link/loglm?package=stats&version=3.6.2&to=MASS)
(package MASS) for fitting log-linear models (which binomial and Poisson GLMs are) to contingency tables.
bigglm
in package biglm for an alternative way to fit GLMs to large datasets (especially those with many cases).
[esoph](/link/esoph?package=stats&version=3.6.2)
, [infert](/link/infert?package=stats&version=3.6.2)
and[predict.glm](/link/predict.glm?package=stats&version=3.6.2)
have examples of fitting binomial glms.
Examples
# NOT RUN {
## 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)
# }
# NOT RUN {
summary(glm.D93)
# }
# NOT RUN {
## Computing AIC [in many ways]:
(A0 <- AIC(glm.D93))
(ll <- logLik(glm.D93))
A1 <- -2*c(ll) + 2*attr(ll, "df")
A2 <- glm.D93$family$aic(counts, mu=fitted(glm.D93), wt=1) +
2 * length(coef(glm.D93))
stopifnot(exprs = {
all.equal(A0, A1)
all.equal(A1, A2)
all.equal(A1, glm.D93$aic)
})
# }
# NOT RUN {
## an example with offsets from Venables & Ripley (2002, p.189)
utils::data(anorexia, package = "MASS")
anorex.1 <- glm(Postwt ~ Prewt + Treat + offset(Prewt),
family = gaussian, data = anorexia)
summary(anorex.1)
# }
# NOT RUN {
# 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))
## Aliased ("S"ingular) -> 1 NA coefficient
(fS <- glm(lot2 ~ log(u) + log(u^2), data = clotting, family = Gamma))
tools::assertError(update(fS, singular.ok=FALSE), verbose=interactive())
## -> .. "singular fit encountered"
# }
# NOT RUN {
## for an example of the use of a terms object as a formula
demo(glm.vr)
# }
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