Fitting Generalized Linear Models

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Fitting Generalized Linear Models

Syntax

glm(formula, family=gaussian, data, weights, subset,
        na.action=na.fail, start=NULL, offset=NULL,
        control=glm.control(epsilon=0.0001, maxit=10,
                trace=F),
        model=T, method=glm.fit, x=F, y=T)

summary(glm.obj, dispersion=NULL, correlation=TRUE,
        na.action=na.omit)
anova(glm.obj, ...)

coefficients(glm.obj)
deviance(glm.obj)
df.residual(glm.obj)
effects(glm.obj)
family(glm.obj)
fitted.values(glm.obj)
residuals(glm.obj, type="deviance")

glm.control(epsilon=0.0001, maxit=10, trace=FALSE) 
glm.fit(x, y, weights=rep(1, nrow(x)),
        start=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 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.
`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.obj`	an object of class `glm`.
`dispersion`	the dispersion parameter for the fitting family. By default the dispersion parameter is obtained from `glm.obj`.
`correlation`	should the correlation matrix of the estimated parameters be printed.
`type`	the type of residuals which should be returned. The alternatives are: `"deviance"`, `"pearson"`, `"working"`, `"response"`.

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. A typical predictor has the form reponse ~ terms where response is the (numeric) response vector and terms is a series of terms which specifies a linear predictor for response. 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 can be used to obtain or print a summary of the results and the function anova and be used to produce and 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.