

glm {base}                                   R Documentation

_F_i_t_t_i_n_g _G_e_n_e_r_a_l_i_z_e_d _L_i_n_e_a_r _M_o_d_e_l_s

_D_e_s_c_r_i_p_t_i_o_n_:

     `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.

_U_s_a_g_e_:

     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)

_A_r_g_u_m_e_n_t_s_:

 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 observa-
          tions 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 observa-
          tions.  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 com-
          ponent to be included in the linear predictor dur-
          ing 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 pro-
          cess should be returned as components of the
          returned value.

_D_e_t_a_i_l_s_:

     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 num-
     bers 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 interac-
     tions of all terms in `first' with all terms in `sec-
     ond'.  The specification `first*second' indicates the
     cross of `first' and `second'.  This is the same as
     `first+second+first:second'.

_V_a_l_u_e_:

     `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'.

_S_e_e _A_l_s_o_:

     `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.

_E_x_a_m_p_l_e_s_:

     ## 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)

