glm                   package: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, start = NULL, offset = NULL,
         control = glm.control(epsilon=0.0001, maxit=10, trace=FALSE),
         model = TRUE, method = "glm.fit", x = FALSE, y = TRUE,
         contrasts = NULL, ...)
     glm.control(epsilon = 0.0001, maxit = 10, trace = FALSE)
     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)

_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
          ffrom which `glm' is called.

 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 is set by the `na.action' setting
          of `options', and is `na.fail' if that is unset.  The
          ``factory-fresh'' default is `na.omit'.

   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 `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
          model matrix used in the fitting process should be returned
          as components of the returned value.

contrasts: an optional list. See the `contrasts.arg' of
          `model.matrix.default'.

_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
     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'.

_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'.

_N_o_t_e:

     Offsets specified by `offset' will not be included in predictions
     by `predict.glm', whereas those specified by an offset term in the
     formula will be.

_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 Generalized Linear Models".
     ## 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)

