

   FFuunnccttiioonn ttoo ssoollvvee aa GGeenneerraalliizzeedd EEssttiimmaattiioonn EEqquuaattiioonn MMooddeell

        gee(formula, id,
            data, subset, na.action,
            R=NA, b=NA,
            tol=0.001, maxiter=as.integer(25),
            family = gaussian, corstr="independence",
            Mv=1, silent=T, contrasts=NULL,
            scale.fix = F, scale.value = 1, v4.4compat=F)

   AArrgguummeennttss::

    formula: a formula expression as for other regression mod-
             els, of the form response ~ predictors. See the
             documentation of lm and formula for details.

         id: a vector which identifies the clusters.  The
             length of `id' should be the same as the number of
             observations.  Data are assumed to be sorted so
             that observations on a cluster are contiguous rows
             for all entities in the formula.

       data: an optional data frame in which to interpret the
             variables occurring in the `formula', along with
             the `id' and `n' variables.

     subset: expression saying which subset of the rows of the
             data should  be  used in the fit.  This can be a
             logical vector (which is replicated to have length
             equal to the number of observations), or a numeric
             vector indicating which observation numbers are to
             be included, or a  character  vector of the row
             names to be included.  All observations are
             included by default.

   na.action: a function to filter missing data.  For `gee'
             only `na.omit' should be used here.

          R: a square matrix of dimension maximum cluster size
             containing the user specified correlation.  This
             is only appropriate if `corstr="fixed"'.

          b: an initial estimate for the parameters.

        tol: the tolerance used in the fitting algorithm.

    maxiter: the maximum number of iterations.

     family: a `family' object: a list of functions and expres-
             sions for defining link and variance functions.
             Families supported in `gee' are `gaussian`, `bino-
             mial', `poisson', `Gamma', and `quasi'; see the
             `glm' and `family' documentation.  Some links are
             not currently available: `1/mu^2' and `sqrt' have
             not been hard-coded in the cgee engine at present.
             The inverse gaussian variance function is not
             available.  All combinations of remaining func-
             tions can be obtained either by family selection
             or by the use of `quasi'.  Future releases will
             allow S-coded functions for link, variance and
             correlation function specification.

     corstr: a character specifying the Correlation structure.
             The following are permitted: `"independence"'
             `"fixed"' `"stat_M_dep"' `"non_stat_M_dep"'
             `"exchangeable"' `"AR-M"' `"unstructured"'

         Mv: When the corstr is `"stat_M_dep"',
             `"non_stat_M_dep"', or `"AR-M"' then `Mv' must be
             specified.

     silent: a logical variable controlling whether parameter
             estimates at each iteration are printed.

   contrasts: a list giving contrasts for some or all of the
             factors appearing in the model formula.  The ele-
             ments of the list should have the same name as the
             variable and should be either a contrast matrix
             (specifically, any full-rank matrix with as many
             rows as there are levels in the factor), or else a
             function to compute such a matrix given the number
             of levels.

   scale.fix: a logical variable; if true, the scale parameter
             is fixed at the value of `scale.value'

   scale.value: numeric variable giving the value to which the
             scale parameter should be fixed; used only if
             `scale.fix == T'.

   v4.4compat: logical variable requesting compatibility of
             correlation parameter estimates with previous ver-
             sions; the current version revises to be more
             faithful to the Liang and Zeger (1986) proposals
             (compatible with the Groemping SAS macro, version
             2.03)

   DDeessccrriippttiioonn::

        Produces an object of class "gee" which is a General-
        ized Estimation Equation fit of the data.

   DDeettaaiillss::

        Though input data need not be sorted by the variable
        named `"id"', the program will interpret physically
        contiguous records possessing the same value of `id' as
        members of the same cluster.  Thus it is possible to
        use the following vector as an `id' vector to discrimi-
        nate 4 clusters of size 4:
        `c(0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1)'.

   VVaalluuee::

        An object of class `"gee"' representing the fit.

   SSiiddee EEffffeeccttss::

        Offsets must be specified in the model formula, as in
        `glm()'.

   NNOOTTEE::

        This is version 4.8 of this user documentation file,
        revised 98/01/27.  The assistance of Dr B Ripley is
        gratefully acknowledged.

   RReeffeerreenncceess::

        Liang, K.Y. and Zeger, S.L. (1986).  Longitudinal data
        analysis using generalized linear models.  Biometrika
        73 13-22.

        Zeger, S.L. and Liang, K.Y. (1986).  Longitudinal data
        analysis for discrete and continuous outcomes.  Biomet-
        rics 42 121-130.

   SSeeee AAllssoo::

        `glm', `lm', `formula'.

   EExxaammpplleess::

        gee(y ~ x,id)   # Gaussian model with independent correlation structure

        gee(d ~ x1+x2,id,link="logit",family=binomial,corstr="exchangeable")

        gee(d ~ x1+x2,id=id,family=binomial(link=(probit)),
            corstr="stat_M_dep",M=1)

