gee                   package:gee                   R Documentation

Function to solve a Generalized Estimation Equation Model

Description:

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

Usage:

     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)

Arguments:

 formula: a formula expression as for other regression models, 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 expressions for
          defining link and variance functions.  Families supported in
          `gee' are `gaussian`, `binomial', `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 functions 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 elements 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 versions; the current
          version revises to be more faithful to the Liang and Zeger
          (1986) proposals (compatible with the Groemping SAS macro,
          version 2.03) 

Details:

     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 discriminate 4 clusters of size 4: 
     `c(0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1)'.

Value:

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

Side Effects:

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

NOTE:

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

References:

     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. Biometrics 42 121-130.

See Also:

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

Examples:

     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)