gls                   package:nlme                   R Documentation

Fit Linear Model Using Generalized Least Squares

Description:

     This function fits a linear model using generalized least squares.
     The errors are allowed to be correlated and/or have unequal
     variances.

Usage:

     gls(model, data, correlation, weights, subset, method, na.action,
         control, verbose)
     ## S3 method for class 'gls':
     update(object, model., ..., evaluate = TRUE)

Arguments:

  object: an object inheriting from class 'gls', representing a
          generalized least squares fitted linear model.

   model: a two-sided linear formula object describing the model, with
          the response on the left of a '~' operator and the terms,
          separated by '+' operators, on the right.

  model.: Changes to the model - see 'update.formula' for details.

    data: an optional data frame containing the variables named in
          'model', 'correlation', 'weights', and 'subset'. By default
          the variables are taken from the environment from which 'gls'
          is called.

correlation: an optional 'corStruct' object describing the within-group
          correlation structure. See the documentation of 'corClasses'
          for a description of the available 'corStruct' classes. If a
          grouping variable is to be used, it must be specified in the
          'form' argument to the 'corStruct' constructor. Defaults to
          'NULL', corresponding to uncorrelated  errors.

 weights: an optional 'varFunc' object or one-sided formula describing
          the within-group heteroscedasticity structure. If given as a
          formula, it is used as the argument to 'varFixed',
          corresponding to fixed variance weights. See the
          documentation on 'varClasses' for a description of the
          available 'varFunc' classes. Defaults to 'NULL',
          corresponding to homoscesdatic errors.

  subset: an optional expression indicating which subset of the rows of
          'data' should  be  used in the fit. This can be a logical
          vector, 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.

  method: a character string.  If '"REML"' the model is fit by
          maximizing the restricted log-likelihood.  If '"ML"' the
          log-likelihood is maximized.  Defaults to '"REML"'.

na.action: a function that indicates what should happen when the data
          contain 'NA's.  The default action ('na.fail') causes 'gls'
          to print an error message and terminate if there are any
          incomplete observations.

 control: a list of control values for the estimation algorithm to
          replace the default values returned by the function
          'glsControl'. Defaults to an empty list.

 verbose: an optional logical value. If 'TRUE' information on the
          evolution of the iterative algorithm is printed. Default is
          'FALSE'.

     ...: some methods for this generic require additional arguments. 
          None are used in this method.

evaluate: If 'TRUE' evaluate the new call else return the call.

Value:

     an object of class 'gls' representing the linear model fit.
     Generic functions such as 'print', 'plot', and  'summary' have
     methods to show the results of the fit. See 'glsObject' for the
     components of the fit. The functions 'resid', 'coef', and 'fitted'
     can be used to extract some of its components.

Author(s):

     Jose Pinheiro jcp@research.bell-labs.com, Douglas Bates
     bates@stat.wisc.edu

References:

     The different correlation structures available for the
     'correlation' argument are described in Box, G.E.P., Jenkins,
     G.M., and Reinsel G.C. (1994), Littel, R.C., Milliken, G.A.,
     Stroup, W.W., and Wolfinger, R.D. (1996), and Venables, W.N. and
     Ripley, B.D. (1997). The use of variance functions for linear  and
     nonlinear models is presented in detail in Carroll, R.J. and
     Ruppert, D. (1988) and Davidian, M. and Giltinan, D.M. (1995).  

     Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994) "Time Series
     Analysis: Forecasting and Control", 3rd Edition, Holden-Day. 

     Carroll, R.J. and Ruppert, D. (1988) "Transformation and Weighting
     in Regression", Chapman and Hall.

     Davidian, M. and Giltinan, D.M. (1995) "Nonlinear Mixed Effects
     Models for Repeated Measurement Data", Chapman and Hall.

     Littel, R.C., Milliken, G.A., Stroup, W.W., and Wolfinger, R.D.
     (1996) "SAS Systems for Mixed Models", SAS Institute.

     Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S
     and S-PLUS", Springer, esp. pp. 100, 461.  

     Venables, W.N. and Ripley, B.D. (1997) "Modern Applied Statistics
     with S-PLUS", 2nd Edition, Springer-Verlag.

See Also:

     'corClasses', 'glsControl', 'glsObject', 'glsStruct', 'plot.gls', 
     'predict.gls',  'qqnorm.gls',  'residuals.gls',  'summary.gls', 
     'varClasses', 'varFunc'

Examples:

     # AR(1) errors within each Mare
     fm1 <- gls(follicles ~ sin(2*pi*Time) + cos(2*pi*Time), Ovary,
                correlation = corAR1(form = ~ 1 | Mare))
     # variance increases as a power of the absolute fitted values
     fm2 <- update(fm1, weights = varPower())

