

gls(nlme)                                    R Documentation

_F_i_t _L_i_n_e_a_r _M_o_d_e_l _U_s_i_n_g _G_e_n_e_r_a_l_i_z_e_d _L_e_a_s_t _S_q_u_a_r_e_s

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

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

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

     gls(model, data, correlation, weights, subset, method, na.action,
         control, verbose)

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

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

    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 docu-
          mentation of `corClasses' for a description of the
          available `corStruct' classes. If a grouping vari-
          able 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 `var-
          Classes' for a description of the available `var-
          Func' 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 observa-
          tions.

 control: a list of control values for the estimation algo-
          rithm 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'.

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

     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.

_A_u_t_h_o_r_(_s_)_:

     Jose Pinheiro and Douglas Bates

_R_e_f_e_r_e_n_c_e_s_:

     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 mod-
     els is presented in detail in Carroll, R.J. and Rup-
     pert, 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 Wolfin-
     ger, R.D. (1996) "SAS Systems for Mixed Models", SAS
     Institute.

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

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

     `glsControl', `glsObject', `varFunc', `corClasses',
     `varClasses'

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

     library(nlme)
     data(Ovary)
     # 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 <- gls(follicles ~ sin(2*pi*Time) + cos(2*pi*Time), Ovary,
                weights = varPower())

