gls {nlme}

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 homoscedastic 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 NAs. 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.

Details

offset terms in model are an error since 3.1-157 (2022-03): previously they were silently ignored.

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)

José Pinheiro and Douglas Bates [e-mail]

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. (2002). 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. (2002) "Modern Applied Statistics with S", 4th 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())