# gls

0th

Percentile

##### Fit Linear Model Using Generalized Least Squares

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

Keywords
models
##### Usage
gls(model, data, correlation, weights, subset, method, na.action,
control, verbose)
##### Arguments
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.
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,
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 do
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
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.
##### 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.

##### 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.

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

glsControl, glsObject, varFunc, corClasses, varClasses
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())