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

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

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.

- 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

`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.

José Pinheiro and Douglas Bates bates@stat.wisc.edu

`offset`

terms in `model`

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

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.

`corClasses`

,
`glsControl`

,
`glsObject`

,
`glsStruct`

,
`plot.gls`

,
`predict.gls`

,
`qqnorm.gls`

,
`residuals.gls`

,
`summary.gls`

,
`varClasses`

,
`varFunc`

```
# 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())
```

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