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
summary have methods to show the results of the fit. See
glsObject for the components of the fit. The functions
an object inheriting from class
a generalized least squares fitted linear 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.
Changes to the model -- see
an optional data frame containing the variables named in
subset. By default the variables are taken from the
environment from which
gls is called.
corStruct object describing the
within-group correlation structure. See the documentation of
corClasses for a description of the available
classes. If a grouping variable is to be used, it must be specified in
form argument to the
constructor. Defaults to
NULL, corresponding to uncorrelated
varFunc object or one-sided formula
describing the within-group heteroscedasticity structure. If given as
a formula, it is used as the argument to
corresponding to fixed variance weights. See the documentation on
varClasses for a description of the available
classes. Defaults to
NULL, corresponding to homoscedastic
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.
a character string. If
"REML" the model is fit by
maximizing the restricted log-likelihood. If
log-likelihood is maximized. Defaults to
a function that indicates what should happen when the
NAs. The default action (
gls to print an error message and terminate if there are any
a list of control values for the estimation algorithm to
replace the default values returned by the function
Defaults to an empty list.
an optional logical value. If
TRUE information on
the evolution of the iterative algorithm is printed. Default is
some methods for this generic require additional arguments. None are used in this method.
TRUE evaluate the new call else return the call.
José Pinheiro and Douglas Bates email@example.com
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.
# 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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