This function fits a nonlinear model using generalized least squares. The errors are allowed to be correlated and/or have unequal variances.
gnls(model, data, params, start, correlation, weights, subset,
na.action, naPattern, control, verbose)
an object of class gnls, also inheriting from class gls,
representing the nonlinear model fit. Generic functions such as
print, plot and summary have methods to show the
results of the fit. See gnlsObject for the components of the
fit. The functions resid, coef, and fitted can be
used to extract some of its components.
a two-sided formula object describing the
model, with the response on the left of a ~ operator and
a nonlinear expression involving parameters and covariates on the
right. If data is given, all names used in the formula should
be defined as parameters or variables in the data frame.
an optional data frame containing the variables named in
model, correlation, weights,
subset, and naPattern. By default the variables are
taken from the environment from which gnls is called.
an optional two-sided linear formula of the form
p1+...+pn~x1+...+xm, or list of two-sided formulas of the form
p1~x1+...+xm, with possibly different models for each
parameter. The p1,...,pn represent parameters included on the
right hand side of model and x1+...+xm define a linear
model for the parameters (when the left hand side of the formula
contains several parameters, they are all assumed to follow the same
linear model described by the right hand side expression). A 1
on the right hand side of the formula(s) indicates a single fixed
effects for the corresponding parameter(s). By default, the
parameters are obtained from the names of start.
an optional named list, or numeric vector, with the
initial values for the parameters in model. It can be omitted
when a selfStarting function is used in model, in which
case the starting estimates will be obtained from a single call to the
nls function.
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.
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.
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 function that indicates what should happen when the
data contain NAs. The default action (na.fail) causes
gnls to print an error message and terminate if there are any
incomplete observations.
an expression or formula object, specifying which returned values are to be regarded as missing.
a list of control values for the estimation algorithm to
replace the default values returned by the function gnlsControl.
Defaults to an empty list.
an optional logical value. If TRUE information on
the evolution of the iterative algorithm is printed. Default is
FALSE.
José Pinheiro and Douglas Bates bates@stat.wisc.edu
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 Carrol, R.J. and Rupert,
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.
Carrol, R.J. and Rupert, 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. (2002) "Modern Applied Statistics with S", 4th Edition, Springer-Verlag.
Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer.
corClasses,
gnlsControl, gnlsObject,
gnlsStruct,
predict.gnls,
varClasses,
varFunc
# variance increases with a power of the absolute fitted values
fm1 <- gnls(weight ~ SSlogis(Time, Asym, xmid, scal), Soybean,
weights = varPower())
summary(fm1)
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