gnls - R Documentation

`gnls` Fit Nonlinear Model Using Generalized Least Squares

Description

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

Usage

gnls(model, data, params, start, correlation, weights, subset,
     na.action, naPattern, control, verbose)

Arguments

`model`	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.
`data`	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.
`params`	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`.
`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.
`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.
`na.action`	a function that indicates what should happen when the data contain `NA`s. The default action (`na.fail`) causes `gnls` to print an error message and terminate if there are any incomplete observations.
`naPattern`	an expression or formula object, specifying which returned values are to be regarded as missing.
`control`	a list of control values for the estimation algorithm to replace the default values returned by the function `gnlsControl`. 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 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.

Author(s)

José Pinheiro and Douglas Bates [email protected]

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 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.

Examples

# variance increases with a power of the absolute fitted values
fm1 <- gnls(weight ~ SSlogis(Time, Asym, xmid, scal), Soybean,
            weights = varPower())
summary(fm1)

gnls Fit Nonlinear Model Using Generalized Least Squares