nlsqr.gn: Generalized Least Square estimate.

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

Generalized Least Square estimate of a nonlinear function, Using QR-decomposition of Gradient matrix.

Usage

nlsqr.gn(formula, data, start = getInitial(formula, data), 
control = nlr.control(tolerance = 0.001,
minlanda = 1/2^10, maxiter = 25 * length(start)), vm, rm = eiginv(t(chol(vm))))

Arguments

formula	nl.form object of the nonlinear function model. See nl.form object.
data	list of data with the response and predictor as name of variable.
start	list of starting value parameter, name of parameters must be represented as names of variable in the list.
control	nlr.control object, include tolerance, maxiter,... see nlr.control.
vm	Covariance matrix of residuals, used for nonlinear generalized M-estimate.
rm	optional correlation matrix, used for nonlinear generalized M-estimate. rm is correlation matrix of vm, thus only vm is enough to be given. It can be given by user also but not necessary automatically will be calculated by argument eiginv(t(chol(vm))).

Details

It is used to minimize the square loss function, using QR-decomposition of gradient matrix, thus the nonlinear function model formula must return back Gradient. nlsqr.gn work with a general variance covariance matrix, such as heteroscedastic or weights in variance, and partially autocorrelated with any general format.

Value

result is object of nl.fitt.gn for generalized fitt when covariance or correlation matrix is given.

parameters	nonlinear regression parameter estimate of θ.
correlation	of fited model.
form	nl.form object of called nonlinear regression model.
response	computed response.
predictor	computed (right side of formula) at estimated parameter with gradient and hessian attributes.
curvature	list of curvatures, see curvature function.
history	matrix of convergence history, collumns include: convergence index, parameters, minimized objective function, convergence criterion values, or other values. These values will be used in plot function in ploting history.
method	fittmethod object of method used for fitt.
data	list of called data.
sourcefnc	Object of class "callorNULL" source function called for fitt.
Fault	Fault object of error, if no error Fault number = 0 will return back.
vm	covariance matrix, diagonal of variance model predicted values.
rm	cholesky decomposition of vm.
gresponse	transformed of response by rm, include gradinet and hessian attributes.
gpredictor	transformed of predictor by rm, include gradinet and hessian attributes.

Note

This is a generalized form of nlsqr function. It is fast algorithm based on gradient. If gradient does not exist one can use nlsnm function.

This function call by nlr, for compatibility it is better to call from nlr rather than directly by user.

Author(s)

Hossein Riazoshams, Jan 2010. Email: [e-mail] URL http://www.riazoshams.com/nlr/

References

Seber, G., A. F. and Wild, C. J. (2003). Nonlinear Regression. New York: John Wiley & Sons, Inc.

See Also

nl.form, nlsnm, nlr.control, nl.fitt, curvature, Fault,nlsqr

Examples

## The function is currently defined as
"nlsqr.gn"

nlr documentation built on July 31, 2019, 5:09 p.m.