nlr (version 0.1-3)

nlsqr.gn: Generalized Least Square estimate.

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))).

Value

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

parameters

nonlinear regression parameter estimate of \(\theta\).

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.

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.

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

# NOT RUN {
## The function is currently defined as
"nlsqr.gn"
# }