nlmest.NLM: Nonlinear MM-estimate.

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

MM-estimate of a nonlinear function, Using Mixture of Newton and Levenberg-Marquardt method. Parameters estimates by robust MM-estimate by minimizing the sum of robust rho function.

Usage

nlmest.NLM(formula, data, start = getInitial(formula, data), robfunc, 
control = nlr.control(tolerance = 1e-04, 
minlanda = 1/2^25, maxiter = 25 * length(start)), vm = NULL, rm = NULL, ...)

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. In heterogeneous case if it include response variable values of heterogenous variance function it asume variance function is function of predictor H(x_i,τ), otherwise it assume is a function of predictor H(f(x_i,θ),τ).
start	list of starting value parameter, name of parameters must be represented as names of variable in the list.
robfunc	nl.form object of robust function used for downgrading.
control	nlr.control object, include tolerance, maxiter,... see nlr.control.
vm	optional 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))).
...	any other argument passed to formula, robfnc, or optimization function.

Details

This function is mixture of Levenberg Marquardt, Newton and Steepest descent, is derivative base optimization method. It is used to minimize the robust loss function using ρ function. This method is very fast and used for when the gradient of colaborating functions exists.

Due to wrong effect of outlier in creating singularity in hessian matrix the levenberg Marquardt is used to remedy the effect. Morover for fast convergence when hessian is non singular Newton with Steepest descent is applied.

Value

result is object of nl.fitt.rob (nonlinear fitt robust) for homogeneous variance, and nl.fitt.rgn for heterogeneous and autocorrelated error (nonlinear fitt robust generalized), see nl.fitt.rgn object detail.

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.
htheta	robust loss value including gradient and hessain attributes.
rho	computed robust rho function, including gradient and hessain attributes.
ri	estimated residuals, including gradient and hessain attributes.
curvrob	curvature
robform	nl.form object of robust loss rho function.

if vm is not NULL the nl.fitt.rgn include following extra slots:

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

starting values start it must contains initial value for 'sigma'.

nlr package for estimating robust MM, try to acheive the optimization convergence using nlmest.NLM or nlmest.WF or nlmest.LM, either of them that does not attain convergence other method might be used.

nlmest.NLM.sCase2 compute singularity case as optim.NLM optimization. Can be computed this case by using singularCase=2 argument in nlr.control.

nlmest.NLMf Compute the procedure with fixed scale value, the result is not MM-estimate.

This function is called from nlr, for compatibility it is more efficient to be called by nlr than callind directly.

Author(s)

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

References

Riazoshams H, Midi H, and Ghilagaber G, 2018,. Robust Nonlinear Regression, with Application using R, Joh Wiley and Sons.

See Also

nlmest.LM, nlmest.WF, nl.form, nl.fitt.rob, nl.fitt.rgn, nlr.control

Examples

# functioned defined as 
"nlmest.NLM"

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