dfr.robhetro: Derivative free (RME)

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

(RME) for nonlinear regression with heteroscedastic variance, when the variance of error is general parameteric function of unkown parameters. Robust form of CME (See dfr.hetro).

Usage

dfr.robhetro(formula, data, start = getInitial(formula, data), control = nlr.control(
tolerance = 1e-05, minlanda = 1/2^10, maxiter = 100 * length(start)), robfunc, varmodel, 
tau = NULL, method = "NLM", ...)

Arguments

formula	nl.form object of the nonlinear function model.
data	list of data include responce and predictor.
start	list of parameter values of nonlinear model function (θ).
control	list of nlr.control for controling convergence criterions.
robfunc	nl.form object of robust function used for downgrading.
varmodel	nl.fomr object of variance function model for heteroscedastic variance.
tau	list of initial values for variance model function varmodel argument.
method	="NLM" means using nlmest.NLM function,or ="NM" means using derivative free nlmest.NM function
...	extra arguments to nonlinear regression model, heteroscedastic variance function, robust loss function or its tuning constants.

Details

In stage 1 the nonlinear model parameter estimates by robust MM-estimate, Stage 2 compute robust sample variance of data, Stage 3 estimate the parameter of variance function model by maximizing the robustified form of chi-square pseudo-likelihood function. Stage 4 estimate the final value of function model parameter by generalized robust MM-estimate.

Value

nl.fitt.rgn for heterogeneous and autocorrelated error (nonlinear fitt robust generalized) will return.

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.
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.
hetro	nl.fitt.rob object of fited variance odel: parametersestimate of variance parameter τ formnl.form object of called varmodel. predictorvariance model computed at estimated parameter, H(x;\hatτ) responsesample variance computed used as response variable. historymatrix of convergence history, collumns include: convergence index, parameters, minimized objective function, convergence criterion values, or other values. methodfittmethod object of method used for fitt. dataresponse (z_i) and predictor t variable values, used to computing the variance model. sourcefncObject of class "callorNULL" source function called for fitt. FaultFault object of error, if no error Fault number = 0 will return back. hthetarobust loss value including gradient and hessain attributes, for variance model. In fact is loglikelihood values. rhocomputed robust rho function, including gradient and hessain attributes.
others	$refvar reference variance. variance of zi's.

Note

Heteroscedastic variance can have several cases, this function assume variance is parameteric function of predictor (H(t;τ)). If data does not include the predictor variable of varmodel (t), the predicted of function model f(x;\hat θ) will replace for (t), otherwise user have to defin (t) or (x) as predictor variable of (H).

This function is derivative free form of nl.robhetro and robust form of dfr.hetro. Since it is slow algorithm it is recomneded to use larger values for maximum number of iterations in nlr.control options.

Author(s)

Hossein Riazoshams

References

Riazoshams, H,. 2010. Outlier detection and robust estimation methods for nonlinear regression having autocorrelated and heteroscedastic errors. PhD thesis disertation, University Putra Malaysia.

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

See Also

dfr.hetro, nlr.control, fittmethod, nl.form, nl.fitt.rob, nl.fitt.rgn, nlr.control

Examples

ntpstart=list(p1=.12,p2=6,p3=1,p4=33)
ntpstarttau=list(tau1=-.66,tau2=2,tau3=.04)
datalist=list(xr=ntp$dm.k,yr=ntp$cm.k)
rbhfitt <- dfr.robhetro(formula=nlrobj1[[16]],data=datalist,start=ntpstart,
robfunc=nl.robfuncs[["hampel"]],tau=ntpstarttau,varmodel=nlrobjvarmdls3[[2]],robscale=T,
method="NM",control=nlr.control(tolerance=1e-8))
rbhfitt$parameters

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