nl.robhetroWM: Weighted M-estimate.

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

Weighted M-estimate is robustified form of MLE, for nonlinear regression with heteroscedastic error, when variance is parameteric fucntion form. Both nonliner regression model parameter and variance function parameters compute simultanously by minizing the robustified objective function form.

Usage

nl.robhetroWM(formula, data, start = getInitial(formula, data), 
control = nlr.control(tolerance = 1e-04, minlanda = 1/2^10, 
maxiter = 50 * length(start), derivfree = T), robfunc, varmodel, tau = varmodel$par, ...)

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. in f(x,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.
...	extra arguments to nonlinear regression model, heteroscedastic variance function, robust loss function or its tuning constants.

Details

For minimizing the objective function simultaneously for theta and tau, derivative free method Nelder-Mead is used.

Value

return object nl.fitt.rgn for nonlienar regression with heterogeneous error.

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.
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 likelihood value including gradient and hessain attributes.
rho	computed robust rho function, including gradient and hessain attributes.
ri	estimated residuals, including gradient and hessain attributes.
robform	nl.form object of robust loss rho function.
vm	covariance matrix, diagonal of variance model predicted values.
rm	cholesky decomposition of vm.
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.
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).

Author(s)

Lim, C., Sen, P. K., Peddada, S. D.

References

Lim, C., Sen, P. K., Peddada, S. D. (2010). Statistical inference in nonlinear regression under heteroscedasticity. Sankhya B 72:202-218.

See Also

fittmethod, nl.form, nl.fitt.rob, nl.fitt.rgn

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)
datalist[[nlrobjvarmdls3[[2]]$independent]]<-ntp$dm.k
# ntp data fitt
# tolerance is set as 1e-3 for testing purposes
# is not accurate enough, user can increase it.
bb1 <- nl.robhetroWM(formula=nlrobj1[[15]],data=datalist,
start=ntpstart,robfunc=nl.robfuncs[["least square"]],
tau=ntpstarttau,varmodel=nlrobjvarmdls3[[2]],control=nlr.control(tolerance=1e-3,maxiter=1500))
bb1$parameters
#---------------- hampel -----------------
aa1 <- nl.robhetroWM(formula=nlrobj1[[15]],data=datalist,start=ntpstart,
robfunc=nl.robfuncs[["hampel"]],derivfree=T,
tau=ntpstarttau,varmodel=nlrobjvarmdls3[[2]],
control=nlr.control(tolerance=1e-3,maxiter=1500))#,delta=c(0.2,1,1,160,.2,1,.03))
aa1$parameters

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