nl.robhetroLS: Robust Generalized Multistage Estimate (RGME).
In nlr: Nonlinear Regression Modelling using Robust Methods

Description Usage Arguments Details Value Note Author(s) References See Also Examples

(RGME) for heteroscedastic error case, robust form of CLsME (See nl.hetroLS)

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  nl.robhetroLS(formula, data, start = getInitial(formula, data), 
  control = nlr.control(tolerance = 1e-05, minlanda = 1/2^10, 
  maxiter = 30 * length(start), robscale = T), robfunc, varmodel, tau = varmodel$par, ...)

`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.

Robustified form of Least square based estimate for nonlinear regression with hetroscedastic error when variance is a general function of unkown parameters.

return object nl.fitt.rgn for nonlinear regression wuth 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.
`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 form`nl.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. method`fittmethod` 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. Fault`Fault` 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.

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

Hossein Riazoshams, May 2014. Email: riazihosein@gmail.com URL http://www.riazoshams.com/nlr/

Riazoshams, H. (2012), Robustifying the Least Squares estimate of parameters of variance model function in nonlinear regression with heteroscedastic variance, Poster Presentation, Royal Statistical Society Conference (RSS) 2012, Telford, UK.

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