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#******************************************************************************
#* +------------------------------------------------------------------------+ *
#* | Function 'nl.rhetro', MM robust estimate of a nonlinear function. | *
#* | with hetro variance model function. | *
#* | generalized | *
#* | Note: becarefull to using this function when there is not outlier, it | *
#* | may not work witout outlier, in this case better to use nlmest | *
#* | the problem is in part of two (p2) in hessian its big here. | *
#* | argumnts: | *
#* | formula: 'nl.form' object, the function mode. | *
#* | data: data, contains dependents and independents, | *
#* | data.frame, list or named matrix it can be. | *
#* | start: starting values, it must contains 'sigma', selstart | *
#* | for nl.form object is not created yet, take cre of it. | *
#* | varmodel: var function, it must be nl.form of variance models | *
#* | tau: starting value of tau. if is null the stored value in | *
#* | vardnc object of nl.form will be stored. | *
#* | ...: can be entries for robust loss function parameters. | *
#* | Method: is to control when error happens and need control | *
#* | manually, program try to control errors but other | *
#* | un predicted error like log(0) may happens. | *
#* | | *
#* | Important Note: variance must be a product function in sigma, i.e. | *
#* | varfunc = sigma^2 * h(f,tau) | *
#* | in feature the general form will be added. | *
#* +------------------------------------------------------------------------+ *
#******************************************************************************
nl.robhetroLS <- function(formula, data, start=getInitial(formula,data),
control=nlr.control(tolerance=0.00001, minlanda=1 / 2 ^ 10, maxiter=30 * length(start),robscale=T),robfunc,varmodel,
tau=varmodel$par,...){
tolerance <- control$tolerance
maxiter <- control$maxiter
minlanda <- control$minlanda
trace <- control$trace
stage1 <- nlmest.NLM(formula, data=data, start=start,robfunc=robfunc,control=control,...)
if(is.Fault(stage1)) return(stage1)
if(control$trace) print(stage1$parameters)
t <- predict(stage1,newdata=data)
ri <- residuals(stage1)
n <- length(ri)
nrp <- nonrepl(list(x=data[[formula$independent]],y=data[[formula$dependent]]))
fdata <- NULL
fdata[[formula$independent]] <- nrp$x[nrp$xm]
fdata[[formula$dependent]] <- nrp$y[nrp$xm]
z <- rzvalues(ri,nrp$ni,nrp$xo)#[nrp$xm] # variance z=zi , si^2 #
vdata<-as.list(NULL)
vdata[[varmodel$dependent]] = z[nrp$xm]
if(is.null(data[[varmodel$independent]]))
vdata[[varmodel$independent]] <- predict(stage1,newdata=fdata) # non replicated #
else
vdata[[varmodel$independent]] <- data[[varmodel$independent]][nrp$xm] # non replicated #
wi <- pmax(1,nrp$ni-1)
vm <- diag(wi)
rm <- diag(1.0/sqrt(wi))
###################################### step 1 iteration 1 ############
startv <- tau
data2 <-c(vdata,tau)
varcomp <- eval(varmodel,data2)
g <- 2.0 * as.numeric(varcomp$predictor)^2 / wi / tau$sg^2 ### then v(Rzi)=sg^2
vm <- diag(g)
rm <- diag(1.0/sqrt(g))
# print("start stage 2---1--===============================================================")
stage2 <- nlmest.WF(varmodel, data=vdata, start=tau,control=nlr.control(tolerance=tolerance, minlanda=minlanda, maxiter=5*maxiter,trace=trace,robscale=control$robscale),robfunc=robfunc,vm=vm,rm=rm,...)
if(is.Faultwarn(stage2) || stage2$parameters$sg<0){
# print("error in first try stage2..1... will try new initial value nl.robhetroLS")
start.tau <- getInitial(varmodel,vdata)
stage2 <- nlmest.NLM(varmodel, data=vdata, start=tau,control=nlr.control(tolerance=tolerance, minlanda=minlanda, maxiter=5*maxiter,trace=trace,robscale=control$robscale),robfunc=robfunc,vm=vm,rm=rm,...)
if(is.Fault(stage2)) return(stage2)
}
if(control$trace) print(stage2$parameters)
###################################### step 2 iteration 2#############
# print("second iteration step 2-2...............................................")
startv <- stage2$parameters[names(varmodel$par)]
data2 <-c(vdata,startv)
varcomp <- eval(varmodel,data2)
g <- 2.0 * as.numeric(varcomp$predictor)^2 / wi / startv$sg^2
vm <- diag(g)
rm <- diag(1.0/sqrt(g))
stage2 <- nlmest.WF(varmodel, data=vdata, start=startv,control=nlr.control(tolerance=tolerance*5, minlanda=minlanda, maxiter=5*maxiter,trace=trace,robscale=control$robscale),robfunc=robfunc,vm=vm,rm=rm,...)
if(is.Fault(stage2) || stage2$parameters$sg<0){
print("error in first try stage2..2... will try new initial value nl.robhetroLS")
stage2 <- nlmest.NLM(varmodel, data=vdata, start=startv,control=nlr.control(tolerance=tolerance*5, minlanda=minlanda, maxiter=5*maxiter,trace=trace,robscale=control$robscale),robfunc=robfunc,vm=vm,rm=rm,...)
if(is.Fault(stage2)) return(stage2)
}
if(control$trace) print(stage2$parameters)
############################################ stage 3
ps <- stage1$parameters[names(formula$par)]
vcn <- predict(stage2,newdata=vdata)
vc <- rep(0,n)
for (i in nrp$xo){
vc[nrp$xo==i]=vcn[i]
}
g <- (vc/stage2$parameters$sg^2)
vmat <- diag(g)
umat <- diag(sqrt(g))
tumat <- t(umat)
rmat <- diag(1.0 / diag(tumat)) #eiginv(tumat,stp=F)
if(is.Fault(rmat)) return(rmat)
stage3 <- nlmest.NLM(formula, data=data, start=ps,control=nlr.control(maxiter=5*maxiter,tolerance=tolerance*10,minlanda=minlanda/10,trace=trace,robscale=control$robscale),vm=vmat,rm=rmat,robfunc=robfunc,...)
if(is.Faultwarn(stage3)){
# if(! is.Fault(stage3)) #ps<-stage3$parameters[names(formula$par)]
print("Warning: stage 3 not converged, will try another method WF")
stage32 <- nlmest.WF(formula, data=data, start=ps,control=nlr.control(tolerance=tolerance*10,minlanda=minlanda/10, maxiter=maxiter*5,trace=trace,robscale=control$robscale),vm=vmat,rm=rmat,robfunc=robfunc,...)
if(is.Faultwarn(stage32)){
if(! is.Fault(stage32)) ps<-stage32$parameters[names(formula$par)]
else ps <- start
stage3 <- nlmest.NLM(formula, data=data, start=start,
control=nlr.control(tolerance=tolerance*20, minlanda=minlanda, maxiter=maxiter,trace=trace,robscale=control$robscale),vm=vmat,rm=rmat,robfunc=robfunc,...)
if(is.Fault(stage3) & (! is.Fault(stage32))) stage3<-stage32
}
else stage3 <- stage32
}
result <- stage3
if(is.Fault(stage3)) return(stage3)
result@method@methodID <- 2
result@method@subroutine <- "nl.robhetroLS"
nvdata<-as.list(NULL)
nvdata[[varmodel$independent]]<-vdata[[varmodel$independent]][nrp$xo]
nvdata[[varmodel$dependent]]<-vdata[[varmodel$dependent]][nrp$xo]
result@hetro<-nl.fitt.rob(
parameters= stage2$parameters,
form= varmodel,
predictor = stage2$predictor,
response = stage2$response,
history = stage2$history,
method = stage2$method,
data = nvdata,
sourcefnc = stage2$sourcefnc,
Fault = Fault(),
others = list(refvar=stage2$others$refvar),
htheta = stage2$htheta,
rho = stage2$rho)
return(result)
}
#+#################################################################################+
#| |
#| End of the object 'nl.robhetro' |
#| |
#| Nov 2009 |
#| |
#| Hossein Riazoshams, UPM, INSPEM |
#| |
#+#################################################################################+
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