R/fit.R

In VFP: Variance Function Program

# TODO: Add comment
# 
# Author: schueta6
###############################################################################



#' Internal Function Model 2.
#' @param x		(numeric) parameter

powfun2simple <- function(x) 
{
	list(
			predictors=list(beta1 = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( predictors[1],"*",variables[1],"^2")
			}
	)
}
class(powfun2simple) <- "nonlin"

#' Internal Function Model 3.
#' @param x		(numeric) parameter

powfun3 <- function(x)
{
	cutval 	<- 0.95
	xmax	<- max(x)
	list(
			predictors=list(beta1 = 1, beta2 = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( "exp(",predictors[1],")*(1+(exp(",predictors[2],")-",cutval,")*",variables[1],"/",xmax,")")
			}
	)
}
class(powfun3) <- "nonlin"

#' Internal Function Model 3.
#' @param x		(numeric) parameter

powfun3simple <- function(x)
{
	cutval <- 0.95
	list(
			predictors=list(beta1 = 1, beta2 = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( predictors[1],"+",predictors[2],"*",variables[1],"^2")
			}
	)
}
class(powfun3simple) <- "nonlin"



#' Internal Function Model 4.
#' @param x			(numeric) parameter 1
#' @param potenz	(numeric) parameter 2

powfun4 <- function(x, potenz)
{
	cutval 	<- 0.95
	xmax	<- max(x)
	list(
			predictors=list(beta1 = 1, beta2 = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( "exp(",predictors[1],")*(1+(exp(",predictors[2],")-",cutval,")*",variables[1],"/",xmax,")^",potenz)
			}
	)
}
class(powfun4) <- "nonlin"


#' Internal Function Model 4.
#' @param x			(numeric) parameter 1
#' @param potenz	(numeric) parameter 2

powfun4simple <- function(x, potenz)
{
	list(
			predictors=list(beta1 = 1, beta2 = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( "(",predictors[1],"+",predictors[2],"*",variables[1],")^",potenz)
			}
	)
}
class(powfun4simple) <- "nonlin"


#' Internal Function Model 5.
#' @param x			(numeric) parameter 1

powfun5 <- function(x)
{
	cutval 	<- 0.95
	xmax	<- max(x)	
	
	list(
			predictors=list(beta1 = 1, beta2 = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( "exp(",predictors[1],")*(1+(exp(",predictors[2],")-",cutval,")*",variables[1],"/",xmax,")")
			}
	)
}
class(powfun5) <- "nonlin"

#' Internal Function Model 5.
#' @param x		(numeric) parameter 1
#' @param K		(numeric) parameter 2

powfun5simple <- function(x,K)
{
	list(
			predictors=list(beta1 = 1, beta2 = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( predictors[1],"+",predictors[2],"*",variables[1],"^", K)
			}
	)
}
class(powfun5simple) <- "nonlin"


#' Internal Function Model 6.
#' @param x			(numeric) parameter 1

powfun6 <- function(x)
{
	list(
			predictors=list(beta1 = 1, beta2 = 1,beta3=1, pot = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( "exp(",predictors[1],")*(1+(atan(",predictors[2],")/pi-0.5)*",variables[1],
						"*exp(",predictors[3],")*(1+exp(",predictors[4],")-(",variables[1],"*exp(",predictors[3],
						"))^exp(",predictors[4],"))/exp(",predictors[4],"))")
			}
	)
}
class(powfun6) <- "nonlin"

#' Internal Function Model 6.
#' @param x			(numeric) parameter 1

powfun6simple <- function(x)
{
	list(
			predictors=list(beta1 = 1, beta2 = 1,beta3=1, pot = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( predictors[1],"+",predictors[2],"*",variables[1],"+",predictors[3],"*",variables[1],"^",predictors[4])
			}
	)
}
class(powfun6simple) <- "nonlin"


#' Internal Function Model 7.
#' @param x			(numeric) parameter 1

powfun7 <- function(x)
{
	cutval <- 0.95
	xmax	<- max(x)
	
	list(
			predictors=list(beta = 1, beta2=1, pot = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( "exp(",predictors[1],")*(1+(exp(",predictors[2],")-",cutval,")*(",variables[1],"/",xmax,")^((0.1+10*exp(",predictors[3],"))/(1+exp(",predictors[3],"))))")
			}
	)
}
class(powfun7) <- "nonlin"


#' Internal Function Model 7.
#' @param x			(numeric) parameter 1

powfun7simple <- function(x)
{
	list(
			predictors=list(beta = 1, beta2=1, pot = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( predictors[1],"+",predictors[2],"*",variables[1],"^",predictors[3])
			}
	)
}
class(powfun7simple) <- "nonlin"


#' Internal Function Model 8.
#' @param x			(numeric) parameter 1
#' @param C			(numeric) parameter 2
#' @param signJ		(numeric) parameter 3

powfun8 <- function(x, C,signJ)
{
	cutval <- 0.95
	
	list(
			predictors=list(beta1 = 1, beta2 = 1, beta3 = 1), 
			variables=list(substitute(x/C)),
			term=function(predictors,variables){
				paste( "exp(",predictors[1],")*(1+(exp(",predictors[2],")-",cutval,")*",variables[1],")^(",signJ,"*(0.1+10*exp(",predictors[3],"))/(1+exp(",predictors[3],")))")
			}
	)
}
class(powfun8) <- "nonlin"


#' Internal Function Model 8.
#' @param x			(numeric) parameter 1

powfun8simple <- function(x)
{
	list(
			predictors=list(beta1 = 1, beta2 = 1, pot = 1), 
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( "(",predictors[1],"+",predictors[2],"*",variables[1],")^",predictors[3],sep=" ")
			}
	)
}
class(powfun8simple) <- "nonlin"

#' Internal Function Model 9.
#' @param x			(numeric) parameter 1

powfun9simple <- function(x)
{
	list(
			predictors=list(beta1 = 1,  pot = 1),
			variables=list(substitute(x)),
			term=function(predictors,variables){
				paste( predictors[1],"*",variables[1],"^",predictors[2],sep=" ")
			}
	)
}
class(powfun9simple) <- "nonlin"



#' Estimate (Im)Precision-Profiles Modeling the Relationship 'Var ~ Mean'.
#' 
#' This function fits one out of ten or any subset of ten non-linear functions at once. This is done on 
#' precision data consisting of information about the variance, concentration at which this variance
#' was observed and the respective degrees of freedom. Provided data must contain at least three columns with
#' this information. There are following variance-functions covered: \cr
#' \itemize{
#'	 \item{constant variance}{ \eqn{sigma^2}}
#'	 \item{constant CV}{\eqn{ sigma^2=beta_1*u^2 }}
#'	 \item{mixed constant, proportional variance}{ \eqn{sigma^2=beta_1+beta_2*u^2}}
#'	 \item{constrained power model, constant exponent}{ \eqn{sigma^2=(beta_1+beta_2*u)^K}}
#'	 \item{alternative constrained power model}{ \eqn{sigma^2=beta_1+beta_2*u^K}}
#'	 \item{alternative unconstrained power model for VF's with a minimum}{ \eqn{sigma^2=beta_1+beta_2*u+beta_3*u^J}}
#'	 \item{alternative unconstrained power model}{ \eqn{sigma^2=beta_1+beta_2*u^J}}
#'	 \item{unconstrained power model (default model of Sadler)}{ \eqn{sigma^2=(beta_1 + beta_2 * u)^J}}
#' 	 \item{CLSI EP17 similar model}{ \eqn{sigma^2=beta_1 * u^J}}
#'	 \item{Exact CLSI EP17 model (fit by linear regression on logarithmic scale)}{ \eqn{cv=beta_1 * u^J}}
#' }
#' Fitting all ten models is somehow redundant if constant 'C' is chosen to be equal to 2, since models 3 and 5 are
#' equivalent and these are constrained versions of model 7 where the exponent is also estimated. The latter also applies to model
#' 4 which is a constrained version of model 8. Note that model 10 fits the same predictor function as model 9 using simple linear 
#' regression on a logarithmic scale. Therefore, regression statistics like AIC, deviance etc. is not directly comparable 
#'to that of models 1 to 9.  Despite these possible redundancies, as computation time is not critical here for typical
#' precision-profiles (of in-vitro diagnostics precision experiments) we chose to offer batch-processing as well.
#' During computation, all models are internally reparameterized so as to guarantee that the variance function is positive in the
#' range 'u' from 0 to 'u_max'. In models 7 and 8, 'J' is restricted to 0.1<J<10 to avoid the appearance of sharp hooks. 
#' Occasionally, these restrictions may lead to a failure of convergence. This is then a sign that the model parameters
#' are on the boundary and that the model fits the data very badly. This should not be taken as reason for concern. 
#' It occurs frequently for model 6 when the variance function has no minimum, which is normally the case. 
#' 
#' Functions \code{\link{predict.VFP}} and \code{\link{predictMean}} are useful to make inference based on a fitted model.
#' It is possible to derive concentrations at which a predefined variability is reached, which is sometimes referred to as
#' "functional sensitivity" and/or "limit of quantitation" (LoQ). Funtion \code{\link{predictMean}} returns the fitted value
#' at which a user-defined variance ("vc"), SD or CV is reached with its corresponding 100(1-alpha)\% CI derived from the CI of
#' the fitted model. The plotting method for objects of class 'VFP' can automatically add this information to a plot using 
#' arguments 'Prediction' and 'Pred.CI' (see \code{\link{plot.VFP}} for details. Function \code{\link{predict.VFP}} makes 
#' predictions for specified mean-values based on fitted models.  
#' 
#' Note, that in cases where a valid solution was found in the re-parameterized space but the final fit with 'gnm' in the
#' original parameter-space did not converge no variance-covariance matrix can be estimated. Therefore, no confidence-intervals
#' will be available downstream.
#' 
#' @param Data			(data.frame, matrix) containing mean-values, estimated variances and degrees of freedom for each sample
#' @param model.no		(integer) in 1:10, may be any combination of these integer-values specifying models 1 to 10 which
#' 						are consequently fitted to the data;  defaults to 7
#' @param K				(numeric) value defining the constant used in models 4 and 5; defaults to 2
#' @param startvals		(numeric) vector of start values for the optimization algorithm, only used if a single model
#' 						is specified by the user, otherwise, start values will be sought automatically
#' @param quiet			(logical) TRUE = all output messages (warnings, errors) and regular console output is suppressed and can
#' 						be found in elements "stderr" and "stdout" of the returned object
#' @param col.mean		(character) string specifying a column/variable in 'Data' containing mean-values; defaults to "Mean"
#' @param col.var		(character) string specifying a column/variable in 'Data' containing the variances; Defaults to "VC"
#' @param col.df		(character) string specifying a column/variable in 'Data' containing the degrees of freedom; defaults to "DF"
#' @param col.sd		(character) string (optional) specifying a column/variable in 'Data' containing the SD-values,
#' 						used for model 10 to derive more precise CV-values compared to derivation from 'col.var' in case
#' 						'col.cv' is not specified directly. Note that column "col.var" must nevertheless be set and existing
#' @param col.cv		(character) string (optional) specifying a column/variable in 'Data' containing the CV-values,
#' 						if missing, first 'col.sd' is checked, if missing 'col.var' used to derive per-sample CV-values. 
#'                      Note that column "col.var" must nevertheless be set and existing
#' @param minVC			(numeric) value assigned to variances being equal to zero, defaults to NA, which results in removing
#' 						these observations; could also be set to the smallest possible positive double (\code{.Machine$double.eps}) 
#' @param ...			additional parameters passed forward, e.g. 'vc' of function \code{\link{getMat.VCA}} for selecting a 
#' 						specific variance component in case of 'Data' being a list of 'VCA'-objects (see examples)
#' 
#' @return (object) of class 'VFP' with elements:\cr
#' \item{Models}{objects of class 'gnm' representing the fitted model}
#' \item{RSS}{residual sum of squares for each fitted model}
#' \item{AIC}{the Akaike information criterion for each fitted model}
#' \item{Deviance}{the deviance for each fitted model}
#' \item{Formulas}{formula(s) as expression for each fitted model}
#' \item{Mu.Func}{function(s) to transform mean value to re-parameterized scale}
#' \item{Mu}{list of transformed mean values}
#' \item{Data}{the original data set provided to fit model(s)}
#' \item{K}{constant as specified by the user}
#' \item{startvals}{start values as specified by the user}
#' \item{errors}{messages of all errors caught}
#' \item{output}{if 'quiet=TRUE' all output that was redirected to a file}
#' \item{warning}{messages of all warnings caught}
#' \item{notes}{all other notes caught during execution}
#' 
#' @author 	Florian Dufey \email{florian.dufey@@roche.com}, 
#' 			Andre Schuetzenmeister \email{andre.schuetzenmeister@@roche.com}
#' 
#' @seealso \code{\link{plot.VFP}}, \code{\link{predict.VFP}}, \code{\link{predictMean}}
#' 
#' @examples 
#' \donttest{
#' # load VCA-package and data
#' library(VCA)
#' data(VCAdata1)
#' # perform VCA-anaylsis
#' lst <- anovaVCA(y~(device+lot)/day/run, VCAdata1, by="sample")
#' # transform list of VCA-objects into required matrix
#' mat <- getMat.VCA(lst)		# automatically selects "total"
#' mat
#' 
#' # fit all 9 models batch-wise
#' res <- fit.vfp(model.no=1:10, Data=mat)
#' 
#' # if 'mat' is not required for later usage, following works
#' # equally well
#' res2 <- fit.vfp(lst, 1:10)
#' 
#' # plot best-fitting model
#' plot(res)
#' plot(res, type="cv")
#' plot(res, type="cv", ci.type="lines", ci.col="red",
#' 		Grid=list(col="wheat"), Points=list(pch=2, lwd=2, col="black"))
#' 
#' # now derive concentation at which a specific reproducibility-
#' # imprecision of 10\% is reached and add this to the plot
#' pred <- plot(res, type="cv", ci.type="band", 
#' 				ci.col=as.rgb("red", .25), Grid=list(col="orange"), 
#' 				Points=list(pch=2, lwd=2, col="black"),
#' 				Prediction=list(y=10, col="red"), Pred.CI=TRUE)
#' 
#' # (invisibly) returned object contains all relevant information
#' pred
#' 
#' # same for repeatability
#' mat.err <- getMat.VCA(lst, "error")
#' res.err <- fit.vfp(1:10, Data=mat.err)
#' 
#' # without extracting 'mat.err'
#' res.err2 <- fit.vfp(lst, 1:10, vc="error")
#' 
#' plot(res.err)
#' 
#' #######################################################################
#' # another example using CA19_9 data from CLSI EP05-A3
#' 
#' data(CA19_9)
#' 
#' # fit reproducibility model to data
#' fits.CA19_9 <- anovaVCA(result~site/day, CA19_9, by="sample")
#' 
#' # fit within-laboratory-model treating site as fixed effect
#' fits.ip.CA19_9 <- anovaMM(result~site/(day), CA19_9, by="sample")
#' 
#' # the variability "between-site" is not part of "total"
#' fits.ip.CA19_9[[1]]
#' fits.CA19_9[[1]]
#' 
#' # extract repeatability
#' rep.CA19_9 <- getMat.VCA(fits.CA19_9, "error")
#' 
#' # extract reproducibility
#' repro.CA19_9 <- getMat.VCA(fits.CA19_9, "total")
#' 
#' # extract intermediate-precision (within-lab)
#' ip.CA19_9 <- getMat.VCA(fits.ip.CA19_9, "total")
#' 
#' # fit model (a+bX)^C (model 8) to all three matrices
#' 
#' mod8.repro 	<- fit.vfp(repro.CA19_9, 8)
#' mod8.ip		<- fit.vfp(ip.CA19_9, 8)
#' mod8.rep		<- fit.vfp(rep.CA19_9, 8)
#' 
#' # plot reproducibility precision profile first
#' # leave enough space in right margin for a legend
#' plot(mod8.repro, mar=c(5.1, 7, 4.1, 15), 
#' 		type="cv", ci.type="none", Model=FALSE,
#' 		Line=list(col="blue", lwd=3), 
#' 		Points=list(pch=15, col="blue", cex=1.5),  
#' 		xlim=c(10, 450), ylim=c(0,10),
#' 		Xlabel=list(text="CA19-9, kU/L (LogScale) - 3 Patient Pools, 3 QC Materials",
#' 				cex=1.5), Title=NULL,
#' 		Ylabel=list(text="% CV", cex=1.5),
#' 		Grid=NULL, Crit=NULL, log="x")
#' 
#' # add intermediate precision profile
#' plot	(mod8.ip, type="cv", add=TRUE, ci.type="none",
#' 		Points=list(pch=16, col="deepskyblue", cex=1.5),
#' 		Line=list(col="deepskyblue", lwd=3), log="x")
#' 
#' # add repeatability precision profile
#' plot(	mod8.rep, type="cv", add=TRUE, ci.type="none",
#' 		Points=list(pch=17, col="darkorchid3", cex=1.5),
#' 		Line=list(col="darkorchid3", lwd=3), log="x")
#' 
#' # add legend to right margin
#' legend.rm( x="center", pch=15:17, col=c("blue", "deepskyblue", "darkorchid3"),
#' 		cex=1.5, legend=c("Reproducibility", "Within-Lab Precision", "Repeatability"),
#' 		box.lty=0)
#' #' }


fit.vfp <- function(Data, model.no = 7, K=2, startvals=NULL, quiet=T, 
		col.mean="Mean", col.var="VC", col.df="DF", 
		col.sd=NULL, col.cv=NULL, minVC=NA, ...) #.Machine$double.eps, ...)
{
	
	Call <- match.call()
	stopifnot(model.no %in% 1:10)
	stopifnot(K>0)
	stopifnot(is.data.frame(Data) || is.matrix(Data) || is(Data, "list") && all(sapply(Data, class) == "VCA"))
	if(is(Data, "list") && all(sapply(Data, class) == "VCA"))
		Data <- getMat.VCA(Data, ...)
	if(is.matrix(Data))
		Data <- as.data.frame(Data)
	
	cn	<- colnames(Data)
	stopifnot(all(c(col.mean, col.var, col.df) %in% cn))
	
	stopifnot(is.numeric(Data[,col.mean]))
	stopifnot(is.numeric(Data[,col.var]))
	stopifnot(is.numeric(Data[,col.df]))
	stopifnot(is.null(col.sd) || is.character(col.sd) && is.numeric(Data[,col.sd]))
	stopifnot(is.null(col.cv) || is.character(col.cv) && is.numeric(Data[,col.cv]))
	
	Data[,col.mean]	<- as.numeric(Data[,col.mean])
	Data[,col.var]  <- as.numeric(Data[,col.var]) 
	Data[,col.df]   <- as.numeric(Data[,col.df])  
	
	ind.NegVC <- which(Data[,col.var] <= 0)
	
	if(length(ind.NegVC) > 0)
	{
		message("Variance(s) <= 0 detected! This/these will be set to 'minVC'!")
		Data[ind.NegVC,col.var] <- minVC
	}
	
	if(!is.null(col.sd))
	{
		Data[,col.sd] <- as.numeric(Data[,col.sd])
		colnames(Data)[which(cn == col.sd)] <- "SD"
	}
	if(!is.null(col.cv))
	{
		Data[,col.cv] <- as.numeric(Data[,col.cv])
		colnames(Data)[which(cn == col.cv)] <- "CV"	
	}
	
	if(quiet)
	{
		file.create("./stdout.log")
	}
	
	errors <- warnings <- messages <- notes <- NULL
	
	skip5 <- FALSE
	if(all(c(3,5) %in% model.no) && K==2)
	{
		skip5 <- TRUE								# models 3 and 5 are identical in case K=2
		if(!quiet)
			message("Model 5 will not be fitted because it is identical to model 3 with 'K=2'!")
		notes <- c(notes, "Model 5 will not be fitted because it is identical to model 3 with 'K=2'!")
	}
	
	if(length(model.no) > 1)
		startvals <- NULL
	
	if(col.mean != "Mean")
	{
		if("Mean" %in% cn)
		{
			Data <- Data[,-which(colnames(Data) == "Mean")]
			cn	 <- colnames(Data)
		}
		colnames(Data)[which(cn == col.mean)] <- "Mean"
	}
	if(col.var != "VC")
	{
		if("VC" %in% cn)
		{
			Data <- Data[,-which(colnames(Data) == "VC")]
			cn	 <- colnames(Data)
		}
		colnames(Data)[which(cn == col.var)] <- "VC"
	}
	if(col.df != "DF")
	{
		if("DF" %in% cn)
		{
			Data <- Data[,-which(colnames(Data) == "DF")]
			cn	 <- colnames(Data)
		}
		colnames(Data)[which(cn == col.df)] <- "DF"
	}
	
	ind.NA <- which(apply(Data[c("Mean", "VC", "DF")], 1, function(x) any(is.na(x))))
	if(length(ind.NA) > 0)
	{
		Data <- Data[-ind.NA,,drop=FALSE]
		message(paste(length(ind.NA), "observation(s) with at least one NA value were removed!"))
	}
	
	Data 		<- subset(Data,"Mean">0)
	Data		<- subset(Data,"VC">0)
	pweights 	<- Data[,"DF"]/2 										# prior weight parameters
	Mean 		<- Data[,"Mean"]
	RSS 		<- Df.resid <- Deviance <- AIC <- numeric(10)
	
	Formulas	<- c( 	"sigma^{2}==beta[1]",									# model 1
			"sigma^{2}==beta[1]*u^{2}",								# model 2
			"sigma^{2}==beta[1]+beta[2]*u^2",						# model 3
			paste("sigma^{2}==(beta[1]+beta[2]*u)^{",K,"}"),		# model 4, replace K by acutal value of K
			paste("sigma^{2}==beta[1]+beta[2]*u^{",K,"}"),			# model 5,                - " -
			"sigma^{2}==beta[1]+beta[2]*u+beta[3]*u^{J}",			# model 6
			"sigma^{2}==beta[1]+beta[2]*u^{J}",						# model 7
			"sigma^{2}==(beta[1]+beta[2]*u)^{J}",					# model 8
			"sigma^{2}==beta[1]*u^{J}",								# model 9
			"cv==beta[1]*u^{J}")									# model 10 (true CLSI EP17 model)
	
	names(RSS) 	<- names(Deviance) <- names(AIC) <- paste0("Model_", 1:10)
	
	res.gnm1 	<- res.gnm2 <- res.gnm3 <- res.gnm4 <- res.gnm5 <- res.gnm6 <- res.gnm7 <- res.gnm8 <- res.gnm9 <- res.mod10 <- NULL
	mittel		<- Mu <- mu.fun <- vector("list", length=9)	
	eps			<- 1.0e-07
#	cutval		<- 0.95 #determines lower boundary in models, values between 0 and 1 are possible
	# find a crude analytical model for the calculation of the start weights
	imin=0
	for(i in 0:2){
		if (i>0) {mindevalt<-mindev}
		mindev <- sum((Data[,"DF"]*(1-weighted.mean(Data[,"VC"]/Data[,"Mean"]^i,pweights)*Data[,"Mean"]^i/Data[,"VC"])^2))
		if (i>0){
			if(mindev<mindevalt){imin=i}
		}
	}
	startVC    <- weighted.mean(Data[,"VC"]/Data[,"Mean"]^imin,pweights)*Data[,"Mean"]^imin+0.05*weighted.mean(Data[,"VC"],pweights)
	
	
	
	################################################################################################################################
	
	if(1 %in% model.no)
	{
		cat("\nModel 1 ")
		my.form1 	<- VC ~ 1					 				#constant VC
		startvals   <- log(weighted.mean(Data[,"VC"],pweights)) #exact solution
		tmp.res 	<- conditionHandler(gnm(formula = my.form1, family = Gamma(link = "log"), data = Data, weights = pweights,
						start=startvals, trace=TRUE), file="./stdout.log")
		if(tmp.res$status != 2)
		{
			coeffs 	<- bt.coef(tmp.res$result, model=1)#
			my.form1simple 	<-  VC ~ 1
			tmp.res <- conditionHandler(gnm(formula = my.form1simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=coeffs, trace=TRUE,iterMax=1), file="./stdout.log")
			res.gnm1 	<- tmp.res$result
			RSS[1] 		<- sum((res.gnm1$y-res.gnm1$fitted.values)^2)
			AIC[1]		<- res.gnm1$aic
			Df.resid[1] <- res.gnm1$df.residual  <- sum(Data[,"DF"])-1
			Deviance[1] <- res.gnm1$deviance
			tmp.msg 	<- " ... finished."
		}
		else
		{
			errors 	<- c(errors, paste0("Model 1 (Errors original space): ", tmp.res$errors))
			tmp.msg <- " ... could not be fitted due to errors."	
		}
		
		messages <- c(messages, paste0("Model 1 (Messages): ", tmp.res$messages))
		warnings <- c(warnings, paste0("Model 1 (Warnings): ", tmp.res$warnings))
		
		startvals   <- NULL
		cat(tmp.msg)
	}
	
	if(2 %in% model.no)
	{
		cat("\nModel 2 ")
		#mu.fun[[2]]	<- function(x) 2*log(x)
		mu 			<- Mu[[2]] <- 2*log(Data[,"Mean"])
		my.form2 	<- VC ~ offset(mu)  # constant CV
		startvals   <- log(weighted.mean(Data[,"VC"]/Data[,"Mean"]^2,pweights)) #exact solution
		tmp.res 	<- conditionHandler(gnm(formula = my.form2, family = Gamma(link = "log"), data = Data, weights = pweights,
						start=startvals, trace=TRUE), file="./stdout.log")
		if(tmp.res$status != 2)
		{
			coeffs 	<- bt.coef(tmp.res$result, model=2)#
			mu		<- Data[,"Mean"]^2
			my.form2simple 	<-  VC ~ powfun2simple(Mean)-1
			
			tmp.res <- conditionHandler(gnm(formula = my.form2simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=coeffs, trace=TRUE,iterMax=0), file="./stdout.log")
			res.gnm2 	<- tmp.res$result
			RSS[2] 		<- sum((res.gnm2$y-res.gnm2$fitted.values)^2)
			AIC[2]		<- res.gnm2$aic
			Df.resid[2] <- res.gnm2$df.residual   <- sum(Data[,"DF"])-1
			Deviance[2] <- res.gnm2$deviance
			tmp.msg 	<- " ... finished."
		}
		else
		{
			errors 	<- c(errors, paste0("Model 2 (Errors original space): ", tmp.res$errors))
			tmp.msg <- " ... could not be fitted due to errors."	
		}
		
		messages <- c(messages, paste0("Model 2 (Messages): ", tmp.res$messages))
		warnings <- c(warnings, paste0("Model 2 (Warnings): ", tmp.res$warnings))
		
		startvals   <- NULL
		cat(tmp.msg)
	}
	
	# models 3 4, and 5 are covered by models and, therefore, do not need to be fitted separately if the more
	# general models optimizing the exponent are fitted per default
	
	
	if (3 %in% model.no) {
		cat("\nModel 3 ")
		mu 				<- Mu[[3]] <- Data[, "Mean"]^2
		mumax			<- max(mu)
		startweights 	<- pweights/startVC^2
		
		if(is.null(startvals))
		{
			st <- lm(VC ~ mu, data=Data,weights=startweights)
			startvals <- t.coef(st$coefficients, Maxi=mumax,model=3)
		}
		else
		{
			startvals <- t.coef(startvals,Maxi=mumax,model=3)
		}
		my.form3	<- VC~ -1 + powfun3(mu) #quadratic model
		tmp.res 	<- conditionHandler(gnm(formula = my.form3, family = Gamma(link = "identity"), data = Data, weights = pweights, start=startvals, trace=TRUE), file="./stdout.log")
		
		if(tmp.res$status != 2)
		{
			coeffs 			<- bt.coef(tmp.res$result, model=3)
			AIC[3]			<- tmp.res$result$aic
			tmp.df			<- tmp.res$result$df.residual
			Deviance[3] 	<- tmp.res$result$deviance
			my.form3simple 	<- VC ~ powfun3simple(Mean)-1
			tmp.res 		<- conditionHandler(gnm(formula = my.form3simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=coeffs, trace=TRUE,iterMax=1000), file="./stdout.log")
			if(tmp.res$status != 2)
			{				
				res.gnm3 	<- tmp.res$result
				RSS[3] 		<- sum((res.gnm3$y-res.gnm3$fitted.values)^2)
				tmp.msg 	<- " ... finished."
			}
			else
			{
				res.gnm3 	<- list(coefficients=coeffs, aic=AIC[3], deviance=Deviance[3], df.residual=tmp.df)
				tmp.msg 	<- paste(" ... estimation of covariance-matrix failed, CIs will not be available!", sep="")
			}
		}
		else
		{
			errors 	<- c(errors, paste0("Model 3 (Errors transformed space): ", tmp.res$errors))
			tmp.msg <- " ... could not be fitted due to errors."
		}
		
		messages <- c(messages, paste0("Model 3 (Messages): ", tmp.res$messages))
		warnings <- c(warnings, paste0("Model 3 (Warnings): ", tmp.res$warnings))
		
		startvals   <- NULL
		cat(tmp.msg)
	}
	
	if(4 %in% model.no)
	{
		cat("\nModel 4 ")
		mu			<- Mu[[4]] <- Data[,"Mean"]
		mumax=max(mu)
		startweights <- pweights/startVC^(2/K)
		VCrootK     <- Data[,"VC"]^(1/K)
		my.form4 	<- VC~-1+powfun4(mu, K) 	#fixed power model 
		if (is.null(startvals)) 
		{
			st <- lm(VCrootK ~ mu, data=Data,weights=startweights)
			startvals <- t.coef(st$coefficients,K=K, Maxi=mumax,model=4)
		}
		else
		{
			startvals <- t.coef(startvals, K=K, Maxi=mumax, model=4)
		}
		
		tmp.res <- conditionHandler(gnm(formula = my.form4, family = Gamma(link = "identity"), data = Data, weights = pweights,
						start=startvals, trace=TRUE), file="./stdout.log")
		
		if(tmp.res$status != 2)
		{
			coeffs 		<- bt.coef(tmp.res$result,K=K, model=4)#
			AIC[4] 		<- tmp.res$result$aic
			Deviance[4] <- tmp.res$result$deviance
			my.form4simple 	<- VC~-1+powfun4simple(Mean, K) #fixed power model 
			tmp.res <- conditionHandler(gnm(formula = my.form4simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=coeffs, trace=TRUE,iterMax=0), file="./stdout.log")
			
			if(tmp.res$status != 2)
			{		
				res.gnm4	<- tmp.res$result
				RSS[4] 		<- sum((res.gnm4$y-res.gnm4$fitted.values)^2)
				Df.resid[4] <- res.gnm4$df.residual   <- sum(Data[,"DF"])-2
				tmp.msg <- " ... finished."
			}
			else
			{
				Df.resid[4] <- sum(Data[,"DF"])-2
				res.gnm4 	<- list(coefficients=coeffs, aic=AIC[4], deviance=Deviance[4], df.residual=Df.resid[4])
				tmp.msg 	<- paste(" ... estimation of covariance-matrix failed, CIs will not be available!", sep="")
			}
		}
		else
		{
			res.gnm4 	<- NULL
			errors 		<- c(errors, paste0("Model 4 (Errors transformed space): ", tmp.res$errors))
			tmp.msg 	<- " ... could not be fitted due to errors."
		}
		messages <- c(messages, paste0("Model 4 (Messages): ", tmp.res$messages))
		warnings <- c(warnings, paste0("Model 4 (Warnings): ", tmp.res$warnings))
		
		startvals 	<- NULL				# re-set start values
		cat(tmp.msg)
	}
	
	if(5 %in% model.no){
		cat("\nModel 5 ")
		if(skip5)
			cat(" ... skipped!")
		else
		{
			mu 				<- Mu[[5]] <- Data[, "Mean"]^K
			mumax			<- max(mu)
			startweights 	<- pweights/startVC^2
			
			if (is.null(startvals)) 
			{
				st <- lm(VC ~ mu, data=Data,weights=startweights)
				startvals	<- t.coef(st$coefficients,Maxi=mumax, model=5)
			}
			else
			{
				startvals	<-t.coef(startvals,Maxi=mumax,Model=5)
			}
			
			my.form5 	<- VC~-1+powfun5(mu)		#const model, requires a fixed power on input
			tmp.res 	<- conditionHandler(gnm(formula = my.form5, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=startvals, trace=TRUE), file="./stdout.log")	
			if(tmp.res$status != 2)
			{
				coeffs 		<- bt.coef(tmp.res$result,K=K, model=5)
				AIC[5]		<- tmp.res$result$aic
				Deviance[5]	<- tmp.res$result$deviance
				my.form5simple <- VC~powfun5simple(Mean,K)-1
				tmp.res <- conditionHandler(gnm(formula = my.form5simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
								start=coeffs, trace=TRUE,iterMax=0), file="./stdout.log")
				
				if(tmp.res$status != 2)
				{
					res.gnm5 	<- tmp.res$result	
					RSS[5] 		<- sum((res.gnm5$y-res.gnm5$fitted.values)^2)
					Df.resid[5] <- res.gnm5$df.residual  <- sum(Data[,"DF"])-2
					tmp.msg <- " ... finished."
				}
				else
				{
					Df.resid[5] <- sum(Data[,"DF"])-2
					res.gnm5 	<- list(coefficients=coeffs, aic=AIC[5], deviance=Deviance[5], df.residual=Df.resid[5])
					tmp.msg 	<- paste(" ... estimation of covariance-matrix failed, CIs will not be available!", sep="")
				}
			}
			else
			{
				res.gnm5 	<- NULL
				errors 		<- c(errors, paste0("Model 5 (Errors transformed space): ", tmp.res$errors))
				tmp.msg 	<- " ... could not be fitted due to errors.\n"	
			}
			messages <- c(messages, paste0("Model 5 (Messages): ", tmp.res$messages))
			warnings <- c(warnings, paste0("Model 5 (Warnings): ", tmp.res$warnings))
			
			startvals   <- NULL
			cat(tmp.msg)
		}
	}
	
	if(6 %in% model.no)
	{
		cat("\nModel 6 ")
		mu				<- Mu[[6]] <- Data[,"Mean"]
		my.form6 		<- VC~-1+ powfun6(mu) #linear + variable power model 
		results			<- vector("list", 5)
		par.ind 		<- 4
		res.ind			<- 1
		res.gnm6 		<- tmp <- NULL
		Parms			<- vector("list", 5)
		SVhist			<- matrix(ncol=4, nrow=0)
		startweights 	<- pweights/startVC^2		
		tmp.msg 		<- " ... could not be fitted due to errors."	
		
		if (is.null(startvals)) 				# use random start values for gnm
		{
			tempdev=1.0e100
			res.gnm6 <- NULL
			for(ldJ in 0:4)
			{
				J  			<- 2^ldJ+0.1
				muJ 		<- mu^J
				st 			<- lm(VC ~ mu+muJ, data=Data,weights=startweights)
				startvals	<-t.coef(c(st$coefficients,J),model=6)
				tmp.res 	<- conditionHandler(gnm(formula = my.form6, family = Gamma(link = "identity"), data = Data, weights = pweights,
								start=startvals, trace=TRUE), file="./stdout.log")							
				
				if(tmp.res$status != 2)
				{
					if(!is.null(tmp.res$result) && tmp.res$result$deviance<tempdev)
					{
						res.gnm6 <- tmp.res$result
						tempdev  <- res.gnm6$deviance
						tmp.msg <- " ... finished."
					}
				}
				else
					errors <- c(errors, paste0("Model 6 (Errors transformed space): ", tmp.res$errors))
			}	
		}
		else									# user-specified start values
		{
			startvals <- t.coef(startvals,model=6)
			tmp.res <- conditionHandler(gnm(formula = my.form6, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=startvals, trace=TRUE), file="./stdout.log")		
			if(tmp.res$status != 2)
			{
				res.gnm6 <- tmp.res$result
				tmp.msg <- " ... finished.\n"
			}
			else
			{
				errors 	<- c(errors, paste0("Model 6 (Errors transformed space): ", tmp.res$errors))
				tmp.msg <- " ... could not be fitted due to errors."		
			}
		}
		
		if(!is.null(res.gnm6))
		{   
			coeffs 		<- bt.coef(res.gnm6, model=6)#
			AIC[6] 		<- res.gnm6$aic
			Deviance[6]	<- res.gnm6$deviance
			my.form6simple 	<- VC~-1+powfun6simple(Mean)
			tmp.res 		<- conditionHandler(gnm(formula = my.form6simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=coeffs, trace=TRUE, iterMax=0), file="./stdout.log")
			
			if(tmp.res$status != 2)
			{
				res.gnm6 		<- tmp.res$result							 
				RSS[6] 			<- sum((res.gnm6$y-res.gnm6$fitted.values)^2)
				Df.resid[6]    	<- res.gnm6$df.residual <- sum(Data[,"DF"])-4
			}
			else
			{
				Df.resid[6] <- sum(Data[,"DF"])-4
				res.gnm6 	<- list(coefficients=coeffs, aic=AIC[6], deviance=Deviance[6], df.residual=Df.resid[6])
				tmp.msg 	<- paste(" ... estimation of covariance-matrix failed, CIs will not be available!", sep="")
			}
		}
		
		messages <- c(messages, paste0("Model 6 (Messages): ", tmp.res$messages))
		warnings <- c(warnings, paste0("Model 6 (Warnings): ", tmp.res$warnings))
		
		startvals 	<- NULL
		cat(tmp.msg)
	}
	
	if(7 %in% model.no)
	{
		cat("\nModel 7 ")
		mu				<- Mu[[7]] <- Data[,"Mean"]
		startweights 	<- pweights/startVC^2
		tmp.msg 		<- " ... could not be fitted due to errors."
		
		if (is.null(startvals) || startvals[3]<0 ) #negative power leads negative sigma^2 for small means
		{
			tempdev		<- 1.0e100
			res.gnm7 	<- NULL
			for(ldJ in -3:3){
				J  			<- 2^ldJ
				muJ			<- mu^J
				st 			<- lm(VC ~ muJ, data=Data,weights=startweights)
				startvals   <-t.coef(c(st$coefficients,J),Maxi=max(muJ),model=7)
				my.form7 	<- VC ~ -1+powfun7(mu) 
				tmp.res  	<- conditionHandler(gnm(formula=my.form7, family=Gamma(link = "identity"), data=Data,
								weights=pweights, start=startvals, trace=TRUE), file="./stdout.log")
				if(tmp.res$status != 2)
				{
					if(!is.null(tmp.res$result) && tmp.res$result$deviance<tempdev)
					{
						res.gnm7 <- tmp.res$result
						tempdev  <- res.gnm7$deviance
						tmp.msg <- " ... finished."
					}
				}
				else
					errors <- c(errors, paste0("Model 7 (Errors transformed space): ", tmp.res$errors))
			}
		}
		else
		{
			my.form7 	<- VC ~ -1+powfun7(mu) 
			startvals[3]			<- max(0.1,min(10,startvals[3]))#restrict starting values to 0.1<startvals[3] <10
			muJmax<-max(mu^startvals[3])
			startvals <- t.coef(startvals,Maxi=muJmax,model=7)
			tmp.res <- conditionHandler(gnm(formula = my.form7, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=startvals, trace=TRUE), file="./stdout.log")
			if(tmp.res$status != 2)
			{
				res.gnm7 <- tmp.res$result
				tmp.msg <- " ... finished."
			}
			else
			{
				errors 	<- c(errors, paste0("Model 7 (Errors transformed space): ", tmp.res$errors))
				tmp.msg	<- " ... could not be fitted due to errors."
			}			
		}
		if(!is.null(res.gnm7))
		{
			coeffs 			<- bt.coef(res.gnm7, model=7)#
			AIC[7] 			<- res.gnm7$aic
			Deviance[7] 	<- res.gnm7$deviance
			my.form7simple 	<- VC~-1+powfun7simple(Mean)
			tmp.res 		<- conditionHandler(gnm(formula = my.form7simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=coeffs, trace=TRUE,iterMax=0), file="./stdout.log")
			
			if(!is.null(tmp.res))
			{
				res.gnm7 	<- tmp.res$result		
				RSS[7] 		<- sum((res.gnm7$y-res.gnm7$fitted.values)^2)
				Df.resid[7] <- res.gnm7$df.residual <- sum(Data[,"DF"])-3
			}
			else
			{
				Df.resid[7] <- sum(Data[,"DF"])-3
				res.gnm7 	<- list(coefficients=coeffs, aic=AIC[7], deviance=Deviance[7], df.residual=Df.resid[7])
				tmp.msg 	<- paste(" ... estimation of covariance-matrix failed, CIs will not be available!", sep="")
			}	
		}
		messages <- c(messages, paste0("Model 7 (Messages): ", tmp.res$messages))
		warnings <- c(warnings, paste0("Model 7 (Warnings): ", tmp.res$warnings))
		
		startvals 	<- NULL
		cat(tmp.msg)
	}
	
	if(8 %in% model.no)
	{
		cat("\nModel 8 ")
		mu			<- Mu[[8]] <- Data[,"Mean"]
		C			<- 	attr(Mu[[8]], "Constant") <- max(mu)
		my.form8 	<- VC~-1+powfun8(mu, C) 
		devns 		<- rep(NA, 1e3)
		tmp.msg		<- " ... could not be fitted due to errors."
		
		if (is.null(startvals)) 		# random start values
		{
			tempdev		<- 1.0e100
			res.gnm8 	<- NULL
			for(ldJ in -3:3){
				J  				<- 2^ldJ
				signJ			<- 1
				my.form8 		<- VC~-1+powfun8(mu, C,signJ) 
				startweights 	<- pweights/startVC^(2/J)
				VCrootJ     	<- Data[,"VC"]^(1/J)
				st 				<- lm(VCrootJ ~ mu, data=Data,weights=startweights)
				startvals		<- t.coef(c(st$coefficients,signJ*J),Maxi=C,signJ=signJ,model=8)
				tmp.res 		<- conditionHandler(gnm(formula = my.form8, family = Gamma(link = "identity"), 
								data = Data, weights = pweights ,start=startvals, 
								trace=TRUE), file="./stdout.log")
				if(tmp.res$status != 2)
				{
					if(!is.null(tmp.res$result))
					{
						if(tmp.res$result$deviance<tempdev)
						{
							res.gnm8 <- tmp.res$result
							sgnJ <- signJ
							tempdev  <- res.gnm8$deviance
							tmp.msg <- " ... finished."
						}
					}
				}
				else
					errors <- c(errors, paste0("Model 8 (Errors transformed space): ", tmp.res$errors))
			}
			for(ldJ in -3:3)
			{
				J  				<- -2^ldJ
				signJ			<- -1				
				my.form8 	<- VC~-1+powfun8(mu, C,signJ) 
				startweights 	<- pweights/startVC^(2/J)
				VCrootJ     	<- Data[,"VC"]^(1/J)
				st 				<- lm(VCrootJ ~ mu, data=Data,weights=startweights)
				startvals		<- t.coef(c(st$coefficients,signJ*J),Maxi=C,signJ=signJ,model=8)
				tmp.res 		<- conditionHandler(gnm(formula = my.form8, family = Gamma(link = "identity"), 
								data = Data, weights = pweights ,start=startvals, 
								trace=TRUE), file="./stdout.log")
				if(tmp.res$status != 2)
				{
					if(!is.null(tmp.res$result))
					{
						if(tmp.res$result$deviance<tempdev)
						{
							res.gnm8 <- tmp.res$result
							sgnJ <- signJ
							tempdev  <- res.gnm8$deviance
							tmp.msg <- " ... finished."
						}
					}
				}
				else
					errors <- c(errors, paste0("Model 8 (Errors transformed space): ", tmp.res$errors))
			}		
		}
		else							# user-specified startvalues
		{
			if(startvals[3]>0){ #restrict range of starting values to 0.1 <|J| <10
				startvals[3]			<- max(0.1,min(10,startvals[3]))
				signJ					<- 1
			}
			else{
				signJ					<- -1
				startvals[3]			<- -max(0.1,min(10,-startvals[3]))
			}
			my.form	<- VC~-1+powfun8(Mean, C,signJ) 
			startvals <-t.coef(startvals,Maxi=C,signJ=signJ,model=8)
			tmp.res <- conditionHandler(gnm(formula = my.form8, family = Gamma(link = "identity"), 
							data = Data, weights = pweights ,start=startvals, 
							trace=TRUE), file="./stdout.log")
			
			if(tmp.res$status != 2)
			{
				if(!is.null(tmp.res$result))
				{
					res.gnm8 	<- tmp.res$result
					sgnJ 		<- signJ
					tmp.msg 	<- " ... finished."
				}
			}
			else
			{
				errors 	<- c(errors, paste0("Model 8 (Errors transformed space): ", tmp.res$errors))
				tmp.msg	<- " ... could not be fitted due to errors."
			}
		}
		if(!is.null(res.gnm8))
		{
			coeffs 			<- bt.coef(res.gnm8,signJ=sgnJ, model=8)
			AIC[8]			<- res.gnm8$aic
			Deviance[8] 	<- res.gnm8$deviance
			my.form8simple 	<- VC~-1+powfun8simple(Mean)
			tmp.res <- conditionHandler(gnm(formula = my.form8simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=coeffs, trace=TRUE,iterMax=0), file="./stdout.log")
			
			if(!is.null(tmp.res))
			{
				
				res.gnm8    <- tmp.res$result
				RSS[8] 		<- sum((res.gnm8$y-res.gnm8$fitted.values)^2)				
				Df.resid[8] <- res.gnm8$df.residual <- sum(Data[,"DF"])-3
				
			}
			else
			{
				Df.resid[8] <- sum(Data[,"DF"])-3
				res.gnm8 	<- list(coefficients=coeffs, aic=AIC[8], deviance=Deviance[8], df.residual=Df.resid[8])
				tmp.msg 	<- paste(" ... estimation of covariance-matrix failed, CIs will not be available!", sep="")
			}	
		}
		messages <- c(messages, paste0("Model 8 (Messages): ", tmp.res$messages))
		warnings <- c(warnings, paste0("Model 8 (Warnings): ", tmp.res$warnings))
		
		startvals 		<- NULL
		cat(tmp.msg)
	}
	
	if(9 %in% model.no)
	{
		cat("\nModel 9 ")
		mu			<- Mu[[9]] <- log(Data[,"Mean"])
		logVC  		<- log(Data[,"VC"])
		my.form9 	<- formula(paste("VC", "~ mu", sep = " ")) 	# variable power model without intercept
		if (is.null(startvals)) 								# random start values
		{
			startweights 	<- pweights
			st 				<- lm(logVC ~ mu, data=Data,weights=startweights)
			startvals		<- c(st$coefficients[1],st$coefficients[2])
		}	
		else
		{
			startvals <-t.coef(startvals,model=9)
		}
		
		tmp.res <- conditionHandler(gnm(formula = my.form9, family = Gamma(link = "log"), data = Data, weights = pweights,
						start=startvals, trace=TRUE), file="./stdout.log")
		
		if(tmp.res$status != 2)
		{
			res.gnm9 <- tmp.res$result
			tmp.msg <- " ... finished."
		}
		else
		{
			errors 	<- c(errors, paste0("Model 9 (Errors transformed space): ", tmp.res$errors))
			tmp.msg	<- " ... could not be fitted due to errors."
		}
		
		if(!is.null(res.gnm9))
		{			
			coeffs 			<- bt.coef(res.gnm9, model=9)#
			AIC[9]			<- res.gnm9$aic
			Deviance[9] 	<- res.gnm9$deviance
			my.form9simple 	<- VC~-1+powfun9simple(Mean)
			tmp.res 		<- conditionHandler(gnm(formula = my.form9simple, family = Gamma(link = "identity"), data = Data, weights = pweights,
							start=coeffs, trace=TRUE, iterMax=0), file="./stdout.log")
			
			if(!is.null(tmp.res ))
			{		
				res.gnm9    	<- tmp.res$result
				RSS[9]			<- sum((res.gnm9$y-res.gnm9$fitted.values)^2)
				Df.resid[9]     <- res.gnm9$df.residual <- sum(Data[,"DF"])-2
			}
			else
			{
				Df.resid[9] <- sum(Data[,"DF"])-2
				res.gnm9 	<- list(coefficients=coeffs, aic=AIC[9], deviance=Deviance[9], df.residual=Df.resid[9])
				tmp.msg 	<- paste(" ... estimation of covariance-matrix failed, CIs will not be available!", sep="")
			}	
		}
		messages <- c(messages, paste0("Model 9 (Messages): ", tmp.res$messages))
		warnings <- c(warnings, paste0("Model 9 (Warnings): ", tmp.res$warnings))
		
		startvals <- NULL
		cat(tmp.msg)
	}
	
	if(10 %in% model.no)
	{
		cat("\nModel 10")
		
		if(!is.null(col.cv))		# minimize error propagation effects by using CV-values directly
		{
			res.mod10 	<- fit.EP17(x=Data$Mean, y=Data$CV, DF=Data$DF, typeY="cv")
		}
		else
		{
			if(!is.null(col.sd))	# second best option
			{
				Data$CV		<- 100*Data$SD/Data$Mean 
				res.mod10 	<- fit.EP17(x=Data$Mean, y=Data$SD, DF=Data$DF, typeY="sd")
			}
			else					# worst option, since VC --> SD --> CV
			{
				Data$CV		<- 100*sqrt(Data$VC)/Data$Mean 	
				res.mod10 	<- fit.EP17(x=Data$Mean, y=Data$VC, DF=Data$DF, typeY="vc")
			}
		}
		
		RSS[10]			<- res.mod10$RSS
		AIC[10]			<- res.mod10$AIC
		Df.resid[10]    <- sum(Data[,"DF"])-2
		Deviance[10]	<- res.mod10$deviance
		cat(" ... finished.")
	}
	
	cat("\n")
	
	if(quiet)						# read logs and remove temporary files
	{
		#try(close(outputLog), silent=TRUE)				
		output 	<- scan("./stdout.log", sep="\n", what="character", quiet=TRUE)			
		try(file.remove("./stdout.log"), silent=TRUE)		
	}
	else
		output <- NULL
	
	mod <- list(
			model1 =res.gnm1,
			model2 =res.gnm2,
			model3 =res.gnm3,
			model4 =res.gnm4,
			model5 =res.gnm5,
			model6 =res.gnm6,
			model7 =res.gnm7,
			model8 =res.gnm8,
			model9 =res.gnm9,
			model10=res.mod10)
	
	ind <- which(!sapply(mod, is.null))
	res <- list(
			Call=Call,
			Models=mod[ind],
			RSS=RSS[ind],
			AIC=AIC[ind],
			GoF.pval=sapply(mod[ind], function(x) pchisq(x$deviance, x$df.residual, lower.tail=FALSE)),
			DF.resid=Df.resid[ind],
			Deviance=Deviance[ind],
			Formulas=Formulas[ind],
			Data=Data,
			K=K,
			startvals=startvals,
			errors=errors,
			output=output,
			warnings=warnings,
			notes=notes)
	
	class(res) <- "VFP"
	
	return(res)
}