"sci.ratio.gen" <-
function(Y, X, Num.Contrast, Den.Contrast, alternative = "two.sided", conf.level = 0.95, method="Plug") {
if(all(c("Plug", "Bonf", "MtI", "Unadj")!=method))
{stop("argument method mis-specified")}
if(all(c("two.sided", "less", "greater")!=alternative))
{stop("argument alternative mis-specified")}
if(nrow(Num.Contrast)!=nrow(Den.Contrast))
{stop("Num.Contrast and Den.Contrast must have same number of rows")}
#NCrowsum<-apply(Num.Contrast, MARGIN=1, FUN=sum)
#DCrowsum<-apply(Den.Contrast, MARGIN=1, FUN=sum)
#if( !all( NCrowsum == DCrowsum ) )
# { cat("Warning: Check whether denominator and numerator contrast matrices are appropriately defined!", "\n") }
NC0<-apply(X=Num.Contrast, MARGIN=1, function(x){all(x==0)})
DC0<-apply(X=Den.Contrast, MARGIN=1, function(x){all(x==0)})
if(any(c(NC0,DC0)))
{cat("Warning: At least one row of the numerator or denominator contrast matrices is a vector with all components equal to zero","\n")}
CMat <- Num.Contrast
DMat <- Den.Contrast
n.comp <- nrow(Num.Contrast)
Lm.Fit <- lm(Y~X-1)
Names.Coeff<-names(Lm.Fit$coef)
colnames(CMat)<-colnames(DMat)<-Names.Coeff
if(is.null(rownames(CMat)) && is.null(rownames(DMat)) )
{ compnames <- paste( "C", 1:nrow(Num.Contrast), sep="") }
else{ if(any(rownames(CMat)!=rownames(DMat)) )
{compnames <- paste(rownames(CMat), rownames(DMat), sep="/")}
else{compnames <- rownames(CMat)}}
Beta.Coeff <- Lm.Fit$coef
if(any( c( ncol(Num.Contrast), ncol(Den.Contrast) )!=length(Beta.Coeff) ))
{stop("Num.Contrast and Den.Contrast must have same number of columns as parameters are fitted in the linear model")}
Degree.f <- Lm.Fit$df
Pooled.Var <- sum(Lm.Fit$residual^2)/Degree.f
gammaC.vec <- (CMat%*%Beta.Coeff)/DMat%*%Beta.Coeff # MLE of the ratios
M <- solve(t(X)%*%X)
CorrMat.plug <- matrix(as.numeric(rep(NA,n.comp*n.comp)), nrow=n.comp)
for(i in 1:n.comp) {
for(j in 1:n.comp) {
CorrMat.plug[i,j] <- (gammaC.vec[i]*DMat[i,] - CMat[i,])%*%M%*%(gammaC.vec[j]*DMat[j,] - CMat[j,])/
(sqrt((gammaC.vec[i]*DMat[i,] - CMat[i,])%*%M%*%(gammaC.vec[i]*DMat[i,] - CMat[i,]))*
sqrt((gammaC.vec[j]*DMat[j,] - CMat[j,])%*%M%*%(gammaC.vec[j]*DMat[j,] - CMat[j,])))
}
}
##
####
#### Solution of quadratic inequality
##
Quad.root <- function(Aj, Bj, Cj){
Discrimi <- Bj^2 - 4*Aj*Cj
if ((Aj > 0)&(Discrimi >= 0)) Limit.s <- (-Bj + plus.minus*sqrt(Discrimi))/(2*Aj)
else Limit.s <- "NSD"
return(Limit.s)}
switch(method,
# UNADJUSTED CI
Unadj={
if (alternative=="two.sided"){
side <- 2
plus.minus <- c(-1,1)
cpUAd <- qt(1- (1-conf.level)/(side), Degree.f, lower.tail = TRUE)
} # End of two-sided CI
if ((alternative=="less")|(alternative=="greater")){
side <- 1
if (alternative=="less") plus.minus <- 1
else plus.minus <- -1
cpUAd <- qt(1- (1-conf.level)/(side), Degree.f, lower.tail = TRUE)
} # End of one-sided CI
UAdCL <- matrix(as.numeric(rep(NA,side*n.comp)),nrow=n.comp)
for(j in 1:n.comp)
{
AjUAd <- (DMat[j,]%*%Beta.Coeff)^2 - (cpUAd^2)*Pooled.Var*DMat[j,]%*%M%*%DMat[j,]
BjUAd <- -2*((CMat[j,]%*%Beta.Coeff)*(DMat[j,]%*%Beta.Coeff) - (cpUAd^2)*Pooled.Var*CMat[j,]%*%M%*%DMat[j,])
CjUAd <- (CMat[j,]%*%Beta.Coeff)^2 - (cpUAd^2)*Pooled.Var*CMat[j,]%*%M%*%CMat[j,]
UAdCL[j,] <- Quad.root(AjUAd, BjUAd, CjUAd)
}
sci.table <- data.frame(UAdCL)
df <- Degree.f; critp <- cpUAd
},
# BONFERRONI-ADJUSTED CI
Bonf={
if (alternative=="two.sided"){
side <- 2
plus.minus <- c(-1,1)
cpBon <- qt(1- (1-conf.level)/(side*n.comp), Degree.f, lower.tail = TRUE)
} # End of two-sided CI
if ((alternative=="less")|(alternative=="greater")){
side <- 1
if (alternative=="less") plus.minus <- 1
else plus.minus <- -1
cpBon <- qt(1- (1-conf.level)/(side*n.comp), Degree.f, lower.tail = TRUE)
} # End of one-sided CI
BonCL <- matrix(as.numeric(rep(NA,side*n.comp)), nrow=n.comp)
for(j in 1:n.comp)
{
AjBon <- (DMat[j,]%*%Beta.Coeff)^2 - (cpBon^2)*Pooled.Var*DMat[j,]%*%M%*%DMat[j,]
BjBon <- -2*((CMat[j,]%*%Beta.Coeff)*(DMat[j,]%*%Beta.Coeff) - (cpBon^2)*Pooled.Var*CMat[j,]%*%M%*%DMat[j,])
CjBon <- (CMat[j,]%*%Beta.Coeff)^2 - (cpBon^2)*Pooled.Var*CMat[j,]%*%M%*%CMat[j,]
BonCL[j,] <- Quad.root(AjBon, BjBon, CjBon)
}
sci.table <- data.frame(BonCL)
df <- Degree.f; critp <- cpBon
},
# MtI-ADJUSTED CI (SIDAK, resp SLEPIAN)
MtI={
if (alternative=="two.sided"){
side <- 2
plus.minus <- c(-1,1)
cpMtI <- qmvt(conf.level, interval=c(0,10),df=as.integer(Degree.f),corr=diag(n.comp),delta=rep(0,n.comp), tail="both", abseps=1e-05)$quantile
} # End of two-sided CI
if ((alternative=="less")|(alternative=="greater")){
side <- 1
if (alternative=="less") plus.minus <- 1
else plus.minus <- -1
cpMtI <- qmvt(conf.level, interval=c(0,10),df=as.integer(Degree.f),corr=diag(n.comp),delta=rep(0,n.comp),
tail="lower.tail", abseps=1e-05)$quantile
} # End of one-sided CI
MtICL <- matrix(as.numeric(rep(NA,side*n.comp)),nrow=n.comp)
for(j in 1:n.comp) {
AjMtI <- (DMat[j,]%*%Beta.Coeff)^2 - (cpMtI^2)*Pooled.Var*DMat[j,]%*%M%*%DMat[j,]
BjMtI <- -2*((CMat[j,]%*%Beta.Coeff)*(DMat[j,]%*%Beta.Coeff) - (cpMtI^2)*Pooled.Var*CMat[j,]%*%M%*%DMat[j,])
CjMtI <- (CMat[j,]%*%Beta.Coeff)^2 - (cpMtI^2)*Pooled.Var*CMat[j,]%*%M%*%CMat[j,]
MtICL[j,] <- Quad.root(AjMtI, BjMtI, CjMtI)
}
sci.table <- data.frame(MtICL)
df <- as.integer(Degree.f); critp <- cpMtI
},
# PLUG-IN-CI
Plug={
if (alternative=="two.sided"){
side <- 2
plus.minus <- c(-1,1)
Cplug <- qmvt(conf.level, interval=c(0,10),df=as.integer(Degree.f),corr=CorrMat.plug,delta=rep(0,n.comp), tail="both", abseps=1e-05)$quantile
} # End of two-sided CI
if ((alternative=="less")|(alternative=="greater")){
side <- 1
if (alternative=="less") plus.minus <- 1
else plus.minus <- -1
Cplug <- qmvt(conf.level, interval=c(0,10),df=as.integer(Degree.f),corr=CorrMat.plug,delta=rep(0,n.comp),
tail="lower.tail", abseps=1e-05)$quantile
} # End of one-sided CI
PlugCL <- matrix(as.numeric(rep(NA,side*n.comp)),nrow=n.comp)
for(j in 1:n.comp) {
AjPlug <- (DMat[j,]%*%Beta.Coeff)^2 - (Cplug^2)*Pooled.Var*DMat[j,]%*%M%*%DMat[j,]
BjPlug <- -2*((CMat[j,]%*%Beta.Coeff)*(DMat[j,]%*%Beta.Coeff) - (Cplug^2)*Pooled.Var*CMat[j,]%*%M%*%DMat[j,])
CjPlug <- (CMat[j,]%*%Beta.Coeff)^2 - (Cplug^2)*Pooled.Var*CMat[j,]%*%M%*%CMat[j,]
PlugCL[j,] <- Quad.root(AjPlug, BjPlug, CjPlug)
}
sci.table <- data.frame(PlugCL)
df <- as.integer(Degree.f); critp <- Cplug
}
)
# end of switch method
if (alternative=="two.sided")
{
names(sci.table) <- c("lower","upper")
}
if (alternative=="less")
{
names(sci.table) <- c("upper")
}
if (alternative=="greater")
{
names(sci.table) <- c("lower")
}
if( any(CorrMat.plug<0) && method=="MtI" && alternative!="two.sided")
{
warning("At least one element of the estimated correlation matrix is negative,
therefore, according to Slepian inequality, the MtI method might yield incorrect estimates.")
}
if (sum(sci.table=="NSD")>0){NSD <- TRUE}
else{NSD <- FALSE}
rownames(sci.table)<-compnames
rownames(gammaC.vec)<-compnames
if(method=="Unadj"| n.comp==1)
{
methodname<-paste( signif(conf.level*100,2), "% confidence interval", sep="")
}
else{
methodname<-paste("Simultaneous", signif(conf.level*100,2), "% confidence intervals", sep="")
}
out<-list(
estimate=gammaC.vec,
CorrMat.est=CorrMat.plug,
Num.Contrast=CMat,
Den.Contrast=DMat,
conf.int=sci.table,
compnames=compnames,
NSD=NSD,
method=method,
methodname=methodname,
alternative=alternative,
conf.level=conf.level,
type="User defined",
Y=Y,
X=X,
fit=Lm.Fit,
df=df,
quantile=critp
)
class(out)<-c("sci.ratio.gen", "sci.ratio")
return(out)
} # END of function sci.ratio.gen
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