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# REGWQ - Ryan / Einot and Gabriel / Welsch test procedure
#
# Author: FrankKonietschke
###############################################################################
regwq <- function(formula, data,alpha, MSE=NULL, df=NULL, silent = FALSE){
dat <- model.frame(formula, data)
if (ncol(dat) != 2) {
stop("Specify one response and only one class variable in the formula")
}
if (is.numeric(dat[, 1]) == FALSE) {
stop("Response variable must be numeric")
}
response <- dat[, 1]
group <- as.factor(dat[, 2])
fl <- levels(group)
a <-nlevels(group)
N <- length(response)
samples <- split(response,group)
n <- sapply(samples,"length")
mm <- sapply(samples,"mean")
vv <- sapply(samples,"var")
if (is.null(MSE)){
MSE <- sum((n-1)*vv)/(N-a)
}
if (is.null(df)){
df <- N-a
}
nc <- a*(a-1)/2
order.h1 <- data.frame(Sample=fl, Size=n, Means=mm,Variance=vv)
ordered <- order.h1[order(order.h1$Means,decreasing=FALSE), ]
rownames(ordered) <- 1:a
#---------------- Compute helping indices ----------#
i <- 1:(a-1)
h1 <- list()
for(s in 1:(a-1)){
h1[[s]]<- i[1:s]
}
vi <- unlist(h1)
j <- a:2
h2 <-list()
for (s in 1:(a-1)){
h2[[s]] <- j[s:1]
}
vj <- unlist(h2)
h3 <- list()
h4 <- list()
for (s in 1:(a-1)){
h3[[s]] <- rep(j[s],s)
h4[[s]] <- rep(i[s],s)
}
Nmean <- unlist(h3)
Step <- unlist(h4)
#--------Compute the Mean Differences---------#
mean.difference <- sapply(1:nc,function(arg){
i <- vi[arg]
j <- vj[arg]
(ordered$Means[j]-ordered$Means[i])
})
mean.difference <- round(mean.difference, 4)
# ------- Compute the test statistics --------#
T <- sapply(1:nc,function(arg){
i<-vi[arg]
j<-vj[arg]
(ordered$Means[j]-ordered$Means[i])/sqrt(MSE/2*(1/ordered$Size[i] + 1/ordered$Size[j]))
})
T <- round(T, 4)
#-------Compute the adjusted p-Values-------#
pvalues <- ptukey(T,Nmean,df,lower.tail=FALSE)
#------Compute the adjusted alpha-levels----#
alpha.level <- 1-(1-alpha)^(Nmean/a)
level1 <- (Nmean==a)
level2 <- (Nmean==a-1)
level3 <- level1 + level2
alpha.level[level3==1] <- alpha
alpha.level <- round(alpha.level,4)
# ----- Compute now the critical value -----#
quantiles <- qtukey(1-alpha.level,Nmean,df)
for (h in 1:(nc-1)){
if (quantiles[h+1] >=quantiles[h]){
quantiles[h+1] <- quantiles[h]
}
}
#---- Calculate the rejected Hypotheses ------#
Rejected1 <- (pvalues<alpha.level)
#------------ Names for the Output -----------#
names.ordered <- sapply(1:nc, function(arg){
i <- vi[arg]
j <- vj[arg]
paste(ordered$Sample[j], "-", ordered$Sample[i], sep="")
})
# ------ Compute now the rejected statistics-----#
for (s in 1:nc){
if (Rejected1[s]==FALSE){
Under1 <- (vj[s]>=vj)
Under2 <- (vi[s]<=vi)
Under3 <- Under1 * Under2
Under4 <- which(Under3==1)
Rejected1[Under4] <- FALSE
}
}
#-----Prepare the pValues for the Output----#
Out1 <- (pvalues < alpha.level)
Out2 <- (Rejected1 == FALSE)
Out3 <- Out1 * Out2
Out4 <- (Out3 == 1)
pvalues <- round(pvalues,4)
quantiles <- round(quantiles,4)
pvalues[Out4] <- paste(">",alpha.level[Out4])
quantiles[Out4] <- paste(">", T[Out4])
variances.output <- data.frame(Overall=MSE, df=df)
Comparison <- data.frame(Comparison=names.ordered,Diff=mean.difference, Statistic=T,Quantiles=quantiles, Adj.P=pvalues, Alpha.Level=alpha.level, Rejected=Rejected1, Layer = Step)
if (!silent)
{
cat("#----REGWQ - Ryan / Einot and Gabriel / Welsch test procedure \n\n")
printRejected(Comparison$Rejected, pvalues, Comparison$Adj.P)
}
#result <- list(Ordered.Means = ordered, Variances=variances.output,
# REGWQ = Comparison)
#diffm<-matrix(c(Comparison["Diff"],rep(NA,length(Comparison["Diff"])*2)),nrow=length(Comparison["Diff"]))
diffm<-cbind(Comparison$Diff,rep(NA,length(Comparison$Diff)),rep(NA,length(Comparison$Diff)))
diffm<-matrix(diffm,nrow=length(Comparison$Diff))
rownames(diffm)<-Comparison$Comparison
return(list(adjPValues=Comparison$Adj.P, rejected=Comparison$Rejected, statistic=Comparison$Statistic,
confIntervals=diffm,errorControl = new(Class='ErrorControl',type="FWER",alpha=alpha)))
}
mutoss.regwq <- function() { return(new(Class="MutossMethod",
label="Ryan / Einot and Gabriel / Welsch test",
errorControl="FWER",
callFunction="regwq",
output=c("adjPValues","rejected","statistic","confIntervals","errorControl"),
info="<h2>Ryan / Einot and Gabriel / Welsch test procedure.
The procedure controls the FWER. </h2>\n\n\
<p> It is based on a stepwise or \
layer approach to significance testing. Sample means are \
ordered from the smallest to the largest. The largest \
difference, which involves means that are r = p steps apart, \
is tested first at alpha level of significance; if significant, \
means that are r < p steps apart are tested at an adjusted alpha level \
of significance and so on. \
The alpha levels are adjusted for the p-1 different\
layers by the formula alpha_p= alpha, if p=k or p=k-1,\
alpha_p = 1-(1-\alpha)^{p/k} otherwise.
</p>\n\
<h3>Reference:</h3>\
<ul>\
<li>Hochberg, Y., Yamhane, A.C. (1987). \"<i> Multiple Comparison Procedures \
</i>\" Wiley, New York. </li>\n\
</ul>",
parameters=list(formula=list(type="formula"), data=list(type="ANY"), alpha=list(type="numeric"),
MSE=list(type="numeric"), df=list(type="numeric"))
)
) }
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