Nothing
pUmbrPK<-function(x,peak=NA,g=NA,method=NA, n.mc=10000){
if(is.na(peak)){
warning("The peak is required for this procedure. If peak is unkown, use pUmbrPU instead.")
return()
}
##From kruskal.test()##
if (is.list(x)) {
if (length(x) < 2L)
stop("'x' must be a list with at least 2 elements")
DNAME <- deparse(substitute(x))
x <- lapply(x, function(u) u <- u[complete.cases(u)])
k <- length(x)
l <- sapply(x, "length")
if (any(l == 0))
stop("all groups must contain data")
g <- factor(rep(1:k, l))
x <- unlist(x)
}
else {
if (length(x) != length(g))
stop("'x' and 'g' must have the same length")
DNAME <- paste(deparse(substitute(x)), "and", deparse(substitute(g)))
OK <- complete.cases(x, g)
x <- x[OK]
g <- g[OK]
if (!all(is.finite(g)))
stop("all group levels must be finite")
g <- factor(g)
l<-as.numeric(table(g))
k <- nlevels(g)
if (k < 2)
stop("all observations are in the same group")
}
N <- length(x)
#####################
outp<-list()
outp$n<-l
outp$stat.name<-paste("Mack-Wolfe Peak Known A",peak)
outp$n.mc<-n.mc
outp$ties<- (length(x) != length(unique(x)))
##When the user doesn't give us any indication of which method to use, try to pick one.
if(is.na(method)){
if(outp$ties){
if(factorial(sum(outp$n))/prod(factorial(outp$n))<=10000){
method<-"Exact"
}
if(factorial(sum(outp$n))/prod(factorial(outp$n))>10000){
method<-"Monte Carlo"
}
}
if(!outp$ties){
method<-"Exact"
}
}
#####################################################################
outp$method<-method
A.calc<-function(obs.data){
U.vec<-numeric((peak*(peak-1)+(k-peak+1)*(k-peak))/2)
U.calc<-function(i,j){
wilcox.test(obs.data[g==levels(g)[i]],obs.data[g==levels(g)[j]])$statistic
}
count<-0
for(i in 2:peak){
for(j in 1:(i-1)) {
count<-count+1
options(warn = (-1));
U.vec[count]<-U.calc(i,j)
options(warn = (0));
}
}
for(i in peak:(k-1)){
for(j in (i+1):k) {
count<-count+1
options(warn = (-1));
U.vec[count]<-U.calc(i,j)
options(warn = (0));
}
}
sum(U.vec)
}
outp$obs.stat<-A.calc(x);
if(!outp$ties){
if(outp$method=="Monte Carlo"){
warning("The exact computation will work for large data, so Monte Carlo methods
are not recommended for this procedure.")
outp$method="Exact"
}
if(outp$method=="Exact"){
num.comb<-factorial(N)/prod(factorial(outp$n))
max.A=0;
for(i in 1:(peak-1)){
max.A=max.A+outp$n[i]*(cumsum(outp$n)[peak]-cumsum(outp$n)[i])
}
for(i in peak:(k-1)){
max.A=max.A+outp$n[i]*(cumsum(outp$n)[k]-cumsum(outp$n)[i])
}
#Remember we need to include 0 as possibility, so following code may appear strange at first;
if(max.A%%2){
even=1;
upper=(max.A-1)/2
}
if(!max.A%%2){
even=0;
upper=max.A/2
}
##Initialize##
freq.dist<-numeric(upper+1);
freq.dist[1]<-1;
##Function##
update<-function(m,n){
size.check<-(n+1)<=upper;
if(size.check){
p=min(m+n,upper)
for(t in (n+1):p){
for(u in upper:t){
freq.dist[u+1]<<-freq.dist[u+1]-freq.dist[u+1-t]
}
}
}
q=min(m,upper)
for(s in 1:q){
for(u in s:upper){
freq.dist[u+1]<<-freq.dist[u+1]+freq.dist[u+1-s]
}
}
}
update(outp$n[peak],cumsum(outp$n)[k]-outp$n[peak])
if(peak>2){
for(i in 1:(peak-2)){
update(outp$n[i],(cumsum(outp$n)[peak-1]-cumsum(outp$n)[i]))
}
}
if(k>peak+1){
for(i in k:(peak+2)){
update(outp$n[i],(cumsum(outp$n)[i-1]-cumsum(outp$n)[peak]))
}
}
low.freq.dist<-freq.dist;
if(even){
freq.dist<-c(low.freq.dist,rev(low.freq.dist))
}
if(!even){
freq.dist<-c(low.freq.dist,rev(low.freq.dist)[-1])
}
prob.dist<-freq.dist/sum(freq.dist)
values<-(0:max.A)
A.dist<-cbind(values,prob.dist)
outp$p.val<-sum(A.dist[values>=outp$obs.stat,2])
}
if(outp$method=="Asymptotic"){
N1<-sum(l[1:peak])
N2<-sum(l[peak:k])
A.star<-(outp$obs.stat-(N1^2+N2^2-sum(l^2)-l[peak]^2)/4)/
sqrt((2*(N1^3+N2^3)+3*(N1^2+N2^2)-sum(l^2*(2*l+3))-l[peak]^2*(2*l[peak]+3)+12*l[peak]*N1*N2-12*l[peak]^2*sum(l))/72)
outp$stat.name<-paste("Mack-Wolfe Peak Known A*",peak)
outp$obs.stat<-A.star
outp$p.val<-1-pnorm(A.star)
}
}
if(outp$ties){
possible.ranks<-as.numeric(rank(x))
if(outp$method=="Asymptotic"){
N1<-sum(l[1:peak])
N2<-sum(l[peak:k])
A.star<-(outp$obs.stat-(N1^2+N2^2-sum(l^2)-l[peak]^2)/4)/
sqrt((2*(N1^3+N2^3)+3*(N1^2+N2^2)-sum(l^2*(2*l+3))-l[peak]^2*(2*l[peak]+3)+12*l[peak]*N1*N2-12*l[peak]^2*sum(l))/72)
outp$stat.name<-paste("Mack-Wolfe Peak Known A*",peak)
outp$obs.stat<-A.star
outp$p.val<-1-pnorm(A.star)
outp$extra<-paste("Ties are present, so exact variance of A",peak," is not available. Reported
asymptotic p-value is therefore larger than the truth.")
}
if(outp$method=="Exact"){
if(factorial(N)/prod(factorial(outp$n))>10000){
use.MC<-(-1)
while(use.MC<0){
use.MC <- as.integer(readline("Ties are present, so exact distributions may be computationally intensive. \n Press 0 for Exact or 1 for Monte Carlo computations."))
use.MC <- ifelse(grepl("\\D",use.MC),NA,as.integer(use.MC))
if(is.na(use.MC)){break} # breaks when hit enter
}
}
if(factorial(N)/prod(factorial(outp$n))<=10000){use.MC=0}
if(use.MC){
outp$method<-"Monte Carlo"
}
if(!use.MC){
possible.orders<-multComb(l)
possible.perms<-t(apply(possible.orders,1,function(x) possible.ranks[x]))
A.stats<-apply(possible.perms,1,A.calc)
A.tab<-table(A.stats)
A.vals<-round(as.numeric(names(A.tab)),5)
A.probs<-as.numeric(A.tab)/sum(A.tab)
outp$p.val<-sum(A.probs[A.vals>=round(outp$obs.stat,5)])
}
}
if(outp$method=="Monte Carlo"){
outp$p.val<-0
for(i in 1:n.mc){
mc.perm<-sample(possible.ranks)
if(A.calc(mc.perm)>=outp$obs.stat){
outp$p.val=outp$p.val+1/n.mc
}
}
}
}
class(outp)<-"NSM3Ch6p"
outp
}
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