R/cUmbrPU.R

In NSM3: Functions and Datasets to Accompany Hollander, Wolfe, and Chicken - Nonparametric Statistical Methods, Third Edition

cUmbrPU<-function(alpha,n, method=NA, n.mc=10000){
  outp<-list()
  outp$stat.name<-paste("Mack-Wolfe Peak Unknown A*(p-hat)")
    
  if(alpha>1||alpha<0||!is.numeric(alpha)){
      cat('Error: Check alpha value! \n')
      return(alpha)
  } 	  

  outp$alpha<-alpha
  outp$n<-n 
  outp$n.mc<-n.mc
  N<-sum(n)
  k<-length(n)
  g<-rep(1:k,outp$n)	 

  ##When the user doesn't give us any indication of which method to use, try to pick one.
  if(is.na(method)){
      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"
      }
  }
  #####################################################################
  
  outp$method<-method
  
  cumulative.sizes<-cumsum(outp$n)
  
  peak.picker<-function(obs.data){
    tmp<-numeric(k)
    for(i in 1:k){
      first<-obs.data[max(1,cumulative.sizes[i-1]+1):cumulative.sizes[i]]
      second<-obs.data[-(max(1,cumulative.sizes[i-1]+1):cumulative.sizes[i])]
      options(warn = (-1));  
      tmp[i]<-(wilcox.test(first,second)$statistic-(outp$n[i]*(cumulative.sizes[k]-outp$n[i])/2))/sqrt(
        outp$n[i]*(cumulative.sizes[k]-outp$n[i])*(cumulative.sizes[k]+1)/12)
      options(warn = (0));
    }
    initial.peak<-peak<-which.max(tmp)
    
    #check for multiple peaks;
    if(1-sum(tmp[-peak]==tmp[peak])){
      return(peak)
    }
    for(i in (initial.peak+1):k){
      if(tmp[i]==tmp[initial.peak]){
        peak<-c(peak,i)
      }
    }
    return(peak)
  }
  
  A.star.calc<-function(obs.data,peak){
    N1<-cumulative.sizes[peak]
    N2<-(cumulative.sizes[k]-max(0,cumulative.sizes[peak-1]))
    exp.Ap<-(N1^2+N2^2-sum(outp$n^2)-outp$n[peak]^2)/4
    var.Ap<-1/72*(2*(N1^3+N2^3)+3*(N1^2+N2^2)-sum(outp$n^2*(2*outp$n+3))
                  -outp$n[peak]^2*(2*outp$n[peak]+3)+12*outp$n[peak]*N1*N2-12*outp$n[peak]^2*cumulative.sizes[k])
    
    
    U.vec<-numeric((peak*(peak-1)+(k-peak+1)*(k-peak))/2)
    U.calc<-function(i,j){
      wilcox.test(obs.data[g==i],obs.data[g==j])$statistic
    }
    
    count<-0
    if(peak>1){
    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));
      }
    }
    }
    if(peak<k){
    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)-exp.Ap)/sqrt(var.Ap)
    
  }
  
  PU.calc<-function(obs.data){
    tmp.peak<-peak.picker(obs.data)
    num.peak<-length(tmp.peak)
    tmp.stat<-numeric(num.peak)
    if(num.peak==1){
      tmp.stat<-A.star.calc(obs.data,tmp.peak)
    }
    if(num.peak>1){
      for(i in 1:num.peak){
        tmp.stat[i]<-A.star.calc(obs.data,tmp.peak[i])
      }
    }
    mean(tmp.stat)
  }
    
  possible.ranks<-1:N
  
  if(outp$method=="Asymptotic"){
    warning("The asymptotic distribution for this statistic is unknown!")
    outp$method=="Monte Carlo"
  }
  if(outp$method=="Exact"){
    possible.orders<-multComb(outp$n)
    possible.perms<-t(apply(possible.orders,1,function(x) possible.ranks[x]))
    
    A.stats<-apply(possible.perms,1,PU.calc)
    A.tab<-table(A.stats)
    A.vals<-round(as.numeric(names(A.tab)),5)
    A.probs<-as.numeric(A.tab)/sum(A.tab)
    A.dist<-cbind(A.vals,A.probs)
    #From cJCK.R;
    upper.tails<-cbind(rev(A.vals),cumsum(rev(A.probs)))
    outp$cutoff.U<-upper.tails[max(which(upper.tails[,2]<=alpha)),1]
    outp$true.alpha.U<-upper.tails[max(which(upper.tails[,2]<=alpha)),2]  
   }

  if(outp$method=="Monte Carlo"){
    mc.dist<-numeric(n.mc)
    for(i in 1:n.mc){
      mc.perm<-sample(possible.ranks)
      mc.dist[i]<-round(PU.calc(mc.perm),10)
    }
	mc.values<-sort(unique(mc.dist))
	mc.probs<-as.numeric(table(mc.dist))/n.mc
	A.dist<-cbind(mc.values,mc.probs)

    #From cJCK.R;
      upper.tails<-cbind(rev(mc.values),cumsum(rev(mc.probs)))
      outp$cutoff.U<-upper.tails[max(which(upper.tails[,2]<=alpha)),1]
      outp$true.alpha.U<-upper.tails[max(which(upper.tails[,2]<=alpha)),2]
  }

  class(outp)<-"NSM3Ch6c"
  outp
}