R/223.CoverageProb_CC_internal.R

In proportion: Inference on Single Binomial Proportion and Bayesian Computations

##### 1.CC-WALD-Coverage Probability
gcovpCWD<-function(n,alp,c,a,b,t1,t2)
{
  ####INPUT n
  x=0:n
  k=n+1

  ####INITIALIZATIONS
  pCW=0
  qCW=0
  seCW=0
  LCW=0
  UCW=0
  s=5000								#Simulation run to generate hypothetical p
  cpCW=matrix(0,k,s)
  ctCW=matrix(0,k,s)							#Cover Pbty quantity in sum
  cppCW=0								#Coverage probabilty
  ctr=0
  ###CRITICAL VALUES
  cv=qnorm(1-(alp/2), mean = 0, sd = 1)
  #WALD METHOD
  for(i in 1:k)
  {
    pCW[i]=x[i]/n
    qCW[i]=1-pCW[i]
    seCW[i]=sqrt(pCW[i]*qCW[i]/n)
    LCW[i]=pCW[i]-((cv*seCW[i])+c)
    UCW[i]=pCW[i]+((cv*seCW[i])+c)
    if(LCW[i]<0) LCW[i]=0
    if(UCW[i]>1) UCW[i]=1
  }
  ####COVERAGE PROBABILITIES
  hp=sort(rbeta(s,a,b),decreasing = FALSE)	#HYPOTHETICAL "p"
  for (j in 1:s)
  {
    for(i in 1:k)
    {
      if(hp[j] > LCW[i] && hp[j] < UCW[i])
      {
        cpCW[i,j]=dbinom(i-1, n,hp[j])
        ctCW[i,j]=1
      }
    }
    cppCW[j]=sum(cpCW[,j])
    if(t1<cppCW[j]&&cppCW[j]<t2) ctr=ctr+1		#tolerance for cov prob - user defined
  }
  CPCW=data.frame(hp,cp=cppCW,method="Continuity corrected Wald")
  # windows()
  # plot(hp,cppCW,type="l",xlab="p",ylab="Coverage Probability",main="Wald_CC")
  # abline(h=1-(alp), lty=2)
  return(CPCW)
}

##### 2.CC-SCORE - Coverage Probability
gcovpCSC<-function(n,alp,c,a,b,t1,t2)
{
  ####INPUT n
  x=0:n
  k=n+1
  ####INITIALIZATIONS
  pCS=0
  qCS=0
  seCS_L=0
  seCS_U=0
  LCS=0
  UCS=0
  s=5000								#Simulation run to generate hypothetical p
  cpCS=matrix(0,k,s)
  ctCS=matrix(0,k,s)							#Cover Pbty quantity in sum
  cppCS=0								#Coverage probabilty
  ctr=0

  ###CRITICAL VALUES
  cv=qnorm(1-(alp/2), mean = 0, sd = 1)
  cv1=(cv^2)/(2*n)
  cv2=cv/(2*n)

  #SCORE (WILSON) METHOD
  for(i in 1:k)
  {
    pCS[i]=x[i]/n
    qCS[i]=1-pCS[i]
    seCS_L[i]=sqrt((cv^2)-(4*n*(c+c^2))+(4*n*pCS[i]*(1-pCS[i]+(2*c))))	#Sq. root term of LL
    seCS_U[i]=sqrt((cv^2)+(4*n*(c-c^2))+(4*n*pCS[i]*(1-pCS[i]-(2*c))))	#Sq. root term of LL
    LCS[i]=(n/(n+(cv)^2))*((pCS[i]-c+cv1)-(cv2*seCS_L[i]))
    UCS[i]=(n/(n+(cv)^2))*((pCS[i]+c+cv1)+(cv2*seCS_U[i]))
    if(LCS[i]<0) LCS[i]=0
    if(UCS[i]>1) UCS[i]=1
  }
  ####COVERAGE PROBABILITIES
  hp=sort(rbeta(s,a,b),decreasing = FALSE)	#HYPOTHETICAL "p"
  for (j in 1:s)
  {
    for(i in 1:k)
    {
      if(hp[j] > LCS[i] && hp[j] < UCS[i])
      {
        cpCS[i,j]=dbinom(i-1, n,hp[j])
        ctCS[i,j]=1
      }
    }
    cppCS[j]=sum(cpCS[,j])						#Coverage Probability
    if(t1<cppCS[j]&&cppCS[j]<t2) ctr=ctr+1		#tolerance for cov prob - user defined
  }
  CPCS=data.frame(hp,cp=cppCS,method="Continuity corrected Wilson")
  # windows()
  # plot(hp,cppCS,type="l",xlab="p",ylab="Coverage Probability",main="Wilson_CC")
  # abline(h=1-(alp), lty=2)
  return(CPCS)
}


##### 3.CC-ARC SINE - Coverage Probability
gcovpCAS<-function(n,alp,c,a,b,t1,t2)
{
  ####INPUT n
  x=0:n
  k=n+1
  ####INITIALIZATIONS
  pCA=0
  qCA=0
  seCA=0
  LCA=0
  UCA=0
  s=5000								#Simulation run to generate hypothetical p
  cpCA=matrix(0,k,s)
  ctCA=matrix(0,k,s)							#Cover Pbty quantity in sum
  cppCA=0									#Coverage probabilty
  ctr=0

  ###CRITICAL VALUES
  cv=qnorm(1-(alp/2), mean = 0, sd = 1)
  #ARC-SINE METHOD
  for(i in 1:k)
  {
    pCA[i]=x[i]/n
    qCA[i]=1-pCA[i]
    seCA[i]=cv/sqrt(4*n)
    LCA[i]=(sin(asin(sqrt(pCA[i]))-seCA[i]-c))^2
    UCA[i]=(sin(asin(sqrt(pCA[i]))+seCA[i]+c))^2
    if(LCA[i]<0) LCA[i]=0
    if(UCA[i]>1) UCA[i]=1
  }
  ####COVERAGE PROBABILITIES
  hp=sort(rbeta(s,a,b),decreasing = FALSE)	#HYPOTHETICAL "p"
  for (j in 1:s)
  {
    for(i in 1:k)
    {
      if(hp[j] > LCA[i] && hp[j] < UCA[i])
      {
        cpCA[i,j]=dbinom(i-1, n,hp[j])
        ctCA[i,j]=1
      }
    }
    cppCA[j]=sum(cpCA[,j])						#Coverage Probability
    if(t1<cppCA[j]&&cppCA[j]<t2) ctr=ctr+1		#tolerance for cov prob - user defined
  }
  CPCA=data.frame(hp,cp=cppCA,method="Continuity corrected ArcSine")
  # windows()
  # plot(hp,cppCA,type="l",xlab="p",ylab="Coverage Probability",main="Arc Sine_CC")
  # abline(h=1-(alp), lty=2)
  return(CPCA)
}
##### 4.LOGIT-WALD - Coverage Probability
gcovpCLT<-function(n,alp,c,a,b,t1,t2)
{
  ####INPUT n
  x=0:n
  k=n+1
  ####INITIALIZATIONS
  pCLT=0
  qCLT=0
  seCLT=0
  lgit=0
  LCLT=0
  UCLT=0
  s=5000								#Simulation run to generate hypothetical p
  cpCLT=matrix(0,k,s)
  ctCLT=matrix(0,k,s)							#Cover Pbty quantity in sum
  cppCLT=0								#Coverage probabilty
  ctr=0

  ###CRITICAL VALUES
  cv=qnorm(1-(alp/2), mean = 0, sd = 1)
  #LOGIT-WALD METHOD
  pCLT[1]=0
  qCLT[1]=1
  LCLT[1] = 0
  UCLT[1] = 1-((alp/2)^(1/n))

  pCLT[k]=1
  qCLT[k]=0
  LCLT[k]= (alp/2)^(1/n)
  UCLT[k]=1

  lgiti=function(t) exp(t)/(1+exp(t))	#LOGIT INVERSE
  for(j in 1:(k-2))
  {
    pCLT[j+1]=x[j+1]/n
    qCLT[j+1]=1-pCLT[j+1]
    lgit[j+1]=log(pCLT[j+1]/qCLT[j+1])
    seCLT[j+1]=sqrt(pCLT[j+1]*qCLT[j+1]*n)
    LCLT[j+1]=lgiti(lgit[j+1]-(cv/seCLT[j+1])-c)
    UCLT[j+1]=lgiti(lgit[j+1]+(cv/seCLT[j+1])+c)
  }
  for(i in 1:k)
  {
    if(LCLT[i]<0) LCLT[i]=0
    if(UCLT[i]>1) UCLT[i]=1
  }
  ####COVERAGE PROBABILITIES
  hp=sort(rbeta(s,a,b),decreasing = FALSE)	#HYPOTHETICAL "p"
  for (j in 1:s)
  {
    for(i in 1:k)
    {
      if(hp[j] > LCLT[i] && hp[j] < UCLT[i])
      {
        cpCLT[i,j]=dbinom(i-1, n,hp[j])
        ctCLT[i,j]=1
      }
    }
    cppCLT[j]=sum(cpCLT[,j])				#Coverage Probability
    if(t1<cppCLT[j]&&cppCLT[j]<t2) ctr=ctr+1		#tolerance for cov prob - user defined

  }
  CPLT=data.frame(hp,cp=cppCLT,method="Continuity corrected Logit Wald")
  return(CPLT)
}

##### 5. WALD_t - Coverage Probability
gcovpCTW<-function(n,alp,c,a,b,t1,t2)
{
  ####INPUT n
  x=0:n
  k=n+1
  ####INITIALIZATIONS
  pCTW=0
  qCTW=0
  seCTW=0
  LCTW=0
  UCTW=0
  DOF=0
  cv=0
  s=5000								#Simulation run to generate hypothetical p
  cpCTW=matrix(0,k,s)
  ctCTW=matrix(0,k,s)							#Cover Pbty quantity in sum
  cppCTW=0
  ctr=0

  #MODIFIED_t-WALD METHOD
  for(i in 1:k)
  {
    if(x[i]==0||x[i]==n)
    {
      pCTW[i]=(x[i]+2)/(n+4)
      qCTW[i]=1-pCTW[i]
    }else
    {
      pCTW[i]=x[i]/n
      qCTW[i]=1-pCTW[i]
    }
    f1=function(p,n) p*(1-p)/n
    f2=function(p,n) (p*(1-p)/(n^3))+(p+((6*n)-7)*(p^2)+(4*(n-1)*(n-3)*(p^3))-(2*(n-1)*((2*n)-3)*(p^4)))/(n^5)-(2*(p+((2*n)-3)*(p^2)-2*(n-1)*(p^3)))/(n^4)
    DOF[i]=2*((f1(pCTW[i],n))^2)/f2(pCTW[i],n)
    cv[i]=qt(1-(alp/2), df=DOF[i])
    seCTW[i]=cv[i]*sqrt(f1(pCTW[i],n))
    LCTW[i]=pCTW[i]-(seCTW[i]+c)
    UCTW[i]=pCTW[i]+(seCTW[i]+c)
    if(LCTW[i]<0) LCTW[i]=0
    if(UCTW[i]>1) UCTW[i]=1
  }
  ####COVERAGE PROBABILITIES
  hp=sort(rbeta(s,a,b),decreasing = FALSE)	#HYPOTHETICAL "p"
  for (j in 1:s)
  {
    for(i in 1:k)
    {
      if(hp[j] > LCTW[i] && hp[j] < UCTW[i])
      {
        cpCTW[i,j]=dbinom(i-1, n,hp[j])
        ctCTW[i,j]=1
      }
    }
    cppCTW[j]=sum(cpCTW[,j])						#Coverage Probability
    if(t1<cppCTW[j]&&cppCTW[j]<t2) ctr=ctr+1		#tolerance for cov prob - user defined
  }
  CPCTW=data.frame(hp,cp=cppCTW,method="Continuity corrected Wald-T")
  # windows()
  # plot(hp,cppCTW,type="l",xlab="p",ylab="Coverage Probability",main="Logit-Wald_CC")
  # abline(h=1-(alp), lty=2)
  return(CPCTW)
}