R/302.Expec_Leng_BASE_All_Graph.R
In RajeswaranV/proportion: Inference on Single Binomial Proportion and Bayesian Computations
Defines functions
PlotexplLR
PlotexplTW
PlotexplLT
PlotexplAS
PlotexplSC
PlotexplWD
PlotexplAll
PlotexplBA
exlim302u
exlim302l
ncf302
gexplEX
PlotexplEX
Documented in
PlotexplAll
PlotexplAS
PlotexplBA
PlotexplEX
PlotexplLR
PlotexplLT
PlotexplSC
PlotexplTW
PlotexplWD
###################################################################################################
#' Plot for Exact method of expected length calculation
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param e - Exact method indicator in [0, 1] {1: Clopper Pearson, 0.5: Mid P}
#' The input can also be a range of values between 0 and 1.
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of Confidence interval for \code{p} based on inverting equal-tailed
#' binomial tests with null hypothesis \eqn{H0: p = p0} using expected length of the \eqn{n + 1} intervals.
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;e=0.5;a=1;b=1
#' PlotexplEX(n,alp,e,a,b)
#' n=5; alp=0.05;e=1;a=1;b=1 #Clopper-Pearson
#' PlotexplEX(n,alp,e,a,b)
#' n=5; alp=0.05;e=c(0.1,0.5,0.95,1);a=1;b=1 #Range including Mid-p and Clopper-Pearson
#' PlotexplEX(n,alp,e,a,b)
#' }
#' @export
##### 1.EXACT EMTHOD Expected Length for a given n and alpha level
PlotexplEX<-function(n,alp,e,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(e)) stop("'e' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp)>1) stop("'alpha' has to be between 0 and 1")
if (any(e>1) || any(e<0)) stop("'e' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ewEX=NULL
ELEX2=gexplEX(n,alp,e,a,b)
ELEX2$e=as.factor(ELEX2$e)
ggplot2::ggplot(ELEX2, ggplot2::aes(x=hp, y=ewEX, color=e))+
ggplot2::labs(title = "Expected length of Exact method") +
ggplot2::labs(y = "Expected length") +
ggplot2::geom_vline(ggplot2::aes(xintercept=0.5),linetype = 2)+
ggplot2::labs(x = "p") +
ggplot2::geom_line()
}
gexplEX<-function(n,alp,e,a,b)
{
nvar=length(e)
res <- data.frame()
for(i in 1:nvar)
{
lu=ncf302(n,alp,e[i],a,b)
res <- rbind(res,lu)
}
return(res)
}
ncf302<-function(n,alp,e,a,b)
{
####INPUT n
x=0:n
k=n+1
####INITIALIZATIONS
LEX=0
UEX=0
s=5000
LEEX=0 #LENGTH OF INTERVAL
ewiEX=matrix(0,k,s) #Expected length quantity in sum
ewEX=0 #Expected Length
#EXACT METHOD
LEX[1]=0
UEX[1]= 1-((alp/(2*e))^(1/n))
LEX[k]=(alp/(2*e))^(1/n)
UEX[k]=1
LEEX[1]=1-((alp/(2*e))^(1/n))
LEEX[k]=1-((alp/(2*e))^(1/n))
for(i in 1:(k-2))
{
LEX[i+1]=exlim302l(x[i+1],n,alp,e)
UEX[i+1]=exlim302u(x[i+1],n,alp,e)
LEEX[i+1]=UEX[i+1]-LEX[i+1]
}
####Expected Length
hp=sort(stats::rbeta(s,a,b),decreasing = FALSE) #HYPOTHETICAL "p"
for (j in 1:s)
{
for(i in 1:k)
{
ewiEX[i,j]=LEEX[i]*stats::dbinom(i-1, n,hp[j])
}
ewEX[j]=sum(ewiEX[,j]) #Expected Length
}
#sumLEEX=sum(LEEX)
ELEX=data.frame(hp,ewEX,e)
return(ELEX)
}
#####TO FIND LOWER LIMITS
exlim302l=function(x,n,alp,e)
{
z=x-1
y=0:z
f1=function(p) (1-e)*stats::dbinom(x,n,p)+sum(stats::dbinom(y,n,p))-(1-(alp/2))
LEX= stats::uniroot(f1,c(0,1))$root
return(LEX)
}
#####TO FIND UPPER LIMITS
exlim302u=function(x,n,alp,e)
{
z=x-1
y=0:z
f2 = function(p) e*stats::dbinom(x,n,p)+sum(stats::dbinom(y,n,p))-(alp/2)
UEX = stats::uniroot(f2,c(0,1))$root
return(UEX)
}
###############################################################################################################
#' Plot the Bayesian method of expected length calculation
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @param a1 - Beta Prior Parameters for Bayesian estimation
#' @param a2 - Beta Prior Parameters for Bayesian estimation
#' @details Plots of Bayesian Highest Probability Density (HPD) and two tailed
#' intervals using expected length of the \eqn{n + 1}
#' intervals for the Beta - Binomial conjugate prior model for the probability of success \code{p}
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1;a1=1;a2=1
#' PlotexplBA(n,alp,a,b,a1,a2)
#' }
#' @export
##### 8.BAYESIAN Expected Length for a given n and alpha level
PlotexplBA<-function(n,alp,a,b,a1,a2)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if (missing(a1)) stop("'a1' is missing")
if (missing(a2)) stop("'a2' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
if ((class(a1) != "integer") & (class(a1) != "numeric") || length(a1)>1 || a1<0 ) stop("'a1' has to be greater than or equal to 0")
if ((class(a2) != "integer") & (class(a2) != "numeric") || length(a2)>1 || a2<0 ) stop("'a2' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
####INPUT n
x=0:n
k=n+1
####INITIALIZATIONS
LBAQ=0
UBAQ=0
LBAH=0
UBAH=0
s=5000
LEBAQ=0 #LENGTH OF INTERVAL
LEBAH=0
ewiBAQ=matrix(0,k,s) #Expected length quantity in sum
ewBAQ=0
ewiBAH=matrix(0,k,s) #Expected length quantity in sum
ewBAH=0 #Expected Length
#library(TeachingDemos) #To get HPDs
for(i in 1:k)
{
#Quantile Based Intervals
LBAQ[i]=stats::qbeta(alp/2,x[i]+a1,n-x[i]+a2)
UBAQ[i]=stats::qbeta(1-(alp/2),x[i]+a1,n-x[i]+a2)
LBAH[i]=TeachingDemos::hpd(stats::qbeta,shape1=x[i]+a1,shape2=n-x[i]+a2,conf=1-alp)[1]
UBAH[i]=TeachingDemos::hpd(stats::qbeta,shape1=x[i]+a1,shape2=n-x[i]+a2,conf=1-alp)[2]
LEBAQ[i]=UBAQ[i]-LBAQ[i]
LEBAH[i]=UBAH[i]-LBAH[i]
}
#sumLEBAQ=sum(LEBAQ)
#sumLEBAH=sum(LEBAH)
####Expected Length
hp=sort(stats::rbeta(s,a,b),decreasing = FALSE) #HYPOTHETICAL "p"
for (j in 1:s)
{
for(i in 1:k)
{
ewiBAQ[i,j]=LEBAQ[i]*stats::dbinom(i-1, n,hp[j])
ewiBAH[i,j]=LEBAH[i]*stats::dbinom(i-1, n,hp[j])
}
ewBAQ[j]=sum(ewiBAQ[,j])
ewBAH[j]=sum(ewiBAH[,j]) #Expected Length
}
ELBAQ=data.frame(hp,ew=ewBAQ,method="Quantile")
ELBAH=data.frame(hp,ew=ewBAH,method="HPD")
df.ba=rbind(ELBAQ,ELBAH)
ggplot2::ggplot(df.ba, ggplot2::aes(x=hp, y=ew))+
ggplot2::labs(title = "Expected length of Bayesian Quantile & HPD based methods") +
ggplot2::labs(y = "Expected Length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(ggplot2::aes(color=method)) +
ggplot2::geom_vline(ggplot2::aes(xintercept=0.5),linetype = 2)+
ggplot2::scale_colour_manual(name='Heading',
values=c('Quantile' ='black',
'HPD' = 'red'),
guide='legend') +
ggplot2::guides(colour = ggplot2::guide_legend(override.aes = list(linetype=c(1,1))))
}
#############################################################################################################
#' Plots the Expected length using 6 base methods (Wald, Wald-T, Likelihood, Score, Logit-Wald, ArcSine)
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details The plots using 6 base methods (Wald, Wald-T, Likelihood, Score, Logit-Wald, ArcSine) for the expected length of \code{n} given \code{alp}, \code{h}, \code{a}, \code{b}, \code{t1} and \code{t2} using all the methods
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n= 10; alp=0.05; a=1;b=1;
#' PlotexplAll(n,alp,a,b)
#' }
#' @export
##### 9.All methods - Expected length
PlotexplAll<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
#### Calling functions and creating df
df.eall= explAll(n,alp,a,b)
ggplot2::ggplot(df.eall, ggplot2::aes(x=hp, y=ew))+
ggplot2::labs(title = "Expected length of 6 base methods") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(ggplot2::aes(color=method)) +
ggplot2::geom_vline(ggplot2::aes(xintercept=0.5),linetype = 1)
}
#############################################################################################################
#' Plots the expected length for Wald method
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Evaluation of Wald-type intervals using sum of length of the \eqn{n + 1}
#' intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplWD(n,alp,a,b)
#' }
#' @export
##### 1.WALD sum of length for a given n and alpha level
PlotexplWD<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.wd= gexplWD(n,alp,a,b)
ddf.wd = lengthWD(n,alp,a,b)
df.wd$gMean=ddf.wd$explMean
df.wd$gMax=ddf.wd$explMax
df.wd$gUL=ddf.wd$explMean+ddf.wd$explSD
df.wd$gLL=ddf.wd$explMean-ddf.wd$explSD
ggplot2::ggplot(data=df.wd, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Wald method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots the expected length for Score method
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of score test approach using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplSC(n,alp,a,b)
#' }
#' @export
##### 2.SCORE - sum of length for a given n and alpha level
PlotexplSC<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.sc= gexplSC(n,alp,a,b)
ddf.sc = lengthSC(n,alp,a,b)
df.sc$gMean=ddf.sc$explMean
df.sc$gMax=ddf.sc$explMax
df.sc$gUL=ddf.sc$explMean+ddf.sc$explSD
df.sc$gLL=ddf.sc$explMean-ddf.sc$explSD
ggplot2::ggplot(data=df.sc, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Score method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots ArcSine method of expected length
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of Wald-type interval for the arcsine transformation of the parameter
#' \code{p} using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplAS(n,alp,a,b)
#' }
#' @export
##### 3. ARC SINE - sum of length for a given n and alpha level
PlotexplAS<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.as= gexplAS(n,alp,a,b)
ddf.as = lengthAS(n,alp,a,b)
df.as$gMean=ddf.as$explMean
df.as$gMax=ddf.as$explMax
df.as$gUL=ddf.as$explMean+ddf.as$explSD
df.as$gLL=ddf.as$explMean-ddf.as$explSD
ggplot2::ggplot(data=df.as, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of ArcSine method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots Logit Wald method of expected length
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of Wald-type interval based on the logit
#' transformation of \code{p} using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplLT(n,alp,a,b)
#' }
#' @export
##### 4.LOGIT-WALD - sum of length for a given n and alpha level
PlotexplLT<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.lt= gexplLT(n,alp,a,b)
ddf.lt = lengthLT(n,alp,a,b)
df.lt$gMean=ddf.lt$explMean
df.lt$gMax=ddf.lt$explMax
df.lt$gUL=ddf.lt$explMean+ddf.lt$explSD
df.lt$gLL=ddf.lt$explMean-ddf.lt$explSD
ggplot2::ggplot(data=df.lt, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Logit Wald method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots Wald-T method of expected length
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of approximate method based on a t_approximation of the
#' standardized point estimator using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplTW(n,alp,a,b)
#' }
#' @export
##### 5.t-WALD - sum of length for a given n and alpha level
PlotexplTW<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.tw= gexplTW(n,alp,a,b)
ddf.tw = lengthTW(n,alp,a,b)
df.tw$gMean=ddf.tw$explMean
df.tw$gMax=ddf.tw$explMax
df.tw$gUL=ddf.tw$explMean+ddf.tw$explSD
df.tw$gLL=ddf.tw$explMean-ddf.tw$explSD
ggplot2::ggplot(data=df.tw, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Wald-T method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots likelihood Ratio method of expected length
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of Likelihood ratio limits using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplLR(n,alp,a,b)
#' }
#' @export
#####6.LIKELIHOOD RATIO - sum of length for a given n and alpha level
PlotexplLR<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.lr= gexplLR(n,alp,a,b)
ddf.lr = lengthLR(n,alp,a,b)
df.lr$gMean=ddf.lr$explMean
df.lr$gMax=ddf.lr$explMax
df.lr$gUL=ddf.lr$explMean+ddf.lr$explSD
df.lr$gLL=ddf.lr$explMean-ddf.lr$explSD
ggplot2::ggplot(data=df.lr, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Likelihood Ratio method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
RajeswaranV/proportion documentation built on June 17, 2022, 9:11 a.m.
R Package Documentation
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Defines functions PlotexplLR PlotexplTW PlotexplLT PlotexplAS PlotexplSC PlotexplWD PlotexplAll PlotexplBA exlim302u exlim302l ncf302 gexplEX PlotexplEX
Documented in PlotexplAll PlotexplAS PlotexplBA PlotexplEX PlotexplLR PlotexplLT PlotexplSC PlotexplTW PlotexplWD
###################################################################################################
#' Plot for Exact method of expected length calculation
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param e - Exact method indicator in [0, 1] {1: Clopper Pearson, 0.5: Mid P}
#' The input can also be a range of values between 0 and 1.
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of Confidence interval for \code{p} based on inverting equal-tailed
#' binomial tests with null hypothesis \eqn{H0: p = p0} using expected length of the \eqn{n + 1} intervals.
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;e=0.5;a=1;b=1
#' PlotexplEX(n,alp,e,a,b)
#' n=5; alp=0.05;e=1;a=1;b=1 #Clopper-Pearson
#' PlotexplEX(n,alp,e,a,b)
#' n=5; alp=0.05;e=c(0.1,0.5,0.95,1);a=1;b=1 #Range including Mid-p and Clopper-Pearson
#' PlotexplEX(n,alp,e,a,b)
#' }
#' @export
##### 1.EXACT EMTHOD Expected Length for a given n and alpha level
PlotexplEX<-function(n,alp,e,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(e)) stop("'e' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp)>1) stop("'alpha' has to be between 0 and 1")
if (any(e>1) || any(e<0)) stop("'e' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ewEX=NULL
ELEX2=gexplEX(n,alp,e,a,b)
ELEX2$e=as.factor(ELEX2$e)
ggplot2::ggplot(ELEX2, ggplot2::aes(x=hp, y=ewEX, color=e))+
ggplot2::labs(title = "Expected length of Exact method") +
ggplot2::labs(y = "Expected length") +
ggplot2::geom_vline(ggplot2::aes(xintercept=0.5),linetype = 2)+
ggplot2::labs(x = "p") +
ggplot2::geom_line()
}
gexplEX<-function(n,alp,e,a,b)
{
nvar=length(e)
res <- data.frame()
for(i in 1:nvar)
{
lu=ncf302(n,alp,e[i],a,b)
res <- rbind(res,lu)
}
return(res)
}
ncf302<-function(n,alp,e,a,b)
{
####INPUT n
x=0:n
k=n+1
####INITIALIZATIONS
LEX=0
UEX=0
s=5000
LEEX=0 #LENGTH OF INTERVAL
ewiEX=matrix(0,k,s) #Expected length quantity in sum
ewEX=0 #Expected Length
#EXACT METHOD
LEX[1]=0
UEX[1]= 1-((alp/(2*e))^(1/n))
LEX[k]=(alp/(2*e))^(1/n)
UEX[k]=1
LEEX[1]=1-((alp/(2*e))^(1/n))
LEEX[k]=1-((alp/(2*e))^(1/n))
for(i in 1:(k-2))
{
LEX[i+1]=exlim302l(x[i+1],n,alp,e)
UEX[i+1]=exlim302u(x[i+1],n,alp,e)
LEEX[i+1]=UEX[i+1]-LEX[i+1]
}
####Expected Length
hp=sort(stats::rbeta(s,a,b),decreasing = FALSE) #HYPOTHETICAL "p"
for (j in 1:s)
{
for(i in 1:k)
{
ewiEX[i,j]=LEEX[i]*stats::dbinom(i-1, n,hp[j])
}
ewEX[j]=sum(ewiEX[,j]) #Expected Length
}
#sumLEEX=sum(LEEX)
ELEX=data.frame(hp,ewEX,e)
return(ELEX)
}
#####TO FIND LOWER LIMITS
exlim302l=function(x,n,alp,e)
{
z=x-1
y=0:z
f1=function(p) (1-e)*stats::dbinom(x,n,p)+sum(stats::dbinom(y,n,p))-(1-(alp/2))
LEX= stats::uniroot(f1,c(0,1))$root
return(LEX)
}
#####TO FIND UPPER LIMITS
exlim302u=function(x,n,alp,e)
{
z=x-1
y=0:z
f2 = function(p) e*stats::dbinom(x,n,p)+sum(stats::dbinom(y,n,p))-(alp/2)
UEX = stats::uniroot(f2,c(0,1))$root
return(UEX)
}
###############################################################################################################
#' Plot the Bayesian method of expected length calculation
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @param a1 - Beta Prior Parameters for Bayesian estimation
#' @param a2 - Beta Prior Parameters for Bayesian estimation
#' @details Plots of Bayesian Highest Probability Density (HPD) and two tailed
#' intervals using expected length of the \eqn{n + 1}
#' intervals for the Beta - Binomial conjugate prior model for the probability of success \code{p}
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1;a1=1;a2=1
#' PlotexplBA(n,alp,a,b,a1,a2)
#' }
#' @export
##### 8.BAYESIAN Expected Length for a given n and alpha level
PlotexplBA<-function(n,alp,a,b,a1,a2)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if (missing(a1)) stop("'a1' is missing")
if (missing(a2)) stop("'a2' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
if ((class(a1) != "integer") & (class(a1) != "numeric") || length(a1)>1 || a1<0 ) stop("'a1' has to be greater than or equal to 0")
if ((class(a2) != "integer") & (class(a2) != "numeric") || length(a2)>1 || a2<0 ) stop("'a2' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
####INPUT n
x=0:n
k=n+1
####INITIALIZATIONS
LBAQ=0
UBAQ=0
LBAH=0
UBAH=0
s=5000
LEBAQ=0 #LENGTH OF INTERVAL
LEBAH=0
ewiBAQ=matrix(0,k,s) #Expected length quantity in sum
ewBAQ=0
ewiBAH=matrix(0,k,s) #Expected length quantity in sum
ewBAH=0 #Expected Length
#library(TeachingDemos) #To get HPDs
for(i in 1:k)
{
#Quantile Based Intervals
LBAQ[i]=stats::qbeta(alp/2,x[i]+a1,n-x[i]+a2)
UBAQ[i]=stats::qbeta(1-(alp/2),x[i]+a1,n-x[i]+a2)
LBAH[i]=TeachingDemos::hpd(stats::qbeta,shape1=x[i]+a1,shape2=n-x[i]+a2,conf=1-alp)[1]
UBAH[i]=TeachingDemos::hpd(stats::qbeta,shape1=x[i]+a1,shape2=n-x[i]+a2,conf=1-alp)[2]
LEBAQ[i]=UBAQ[i]-LBAQ[i]
LEBAH[i]=UBAH[i]-LBAH[i]
}
#sumLEBAQ=sum(LEBAQ)
#sumLEBAH=sum(LEBAH)
####Expected Length
hp=sort(stats::rbeta(s,a,b),decreasing = FALSE) #HYPOTHETICAL "p"
for (j in 1:s)
{
for(i in 1:k)
{
ewiBAQ[i,j]=LEBAQ[i]*stats::dbinom(i-1, n,hp[j])
ewiBAH[i,j]=LEBAH[i]*stats::dbinom(i-1, n,hp[j])
}
ewBAQ[j]=sum(ewiBAQ[,j])
ewBAH[j]=sum(ewiBAH[,j]) #Expected Length
}
ELBAQ=data.frame(hp,ew=ewBAQ,method="Quantile")
ELBAH=data.frame(hp,ew=ewBAH,method="HPD")
df.ba=rbind(ELBAQ,ELBAH)
ggplot2::ggplot(df.ba, ggplot2::aes(x=hp, y=ew))+
ggplot2::labs(title = "Expected length of Bayesian Quantile & HPD based methods") +
ggplot2::labs(y = "Expected Length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(ggplot2::aes(color=method)) +
ggplot2::geom_vline(ggplot2::aes(xintercept=0.5),linetype = 2)+
ggplot2::scale_colour_manual(name='Heading',
values=c('Quantile' ='black',
'HPD' = 'red'),
guide='legend') +
ggplot2::guides(colour = ggplot2::guide_legend(override.aes = list(linetype=c(1,1))))
}
#############################################################################################################
#' Plots the Expected length using 6 base methods (Wald, Wald-T, Likelihood, Score, Logit-Wald, ArcSine)
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details The plots using 6 base methods (Wald, Wald-T, Likelihood, Score, Logit-Wald, ArcSine) for the expected length of \code{n} given \code{alp}, \code{h}, \code{a}, \code{b}, \code{t1} and \code{t2} using all the methods
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n= 10; alp=0.05; a=1;b=1;
#' PlotexplAll(n,alp,a,b)
#' }
#' @export
##### 9.All methods - Expected length
PlotexplAll<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
#### Calling functions and creating df
df.eall= explAll(n,alp,a,b)
ggplot2::ggplot(df.eall, ggplot2::aes(x=hp, y=ew))+
ggplot2::labs(title = "Expected length of 6 base methods") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(ggplot2::aes(color=method)) +
ggplot2::geom_vline(ggplot2::aes(xintercept=0.5),linetype = 1)
}
#############################################################################################################
#' Plots the expected length for Wald method
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Evaluation of Wald-type intervals using sum of length of the \eqn{n + 1}
#' intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplWD(n,alp,a,b)
#' }
#' @export
##### 1.WALD sum of length for a given n and alpha level
PlotexplWD<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.wd= gexplWD(n,alp,a,b)
ddf.wd = lengthWD(n,alp,a,b)
df.wd$gMean=ddf.wd$explMean
df.wd$gMax=ddf.wd$explMax
df.wd$gUL=ddf.wd$explMean+ddf.wd$explSD
df.wd$gLL=ddf.wd$explMean-ddf.wd$explSD
ggplot2::ggplot(data=df.wd, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Wald method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots the expected length for Score method
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of score test approach using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplSC(n,alp,a,b)
#' }
#' @export
##### 2.SCORE - sum of length for a given n and alpha level
PlotexplSC<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.sc= gexplSC(n,alp,a,b)
ddf.sc = lengthSC(n,alp,a,b)
df.sc$gMean=ddf.sc$explMean
df.sc$gMax=ddf.sc$explMax
df.sc$gUL=ddf.sc$explMean+ddf.sc$explSD
df.sc$gLL=ddf.sc$explMean-ddf.sc$explSD
ggplot2::ggplot(data=df.sc, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Score method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots ArcSine method of expected length
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of Wald-type interval for the arcsine transformation of the parameter
#' \code{p} using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplAS(n,alp,a,b)
#' }
#' @export
##### 3. ARC SINE - sum of length for a given n and alpha level
PlotexplAS<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.as= gexplAS(n,alp,a,b)
ddf.as = lengthAS(n,alp,a,b)
df.as$gMean=ddf.as$explMean
df.as$gMax=ddf.as$explMax
df.as$gUL=ddf.as$explMean+ddf.as$explSD
df.as$gLL=ddf.as$explMean-ddf.as$explSD
ggplot2::ggplot(data=df.as, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of ArcSine method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots Logit Wald method of expected length
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of Wald-type interval based on the logit
#' transformation of \code{p} using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplLT(n,alp,a,b)
#' }
#' @export
##### 4.LOGIT-WALD - sum of length for a given n and alpha level
PlotexplLT<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.lt= gexplLT(n,alp,a,b)
ddf.lt = lengthLT(n,alp,a,b)
df.lt$gMean=ddf.lt$explMean
df.lt$gMax=ddf.lt$explMax
df.lt$gUL=ddf.lt$explMean+ddf.lt$explSD
df.lt$gLL=ddf.lt$explMean-ddf.lt$explSD
ggplot2::ggplot(data=df.lt, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Logit Wald method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots Wald-T method of expected length
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of approximate method based on a t_approximation of the
#' standardized point estimator using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplTW(n,alp,a,b)
#' }
#' @export
##### 5.t-WALD - sum of length for a given n and alpha level
PlotexplTW<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.tw= gexplTW(n,alp,a,b)
ddf.tw = lengthTW(n,alp,a,b)
df.tw$gMean=ddf.tw$explMean
df.tw$gMax=ddf.tw$explMax
df.tw$gUL=ddf.tw$explMean+ddf.tw$explSD
df.tw$gLL=ddf.tw$explMean-ddf.tw$explSD
ggplot2::ggplot(data=df.tw, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Wald-T method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
#############################################################################################################
#' Plots likelihood Ratio method of expected length
#' @param n - Number of trials
#' @param alp - Alpha value (significance level required)
#' @param a - Beta parameters for hypo "p"
#' @param b - Beta parameters for hypo "p"
#' @details Plot of Likelihood ratio limits using sum of length of the \eqn{n + 1} intervals
#' @family Expected length of base methods
#' @examples
#' \dontrun{
#' n=5; alp=0.05;a=1;b=1
#' PlotexplLR(n,alp,a,b)
#' }
#' @export
#####6.LIKELIHOOD RATIO - sum of length for a given n and alpha level
PlotexplLR<-function(n,alp,a,b)
{
if (missing(n)) stop("'n' is missing")
if (missing(alp)) stop("'alpha' is missing")
if (missing(a)) stop("'a' is missing")
if (missing(b)) stop("'b' is missing")
if ((class(n) != "integer") & (class(n) != "numeric") || length(n) >1|| n<=0 ) stop("'n' has to be greater than 0")
if (alp>1 || alp<0 || length(alp) >1) stop("'alpha' has to be between 0 and 1")
if ((class(a) != "integer") & (class(a) != "numeric") || length(a)>1 || a<0 ) stop("'a' has to be greater than or equal to 0")
if ((class(b) != "integer") & (class(b) != "numeric") || length(b)>1 || b<0 ) stop("'b' has to be greater than or equal to 0")
hp=ew=method=gMean=gMax=gLL=gUL=NULL
df.lr= gexplLR(n,alp,a,b)
ddf.lr = lengthLR(n,alp,a,b)
df.lr$gMean=ddf.lr$explMean
df.lr$gMax=ddf.lr$explMax
df.lr$gUL=ddf.lr$explMean+ddf.lr$explSD
df.lr$gLL=ddf.lr$explMean-ddf.lr$explSD
ggplot2::ggplot(data=df.lr, mapping=ggplot2::aes(x=hp, y=ew)) +
ggplot2::labs(title = "Expected length of Likelihood Ratio method") +
ggplot2::labs(y = "Expected length") +
ggplot2::labs(x = "p") +
ggplot2::geom_line(mapping=ggplot2::aes(colour=method), show_guide = TRUE) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMean, fill="Mean"),color="orange" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gMax, fill="Max"),color="blue" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gLL, fill="Lower Limit"),color="cyan4" ) +
ggplot2::geom_hline(mapping=ggplot2::aes(yintercept=gUL, fill="Upper Limit"),color="brown" ) +
ggplot2::scale_color_hue("Method") +
ggplot2::scale_fill_manual(
"Metric lines", values=c(1,1,1,1),
guide=ggplot2::guide_legend(override.aes = list(colour=c("orange", "blue", "cyan4","brown"))),
labels=c("Mean", "Max", "Lower Limit(Mean- 1SD)", "Upper Limit(Mean + 1SD)"))
}
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