bootDiffmeanFunc is a support function for bootstrapping method. Its main task is to infer meandifference confidence intervals of distributions for all categories except the first category in idx (idx[2],idx[3],...) minus a target category (idx[1]).
bootDiffmeanFunc(Group, Values, idx, reps, ci, methodType)
Group 
is a vector of categories of each real number in Values 
Values 
is a vector of realnumber values 
idx 
is an order list of categories; idx[1] is a target category while others (idx[2],idx[3],...) are compared against idx[1] in order to compute meandifference confidence intervals. 
reps 
is a number of time of sampling with replacement in a bootstrapping method. 
ci 
is a level of confidence interval inferred. 
methodType 
is a type of method for inferring confidence intervals. It is a parameter of two.boot function of simpleboot package. 
This function returns a list of meandifference confidence intervals of categories idx[2],idx[3],... minus category idx[1].
result
a list of objects that contains meandifference confidence intervals of pairs of distributions.
It contains meandifference confidence intervals of categories idx[2],idx[3],... minus category idx[1].
checkSim3Res is a support function for checking whether an adjacency matrix of inferred
a dominantdistribution network adjMat
is corrected w.r.t. generator SimNonNormalDist().
checkSim3Res(adjMat, flag = 0)
adjMat 
is an adjacency matrix of inferred a dominantdistribution network. 
flag 
is a flag of matrix. It should be set only to shift the low of matrix for comparison. 
This function returns precision, recall, and F1score of inferred adjacency matrix.
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Compare the inferred adjacency matrix with the ground truth
checkSim3Res(adjMat=resultObj$adjMat)
EDOIF is a nonparametric framework based on Estimation Statistics principle. Its main purpose is to infer orders of empirical distributions from different categories base on a probability of finding a value in one distribution that greater than the expectation of another distribution.
Given a set of orderedpair of realcategory values the framework is capable of 1) inferring orders of domination of categories and representing orders in the form of a graph; 2) estimating magnitude of difference between a pair of categories in forms of confidence intervals; and 3) visualizing domination orders and magnitudes of difference of categories.
EDOIF(Values, Group, bootT, alpha, methodType)
Values 
is a vector of realnumber values 
Group 
is a vector of categories of each real number in Values 
bootT 
is a number of times of sample with replacement for bootstrapping. The default is 1000. It must be above zero 
alpha 
is a significance level using in both confidence intervals and ordering inference it has the range [0,1]. The default is 0.05. 
methodType 
is an option for bootstrapping methods:either "perc" or "bca". The "perc" is the default option. 
This class constructor returns an object of EDOIF class.
obj
an object of EDOIF class that contains the results of ordering inference
that can be print in text mode (print(obj)) or graphic mode (plot(obj)).
The obj
consists of the following variables
Values , Group

The main inputs of the framework. They are the double and character vectors respectively. 
bootT , alpha , methodType

The number of bootstrapping, significance level, and bootstrapping method parameters. 
sortedGroupList 
A list of names of categories ascendingly ordered by their means. 
sortedmeanList 
A list of means of categories that are ascendingly ordered. 
MegDiffList[[i]] 
Mean difference confidence intervals and related information of all categories that have higher means than sortedGroupList[i] category. 
confInvsList[i , ]

A mean confidence interval of sortedGroupList[i] category. confInvsList[i,1] is a lower bound and confInvsList[i,2] is an upper bound. 
adjMat[i , j]

An element of adjacency matrix: one if sortedGroupList[j] category dominates sortedGroupList[i] using MannWhitney test, otherwise zero. 
pValMat[i , j]

A pvalue of MannWhitney test for adjMat[i,j]. 
adjDiffMat[i , j]

A lower bound of confidence interval of mean difference for sortedGroupList[j] minus sortedGroupList[i] using methodType bootstrap. 
adjBootMat[i , j]

One if adjDiffMat[i,j] is positive, otherwise, zero. 
netDen 
A network density of dominantdistribution network derived from 
gObj 
An object of iGraph of a dominantdistribution network. 
Chainarong Amornbunchornvej, chai@ieee.org
Run vignette("EDOIF_demo", package = "EDOIF")
in a terminal to learn more details about how to use our package.
# Generate simulation data
nInv<100
initMean=10
stepMean=20
std=8
simData1<c()
simData1$Values<rnorm(nInv,mean=initMean,sd=std)
simData1$Group<rep(c("C1"),times=nInv)
simData1$Values<c(simData1$Values,rnorm(nInv,mean=initMean,sd=std) )
simData1$Group<c(simData1$Group,rep(c("C2"),times=nInv))
simData1$Values<c(simData1$Values,rnorm(nInv,mean=initMean+2*stepMean,sd=std) )
simData1$Group<c(simData1$Group,rep(c("C3"),times=nInv) )
simData1$Values<c(simData1$Values,rnorm(nInv,mean=initMean+3*stepMean,sd=std) )
simData1$Group<c(simData1$Group, rep(c("C4"),times=nInv) )
simData1$Values<c(simData1$Values,rnorm(nInv,mean=initMean+4*stepMean,sd=std) )
simData1$Group<c(simData1$Group, rep(c("C5"),times=nInv) )
# Performing ordering infernce from simData1
resultObj<EDOIF(simData1$Values,simData1$Group)
# Print results in text mode
print(resultObj)
# Plot results in graphic mode
plot(resultObj)
getADJNetDen is a support function for calculating a network density of a dominantdistribution network.
getADJNetDen(adjMat)
adjMat 
is an adjacency matrix of a dominantdistribution network. 
This function returns a value of network density of of a dominantdistribution network for a given adjMat.
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Get a network density of an adjacency matrix
getADJNetDen(adjMat=resultObj$adjMat)
getConfInv is a support function for bootstrapping method. Its main purpose is to compute a mean confidence intervals of all distributions.
getConfInv(Values, Group, GroupList, bootT, alpha, methodType)
Values 
is a vector of realnumber values 
Group 
is a vector of categories of each real number in Values 
GroupList 
is a list of names of categories ascendingly ordered by their means. 
bootT 
is a number of times of sample with replacement for bootstrapping. The default is 1000. It must be above zero 
alpha 
is a significance level using in both confidence intervals and ordering inference it has the range [0,1]. The default is 0.05. 
methodType 
is an option for bootstrapping methods:either "perc" or "bca". The "perc" is the default option. 
This function returns a list of mean confidence intervals.
confInvsList[i , ]

The mean confidence interval of sortedGroupList[i] category. confInvsList[i,1] is a lower bound and confInvsList[i,2] is an upper bound. 
getDominantRADJ is a support function for inferring a dominantdistribution network using meandifference confidence intervals.
getDominantRADJ(MegDiffList, methodType)
MegDiffList 
is a list of objects that contains meandifference confidence intervals inferred by getMegDiffConfInv function. 
methodType 
is an option for bootstrapping methods:either "perc" or "bca". 
This function returns an adjacency matrix of a dominantdistribution network adjMat
and the corresponding lowerbound of mean difference CIs adjDiffMat
.
adjDiffMat[i , j]

A lower bound of confidence interval of mean difference for j minus i using methodType bootstrap. 
adjMat[i , j]

An element of adjacency matrix: One if adjDiffMat[i,j] is positive, otherwise, zero. 
getiGraphNetDen is a support function for calculating a network density of a dominantdistribution network.
getiGraphNetDen(g)
g 
is an object of iGraph class of a dominantdistribution network. 
This function returns a value of network density of of a dominantdistribution network for a given object g.
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Get a network density of an iGraph object
getiGraphNetDen(g=resultObj$gObj)
getiGraphOBJ is a support function for converting a dominantdistribution network adjacency matrix to an iGraph object.
getiGraphOBJ(adjMat, sortedGroupList)
adjMat 
is an adjacency matrix of a dominantdistribution network. 
sortedGroupList 
is a list of names of categories ascendingly ordered by their means. 
This function returns an iGraph object of a dominantdistribution network for a given adjMat.
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Get an iGraph object from an adjacency matrix
igraphObj<getiGraphOBJ(adjMat=resultObj$adjMat,sortedGroupList=resultObj$sortedGroupList)
getMegDiffConfInv is a support function for bootstrapping method. Its main purpose is to compute a meandifference confidence intervals between all pair of distributions.
getMegDiffConfInv(Values, Group, GroupList, bootT, alpha, methodType)
Values 
is a vector of realnumber values 
Group 
is a vector of categories of each real number in Values 
GroupList 
is a list of names of categories ascendingly ordered by their means. 
bootT 
is a number of times of sample with replacement for bootstrapping. The default is 1000. It must be above zero 
alpha 
is a significance level using in both confidence intervals and ordering inference it has the range [0,1]. The default is 0.05. 
methodType 
is an option for bootstrapping methods:either "perc" or "bca". The "perc" is the default option. 
This function returns a list of meandifference confidence intervals.
MegDiffList
a list of objects that contains meandifference confidence intervals of all possible pairs of distributions.
It contains MegDiffList[[1]],...,MegDiffList[[length(GroupList)]].
The MegDiffList
consists of the following variables
MegDiffList[[i]] 
Meandifference confidence intervals and related information of all categories that have higher means than sortedGroupList[i] category. 
getOrder is a support function for inferring a linear order of categories ascendingly sorted by their means.
getOrder(Values, Group)
Values 
is a vector of realnumber values 
Group 
is a vector of categories of each real number in Values 
This function returns two lists: an order list of categories sortedGroupList
and its correspoding list of means sortedmeanList
.
sortedGroupList 
The list of names of categories ascendingly ordered by their means. 
sortedmeanList 
The list of means of categories that are ascendingly ordered. 
# Generate simulation data
simData<SimNonNormalDist(nInv=100,noisePer=0.1)
# Call the function to get the sorted lists
getOrder(Values=simData$Values,Group=simData$Group)
getttestDominantRADJ is a support function for inferring a dominantdistribution network using Student's ttest.
getttestDominantRADJ(Values, Group, GroupList, alpha)
Values 
is a vector of realnumber values 
Group 
is a vector of categories of each real number in Values 
GroupList 
is a list of names of categories ascendingly ordered by their means. 
alpha 
is a significance level using in both confidence intervals and ordering inference it has the range [0,1]. 
This function returns an adjacency matrix of a dominantdistribution network adjMat
and the corresponding pvalues of all category pairs.
adjMat[i , j]

An element of adjacency matrix: one if GroupList[j] category dominates GroupList[i] using Student's ttest, otherwise zero. 
pValMat[i , j]

A pvalue of Student's ttest for adjMat[i,j]. 
getWilcoxDominantRADJ is a support function for inferring a dominantdistribution network using MannWhitney (Wilcoxon) Test.
getWilcoxDominantRADJ(Values, Group, GroupList, alpha)
Values 
is a vector of realnumber values 
Group 
is a vector of categories of each real number in Values 
GroupList 
is a list of names of categories ascendingly ordered by their means. 
alpha 
is a significance level using in both confidence intervals and ordering inference it has the range [0,1]. 
This function returns an adjacency matrix of a dominantdistribution network adjMat
.
and the corresponding pvalues of all category pairs.
adjMat[i , j]

An element of adjacency matrix: one if GroupList[j] category dominates GroupList[i] using MannWhitney test, otherwise zero. 
pValMat[i , j]

A pvalue of MannWhitney test for adjMat[i,j]. 
meanBoot is a support function for bootstrapping method.
Its main purpose is to compute a mean of a given samples from data
selected by indices
.
meanBoot(data, indices)
data 
is a vector of realnumber values 
indices 
is a vector of TRUE/FALSE indices. It allows boot to select samples. 
This function returns a mean of values in data
that have values TRUE within indices
.
plot.EDOIF is a support function for printing all plots of EDOIF framework: dominantdistribution network plot, mean CI plot, and meandifference CI plot.
## S3 method for class 'EDOIF'
plot(x, ..., NList, options, fontSize)
x 
is an object of EDOIF class that contains the results of ordering inference. 
... 
Signature for S3 generic function. 
NList 
is a list of based categories users want to have in meandifference CI plot. 
options 
is an option of reporting EDOIF plot(s): 0 for reporting all plots, 1 for meandifference CI plot, 2 for mean CI plot, and 3 for dominantdistribution network plot. 
fontSize 
is a font size of text for all plots. 
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Plot results in graphic mode
plot(resultObj)
plotGraph is a support function for plotting a dominantdistribution network from an adjacency matrix.
plotGraph(obj, rankFlag = TRUE)
obj 
is an object of EDOIF class that contains the results of ordering inference. 
rankFlag 
is an option for including ranks of categories with in the plot: default is TRUE for including ranks. 
This function returns a list of an object of iGraph for a dominantdistribution network and its plot variable.
graphVar 
An object of iGraph for a dominantdistribution network 
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Plot a dominantdistribution network and return a list of an iGraph object
iGraphList<plotGraph(obj=resultObj)
plotMeanCIs is a support function for plotting mean confidence intervals.
plotMeanCIs(obj, fontSize = 15, rankFlag = TRUE)
obj 
is an object of EDOIF class that contains the results of ordering inference. 
fontSize 
is a font size of text for all plots. 
rankFlag 
is an option for including ranks of categories with in the plot: default is TRUE for including ranks. 
This function returns a list of an object of ggplot class.
pMeanCI 
An object of ggplot class containing the plot of mean confidence intervals 
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Get a list of ggplot object of mean confidence intervals
ggplotList<plotMeanCIs(obj=resultObj)
# Plot mean confidence intervals
plot(ggplotList$pMeanCI)
plotMeanDiffCIs is a support function for plotting differencemean confidence intervals.
plotMeanDiffCIs(obj, NList, fontSize = 15, rankFlag = TRUE)
obj 
is an object of EDOIF class that contains the results of ordering inference. 
NList 
is a list of based categories users want to have in meandifference CI plot. 
fontSize 
is a font size of text for all plots. 
rankFlag 
is an option for including ranks of categories with in the plot: default is TRUE for including ranks. 
This function returns a list of an object of ggplot class.
pDiffCI 
An object of ggplot class containing the plot of meandifference confidence intervals 
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Get a list of ggplot object of meandifference confidence intervals
ggplotList<plotMeanDiffCIs(obj=resultObj)
# Plot meandifference confidence intervals
plot(ggplotList$pDiffCI)
print.EDOIF is a support function for printing results of ordering inference in text.
## S3 method for class 'EDOIF'
print(x, ...)
x 
is an object of EDOIF class that contains the results of ordering inference. 
... 
Signature for S3 generic function. 
# Generate simulation data with 100 samples per categories
simData<SimNonNormalDist(nInv=100)
# Performing ordering infernce from simData
resultObj<EDOIF(simData$Values,simData$Group)
# Print results in text mode
print(resultObj)
SimMixDist is a support function for generating samples from mixture distribution. The main purpose of this function is to generate samples from nonnormal distribution.
SimMixDist(nInv, mean, std, p1, p2)
nInv 
is a number of samples the function will generate. 
mean 
is a mean of a normal distribution part of mixture distribution. 
std 
is a standard deviation of a normal distribution part of mixture distribution. 
p1 
is a ratio of a normal distribution within a mixture distribution. 
p2 
is a ratio of a Cauchy distribution within a mixture distribution. 
This function returns a list of samples V
generated by a mixture distribution.
# Generate simulation data with 100 samples with a mixture distribution
# The distribution consist of the following distributions:
# 1) 10% of uniform distribution range [400,400];
# 2) 50% of normal distribution with mean = 40 and std =8; and
# 3) 40% of Cauchy distribution with location= 45 and scale = 2.
V<SimMixDist(nInv=100,mean=40,std=8,p1=0.1,p2=0.5)
SimNonNormalDist is a support function for generating samples from mixture distribution.
There are five categories. Each categories has nInv
samples.
Categories C1,C2,C3, and C4 are dominated by C5 but none of them dominate each other.
SimNonNormalDist(nInv, noisePer)
nInv 
is a number of samples the function will generate for each category. 
noisePer 
is ratio of uniform distribution within a mixture distribution. It is considered as a uniform noise that make an approach to hardly distinguish whether one distribution dominates another. 
The main purpose of this function is to generate samples that contains domination relation among categories.
This function returns a list of samples Values
and their category Group
generated by a mixture distribution.
Values 
A vector of samples generated by a mixture distribution. 
Group 
A list of categories associated with 
V1 , ... , V5

Lists of sample vectors separated by categories. 
# Generate simulation data with 100 samples per categories with 10% of uniform noise
simData<SimNonNormalDist(nInv=100,noisePer=0.1)