EDOIF demo

C. Amornbunchornvej

2025-04-28

EXAMPLE#1 Simple Simulation & ordering inference

In the first step, we generate a simple dataset. where C1 and C2 are dominated by C3, C3 is dominated by C4, and is C4 dominated by C5. There is no dominant-distribution relation between C1 and C2.

# Simulation section
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) )

The framework is used to analyze the data below.

# Simple ordering inference section
library(EDOIF)

## Loading required package: boot

# parameter setting
bootT=1000 # Number of times of sampling with replacement
alpha=0.05 # significance  significance level

#======= input
Values=simData1$Values
Group=simData1$Group
#=============
A1<-EDOIF(Values,Group,bootT = bootT, alpha=alpha )

We print the result of our framework below.

print(A1) # print results in text

## EDOIF (Empirical Distribution Ordering Inference Framework)
## =======================================================
## Alpha = 0.050000, Number of bootstrap resamples = 1000, CI type = perc
## Using Mann-Whitney test to report whether A ≺ B
## A dominant-distribution network density:0.900000
## Distribution: C2
## Mean:9.482822 95CI:[ 8.006487,11.059085]
## Distribution: C1
## Mean:10.602326 95CI:[ 9.098160,12.081722]
## Distribution: C3
## Mean:51.147217 95CI:[ 49.619133,52.593155]
## Distribution: C4
## Mean:70.054967 95CI:[ 68.498561,71.702038]
## Distribution: C5
## Mean:89.786445 95CI:[ 88.274864,91.203818]
## =======================================================
## Mean difference of C1 (n=100) minus C2 (n=100): C2 ⊀ C1
##  :p-val 0.1459
## Mean Diff:1.119504 95CI:[ -0.893697,3.413313]
## 
## Mean difference of C3 (n=100) minus C2 (n=100): C2 ≺ C3
##  :p-val 0.0000
## Mean Diff:41.664395 95CI:[ 39.696096,43.744448]
## 
## Mean difference of C4 (n=100) minus C2 (n=100): C2 ≺ C4
##  :p-val 0.0000
## Mean Diff:60.572145 95CI:[ 58.410548,62.736461]
## 
## Mean difference of C5 (n=100) minus C2 (n=100): C2 ≺ C5
##  :p-val 0.0000
## Mean Diff:80.303623 95CI:[ 78.221824,82.315763]
## 
## Mean difference of C3 (n=100) minus C1 (n=100): C1 ≺ C3
##  :p-val 0.0000
## Mean Diff:40.544891 95CI:[ 38.556311,42.745753]
## 
## Mean difference of C4 (n=100) minus C1 (n=100): C1 ≺ C4
##  :p-val 0.0000
## Mean Diff:59.452641 95CI:[ 57.287014,61.693098]
## 
## Mean difference of C5 (n=100) minus C1 (n=100): C1 ≺ C5
##  :p-val 0.0000
## Mean Diff:79.184119 95CI:[ 77.030834,81.361752]
## 
## Mean difference of C4 (n=100) minus C3 (n=100): C3 ≺ C4
##  :p-val 0.0000
## Mean Diff:18.907750 95CI:[ 16.712224,21.072367]
## 
## Mean difference of C5 (n=100) minus C3 (n=100): C3 ≺ C5
##  :p-val 0.0000
## Mean Diff:38.639228 95CI:[ 36.470177,40.608937]
## 
## Mean difference of C5 (n=100) minus C4 (n=100): C4 ≺ C5
##  :p-val 0.0000
## Mean Diff:19.731478 95CI:[ 17.459604,21.995552]

The first plot is the plot of mean-difference confidence intervals

plot(A1,options =1)

plot of chunk Fig1

The second plot is the plot of mean confidence intervals

plot(A1,options =2)

plot of chunk Fig2 The third plot is a dominant-distribution network.

out<-plot(A1,options =3)

plot of chunk Fig3

EXAMPLE#2 Non-normal-Distribution Simulation & ordering inference

We generate more complicated dataset of mixture distributions. C1, C2, C3, and C4 are dominated by C5. There is no dominant-distribution relation among C1, C2, C3, and C4.

library(EDOIF)
# parameter setting
bootT=1000
alpha=0.05
nInv<-1200

start_time <- Sys.time()
#======= input
simData3<-SimNonNormalDist(nInv=nInv,noisePer=0.01)
Values=simData3$Values
Group=simData3$Group
#=============
A3<-EDOIF(Values,Group, bootT=bootT, alpha=alpha, methodType ="perc")
A3

## EDOIF (Empirical Distribution Ordering Inference Framework)
## =======================================================
## Alpha = 0.050000, Number of bootstrap resamples = 1000, CI type = perc
## Using Mann-Whitney test to report whether A ≺ B
## A dominant-distribution network density:0.400000
## Distribution: C1
## Mean:81.595459 95CI:[ 78.669686,84.224662]
## Distribution: C2
## Mean:82.015780 95CI:[ 79.979614,83.526797]
## Distribution: C3
## Mean:82.717153 95CI:[ 81.161702,84.228813]
## Distribution: C4
## Mean:83.856352 95CI:[ 79.893810,88.627838]
## Distribution: C5
## Mean:141.992477 95CI:[ 140.284726,143.506157]
## =======================================================
## Mean difference of C2 (n=1200) minus C1 (n=1200): C1 ⊀ C2
##  :p-val 0.1943
## Mean Diff:0.420322 95CI:[ -2.686553,3.689832]
## 
## Mean difference of C3 (n=1200) minus C1 (n=1200): C1 ⊀ C3
##  :p-val 0.2110
## Mean Diff:1.121694 95CI:[ -1.892079,4.309357]
## 
## Mean difference of C4 (n=1200) minus C1 (n=1200): C1 ⊀ C4
##  :p-val 0.7774
## Mean Diff:2.260893 95CI:[ -2.429935,7.494195]
## 
## Mean difference of C5 (n=1200) minus C1 (n=1200): C1 ≺ C5
##  :p-val 0.0000
## Mean Diff:60.397018 95CI:[ 57.479791,63.729265]
## 
## Mean difference of C3 (n=1200) minus C2 (n=1200): C2 ⊀ C3
##  :p-val 0.5158
## Mean Diff:0.701372 95CI:[ -1.581631,3.069064]
## 
## Mean difference of C4 (n=1200) minus C2 (n=1200): C2 ⊀ C4
##  :p-val 0.9496
## Mean Diff:1.840572 95CI:[ -2.506555,6.869621]
## 
## Mean difference of C5 (n=1200) minus C2 (n=1200): C2 ≺ C5
##  :p-val 0.0000
## Mean Diff:59.976697 95CI:[ 57.627067,62.462598]
## 
## Mean difference of C4 (n=1200) minus C3 (n=1200): C3 ⊀ C4
##  :p-val 0.9441
## Mean Diff:1.139199 95CI:[ -2.865575,6.386407]
## 
## Mean difference of C5 (n=1200) minus C3 (n=1200): C3 ≺ C5
##  :p-val 0.0000
## Mean Diff:59.275324 95CI:[ 56.992640,61.560018]
## 
## Mean difference of C5 (n=1200) minus C4 (n=1200): C4 ≺ C5
##  :p-val 0.0000
## Mean Diff:58.136125 95CI:[ 52.704495,62.225454]

plot(A3)

plot of chunk Fig4plot of chunk Fig4plot of chunk Fig4

end_time <- Sys.time()
end_time - start_time

## Time difference of 1.545051 secs

Uniform noise

Generating \(A\) dominates \(B\) with different degrees of uniform noise

library(ggplot2)

nInv<-1000
simData3<-SimNonNormalDist(nInv=nInv,noisePer=0.01)
#plot(density(simData3$V3))

dat <- data.frame(dens = c(simData3$V3, simData3$V5)
                   , lines = rep(c("B", "A"), each = nInv))
#Plot.
p1<-ggplot(dat, aes(x = dens, fill = lines)) + geom_density(alpha = 0.5) +xlim(-400, 400)+ ylim(0, 0.07) + ylab("Density [0,1]") +xlab("Values") + theme( axis.text.x = element_text(face="bold",  
                                      size=12) )
theme_update(text = element_text(face="bold", size=12)  )
p1$labels$fill<-"Categories"
plot(p1)

## Warning: Removed 4 rows containing non-finite outside the scale range
## (`stat_density()`).

plot of chunk Fig5