#FIRST GRAPHIC

pisa <- read.table(".../pisa.txt",header=T,sep="\t", quote="")

#Use of ltm package for Rasch analysis
 
des<-descript(pisa)
m1<-rasch(pisa, constraint =cbind(length(pisa) +1, 1))

abil1<-c(-1.675, -1.3, -0.951, -0.621, -0.3, -0.016, 0.331, 0.652, 0.982, 1.326, 1.69, 2.085)


#MV
#Vector for the boundaries of the total score
anzahl_tot<-rep(0, 13)
for(i in 2:13){ anzahl_tot[i] = anzahl_tot[i-1] + des$items[15-i]}

#Ordering of item difficulties
dffclt_1_ord<-coef(m1, order = T)

#Matrix definition
matxv<-matrix(nrow=317, ncol = 13, dimnames=(list(c(1:317), c("Item.38", "Item.73", "Item.6", "Item.8", 
"Item.39", "Item.67", "Item.37", "Item.5", "Item.64", "Item.7", "Item.72", "Item.75","Summe"))))

matxhelp<-matrix(nrow=317, ncol = 13, dimnames=(list(c(1:317), c("Item.38", "Item.73", "Item.6", "Item.8", 
"Item.39", "Item.67", "Item.37", "Item.5", "Item.64", "Item.7", "Item.72", "Item.75","Summe"))))

#Sorting of the matrix
matxv[,1]<-pisa[,6]
matxv[,2]<-pisa[,11]
matxv[,3]<-pisa[,2]
matxv[,4]<-pisa[,4]
matxv[,5]<-pisa[,7]
matxv[,6]<-pisa[,9]
matxv[,7]<-pisa[,5]
matxv[,8]<-pisa[,1]
matxv[,9]<-pisa[,8]
matxv[,10]<-pisa[,3]
matxv[,11]<-pisa[,10]
matxv[,12]<-pisa[,12]

mtrans<-transform(matxv[,1:12])
mtrans<-mtrans[do.call(order, mtrans),]

for(i in 1:317){
for(j in 1:12){
matxv[i,j]<-mtrans[i,j]
}
matxv[i,13]<-sum(mtrans[i,])
}

scoresort<-rank(matxv[,13],ties.method = c("first"))

for(i in 1:317){
matxhelp[scoresort[i],]<-matxv[i,]
}
for(i in 1:317){
matxv[i,]<-matxhelp[i,]
}


#Creating of matrix visualization
plot(c(1,1), xlim = c(1,317), ylim = c(1,12), ylab = "Items", xlab = "Persons", type = "n", xaxt = "n")
axis(1, at = anzahl_tot)
for(i in 1:317){
for(j in 1:12){
if(matxv[i,j] == 1){
if(exp(abil1[matxv[i,13]] - dffclt_1_ord[13-j])/(1+exp(abil1[matxv[i,13]] - dffclt_1_ord[13-j])) < 0.15){
points(318-i,13-j,pch = 19, col = "red")
}
if(exp(abil1[matxv[i,13]] - dffclt_1_ord[13-j])/(1+exp(abil1[matxv[i,13]] - dffclt_1_ord[13-j])) >= 0.15){
if(matxv[i,13] == 12){ points(318-i,13-j,pch = 20, col = rgb(0,0,0.5))}
if(matxv[i,13] == 11){ points(318-i,13-j,pch = 20, col = rgb(0,0,1))}
if(matxv[i,13] == 10){ points(318-i,13-j,pch = 20, col = rgb(0.25,0.4,1))}
if(matxv[i,13] == 9){ points(318-i,13-j,pch = 20, col = rgb(0,0.2,1))}
if(matxv[i,13] == 8){ points(318-i,13-j,pch = 20, col = rgb(0,0.6,1))}
if(matxv[i,13] == 7){ points(318-i,13-j,pch = 20, col = rgb(0.25,0.8,1))}
if(matxv[i,13] == 6){ points(318-i,13-j,pch = 20, col = rgb(0,1,1))}
if(matxv[i,13] == 5){ points(318-i,13-j,pch = 20, col = rgb(0.25,1,0.8))}
if(matxv[i,13] == 4){ points(318-i,13-j,pch = 20, col = rgb(0,1,0.6))}
if(matxv[i,13] == 3){ points(318-i,13-j,pch = 20, col = rgb(0.25,1,0.4))}
if(matxv[i,13] == 2){ points(318-i,13-j,pch = 20, col = rgb(0,1,0.2))}
if(matxv[i,13] == 1){ points(318-i,13-j,pch = 20, col = rgb(0.5,1,0))}
}
}
if(matxv[i,j] == 0){
if(1 / (1+exp(abil1[matxv[i,13]] - dffclt_1_ord[13-j])) < 0.15){
points(318-i,13-j,pch = 19, col = "red")
}
}
}
}


#SECOND GRAPHIC

pisa2 <- read.table(".../pisa2.txt",header=T,sep="\t", quote="")

des2<-descript(pisa2)
m2<-rasch(pisa2, constraint =cbind(length(pisa2) +1, 1))

abil2<-c(-2.80,-2.56,-2.34,-2.14,-1.95,-1.77,-1.60,-1.43,-1.27,-1.12,-0.97,-0.82,-0.67,-0.53,-0.38,-0.24,-0.09,0.05,0.20,0.35,
0.50,0.66,0.82,0.99,1.16,1.34,1.53,1.73,1.95,2.19,2.46,2.75)

#MV
#Vector for the boundaries of the total score
anzahl_tot2<-rep(0, 33)
for(i in 2:33){ anzahl_tot2[i] = anzahl_tot2[i-1] + des2$items[35-i]}

dffclt_2_ord<-coef(m2, order = T)


matxv<-matrix(nrow=340, ncol = 33, dimnames=(list(c(1:340), c(1:33))))

matxhelp<-matrix(nrow=340, ncol = 33, dimnames=(list(c(1:340), c(1:33))))


matxv[,1]<-pisa2[,21]
matxv[,2]<-pisa2[,10]
matxv[,3]<-pisa2[,9]
matxv[,4]<-pisa2[,8]
matxv[,5]<-pisa2[,31]
matxv[,6]<-pisa2[,30]
matxv[,7]<-pisa2[,11]
matxv[,8]<-pisa2[,6]
matxv[,9]<-pisa2[,16]
matxv[,10]<-pisa2[,2]
matxv[,11]<-pisa2[,13]
matxv[,12]<-pisa2[,25]
matxv[,13]<-pisa2[,19]
matxv[,14]<-pisa2[,24]
matxv[,15]<-pisa2[,5]
matxv[,16]<-pisa2[,12]
matxv[,17]<-pisa2[,1]
matxv[,18]<-pisa2[,26]
matxv[,19]<-pisa2[,23]
matxv[,20]<-pisa2[,29]
matxv[,21]<-pisa2[,20]
matxv[,22]<-pisa2[,32]
matxv[,23]<-pisa2[,28]
matxv[,24]<-pisa2[,7]
matxv[,25]<-pisa2[,27]
matxv[,26]<-pisa2[,4]
matxv[,27]<-pisa2[,3]
matxv[,28]<-pisa2[,22]
matxv[,29]<-pisa2[,15]
matxv[,30]<-pisa2[,17]
matxv[,31]<-pisa2[,18]
matxv[,32]<-pisa2[,14]


mtrans<-transform(matxv[,1:32])
mtrans<-mtrans[do.call(order, mtrans),]

for(i in 1:340){
for(j in 1:32){
matxv[i,j]<-mtrans[i,j]
}
matxv[i,33]<-sum(mtrans[i,])
}

scoresort<-rank(matxv[,33],ties.method = c("first"))

for(i in 1:340){
matxhelp[scoresort[i],]<-matxv[i,]
}
for(i in 1:340){
matxv[i,]<-matxhelp[i,]
}


plot(c(1,1), xlim = c(1,340), ylim = c(1,32), ylab = "Items", xlab = "Persons", type = "n", xaxt = "n")
axis(1, at = anzahl_tot2)
for(i in 1:340){
for(j in 1:32){
if(matxv[i,j] == 1){
if(exp(abil2[matxv[i,33]] - dffclt_2_ord[33-j])/(1+exp(abil2[matxv[i,33]] - dffclt_2_ord[33-j])) < 0.1){
points(341-i,33-j,pch = 19, col = "red")
}
if(exp(abil2[matxv[i,33]] - dffclt_2_ord[33-j])/(1+exp(abil2[matxv[i,33]] - dffclt_2_ord[33-j])) >= 0.1){
if(matxv[i,33] == 32){ points(341-i,33-j,pch = 20, col = "grey99")}
if(matxv[i,33] == 31){ points(341-i,33-j,pch = 20, col = "grey96")}
if(matxv[i,33] == 30){ points(341-i,33-j,pch = 20, col = "grey93")}
if(matxv[i,33] == 29){ points(341-i,33-j,pch = 20, col = "grey90")}
if(matxv[i,33] == 28){ points(341-i,33-j,pch = 20, col = "grey87")}
if(matxv[i,33] == 27){ points(341-i,33-j,pch = 20, col = "grey84")}
if(matxv[i,33] == 26){ points(341-i,33-j,pch = 20, col = "grey81")}
if(matxv[i,33] == 25){ points(341-i,33-j,pch = 20, col = "grey78")}
if(matxv[i,33] == 24){ points(341-i,33-j,pch = 20, col = "grey75")}
if(matxv[i,33] == 23){ points(341-i,33-j,pch = 20, col = "grey72")}
if(matxv[i,33] == 22){ points(341-i,33-j,pch = 20, col = "grey69")}
if(matxv[i,33] == 21){ points(341-i,33-j,pch = 20, col = "grey66")}
if(matxv[i,33] == 20){ points(341-i,33-j,pch = 20, col = "grey63")}
if(matxv[i,33] == 19){ points(341-i,33-j,pch = 20, col = "grey60")}
if(matxv[i,33] == 18){ points(341-i,33-j,pch = 20, col = "grey57")}
if(matxv[i,33] == 17){ points(341-i,33-j,pch = 20, col = "grey54")}
if(matxv[i,33] == 16){ points(341-i,33-j,pch = 20, col = "grey51")}
if(matxv[i,33] == 15){ points(341-i,33-j,pch = 20, col = "grey48")}
if(matxv[i,33] == 14){ points(341-i,33-j,pch = 20, col = "grey45")}
if(matxv[i,33] == 13){ points(341-i,33-j,pch = 20, col = "grey42")}
if(matxv[i,33] == 12){ points(341-i,33-j,pch = 20, col = "grey39")}
if(matxv[i,33] == 11){ points(341-i,33-j,pch = 20, col = "grey36")}
if(matxv[i,33] == 10){ points(341-i,33-j,pch = 20, col = "grey33")}
if(matxv[i,33] == 9){ points(341-i,33-j,pch = 20, col = "grey30")}
if(matxv[i,33] == 8){ points(341-i,33-j,pch = 20, col = "grey27")}
if(matxv[i,33] == 7){ points(341-i,33-j,pch = 20, col = "grey24")}
if(matxv[i,33] == 6){ points(341-i,33-j,pch = 20, col = "grey21")}
if(matxv[i,33] == 5){ points(341-i,33-j,pch = 20, col = "grey18")}
if(matxv[i,33] == 4){ points(341-i,33-j,pch = 20, col = "grey15")}
if(matxv[i,33] == 3){ points(341-i,33-j,pch = 20, col = "grey12")}
if(matxv[i,33] == 2){ points(341-i,33-j,pch = 20, col = "grey9")}
if(matxv[i,33] == 1){ points(341-i,33-j,pch = 20, col = "grey6")}
}
}
if(matxv[i,j] == 0){
if(1 / (1+exp(abil2[matxv[i,33]] - dffclt_2_ord[33-j])) < 0.1){
points(341-i,33-j,pch = 19, col = "red")
}
}
}
}