Dataset TIMSS 2011 of Australian and Taiwanese Students

Mathematics items of TIMSS 2011 of 1773 Australian and Taiwanese students. The dataset data.timssAusTwn contains raw responses while data.timssAusTwn.scored contains scored item responses.

data(data.timssAusTwn)
data(data.timssAusTwn.scored)

Format

A data frame with 1773 observations on the following 14 variables.

M032166

a mathematics item

M032721

a mathematics item

M032757

a mathematics item

M032760A

a mathematics item

M032760B

a mathematics item

M032760C

a mathematics item

M032761

a mathematics item

M032692

a mathematics item

M032626

a mathematics item

M032595

a mathematics item

M032673

a mathematics item

IDCNTRY

Country identifier

ITSEX

Gender

IDBOOK

Booklet identifier

See also

http://www.edmeasurementsurveys.com/TAM/Tutorials/5PartialCredit.htm

http://www.edmeasurementsurveys.com/TAM/Tutorials/6Population.htm

Examples

data(data.timssAusTwn)
raw_resp <- data.timssAusTwn

#Recode data
resp <- raw_resp[,1:11]
      #Column 12 is country code. Column 13 is gender code. Column 14 is Book ID.
all.na <- rowMeans( is.na(resp) )==1
        #Find records where all responses are missing.
resp <- resp[!all.na,]              #Delete records with all missing responses
resp[resp==20 | resp==21] <- 2      #TIMSS double-digit coding: "20" or "21" is a score of 2
resp[resp==10 | resp==11] <- 1      #TIMSS double-digit coding: "10" or "11" is a score of 1
resp[resp==70 | resp==79] <- 0      #TIMSS double-digit coding: "70" or "79" is a score of 0
resp[resp==99] <- 0                 #"99" is omitted responses. Score it as wrong here.
resp[resp==96 | resp==6] <- NA      #"96" and "6" are not-reached items. Treat these as missing.

#Score multiple-choice items        #"resp" contains raw responses for MC items.
Scored <- resp
Scored[,9] <- (resp[,9]==4)*1       #Key for item 9 is D.
Scored[,c(1,2)] <- (resp[,c(1,2)]==2)*1  #Key for items 1 and 2 is B.
Scored[,c(10,11)] <- (resp[,c(10,11)]==3)*1  #Key for items 10 and 11 is C.

#Run IRT analysis for partial credit model (MML estimation)
mod1 <- TAM::tam.mml(Scored)

#Item parameters
mod1$xsi

#Thurstonian thresholds
tthresh <- TAM::tam.threshold(mod1)
tthresh

if (FALSE) {
#Plot Thurstonian thresholds
windows (width=8, height=7)
par(ps=9)
dotchart(t(tthresh), pch=19)
# plot expected response curves
plot( mod1, ask=TRUE)

#Re-run IRT analysis in JML
mod1.2 <- TAM::tam.jml(Scored)
stats::var(mod1.2$WLE)

#Re-run the model with "not-reached" coded as incorrect.
Scored2 <- Scored
Scored2[is.na(Scored2)] <- 0

#Prepare anchor parameter values
nparam <- length(mod1$xsi$xsi)
xsi <- mod1$xsi$xsi
anchor <- matrix(c(seq(1,nparam),xsi), ncol=2)

#Run IRT with item parameters anchored on mod1 values
mod2 <- TAM::tam.mml(Scored2, xsi.fixed=anchor)

#WLE ability estimates
ability <- TAM::tam.wle(mod2)
ability

#CTT statistics
ctt <- TAM::tam.ctt(resp, ability$theta)
write.csv(ctt,"TIMSS_CTT.csv")

#plot histograms of ability and item parameters in the same graph
windows(width=4.45, height=4.45, pointsize=12)
layout(matrix(c(1,1,2),3,byrow=TRUE))
layout.show(2)
hist(ability$theta,xlim=c(-3,3),breaks=20)
hist(tthresh,xlim=c(-3,3),breaks=20)

#Extension
#Score equivalence table
dummy <- matrix(0,nrow=16,ncol=11)
dummy[lower.tri(dummy)] <- 1
dummy[12:16,c(3,4,7,8)][lower.tri(dummy[12:16,c(3,4,7,8)])]<-2

mod3 <- TAM::tam.mml(dummy, xsi.fixed=anchor)
wle3 <- TAM::tam.wle(mod3)
}