TAM (version 4.2-21)

data.numeracy: Dataset Numeracy

Description

Dataset numeracy with unscored (raw) and scored (scored) item responses of 876 persons and 15 items.

Usage

data(data.numeracy)

Format

The format is a list a two entries:

List of 2
$ raw :'data.frame':
..$ I1 : int [1:876] 1 0 1 0 0 0 0 0 1 1 ...
..$ I2 : int [1:876] 0 1 0 0 1 1 1 1 1 0 ...
..$ I3 : int [1:876] 4 4 1 3 4 4 4 4 4 4 ...
..$ I4 : int [1:876] 4 1 2 2 1 1 1 1 1 1 ...
[...]
..$ I15: int [1:876] 1 1 1 1 0 1 1 1 1 1 ...
$ scored:'data.frame':
..$ I1 : int [1:876] 1 0 1 0 0 0 0 0 1 1 ...
..$ I2 : int [1:876] 0 1 0 0 1 1 1 1 1 0 ...
..$ I3 : int [1:876] 1 1 0 0 1 1 1 1 1 1 ...
..$ I4 : int [1:876] 0 1 0 0 1 1 1 1 1 1 ...
[...]
..$ I15: int [1:876] 1 1 1 1 0 1 1 1 1 1 ...

Examples

######################################################################
# (1) Scored numeracy data
######################################################################

data(data.numeracy)
dat <- data.numeracy$scored

#Run IRT analysis: Rasch model
mod1 <- TAM::tam.mml(dat)

#Item difficulties
mod1$xsi
ItemDiff <- mod1$xsi$xsi
ItemDiff

#Ability estimate - Weighted Likelihood Estimate
Abil <- TAM::tam.wle(mod1)
Abil
PersonAbility <- Abil$theta
PersonAbility

#Descriptive statistics of item and person parameters
hist(ItemDiff)
hist(PersonAbility)
mean(ItemDiff)
mean(PersonAbility)
stats::sd(ItemDiff)
stats::sd(PersonAbility)

if (FALSE) {
#Extension
#plot histograms of ability and item parameters in the same graph
oldpar <- par(no.readonly=TRUE)          # save writable default graphic settings
windows(width=4.45, height=4.45, pointsize=12)
layout(matrix(c(1,1,2),3,byrow=TRUE))
layout.show(2)
hist(PersonAbility,xlim=c(-3,3),breaks=20)
hist(ItemDiff,xlim=c(-3,3),breaks=20)

par( oldpar )  # restore default graphic settings
hist(PersonAbility,xlim=c(-3,3),breaks=20)

######################################################################
# (2) Raw numeracy data
######################################################################

raw_resp <- data.numeracy$raw

#score responses
key <- c(1, 1, 4, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1)
scored <- sapply( seq(1,length(key)),
            FUN=function(ii){ 1*(raw_resp[,ii]==key[ii]) } )

#run IRT analysis
mod1 <- TAM::tam.mml(scored)

#Ability estimate - Weighted Likelihood Estimate
Abil <- TAM::tam.wle(mod1)

#CTT statistics
ctt1 <- TAM::tam.ctt(raw_resp, Abil$theta)
write.csv(ctt1,"D1_ctt1.csv")       # write statistics into a file
        # use maybe write.csv2 if ';' should be the column separator

#Fit statistics
Fit <- TAM::tam.fit(mod1)
Fit

# plot expected response curves
plot( mod1, ask=TRUE )
}