Examples with Datasets from Eid and Schmidt (2014)
Examples with datasets from Eid and Schmidt (2014), illustrations with several R packages. The examples follow closely the online material of Hosoya (2014). The datasets are completely synthetic datasets which were resimulated from the originally available data.
data(data.eid.kap4) data(data.eid.kap5) data(data.eid.kap6) data(data.eid.kap7)
data.eid.kap4 is the dataset from Chapter 4.
'data.frame': 193 obs. of 11 variables: $ sex : int 0 0 0 0 0 0 1 0 0 1 ... $ Freude_1: int 1 1 1 0 1 1 1 1 1 1 ... $ Wut_1 : int 1 1 1 0 1 1 1 1 1 1 ... $ Angst_1 : int 1 0 0 0 1 1 1 0 1 0 ... $ Trauer_1: int 1 1 1 0 1 1 1 1 1 1 ... $ Ueber_1 : int 1 1 1 0 1 1 0 1 1 1 ... $ Trauer_2: int 0 1 1 1 1 1 1 1 1 0 ... $ Angst_2 : int 0 0 1 0 0 1 0 0 0 0 ... $ Wut_2 : int 1 1 1 1 1 1 1 1 1 1 ... $ Ueber_2 : int 1 0 1 0 1 1 1 0 1 1 ... $ Freude_2: int 1 1 1 0 1 1 1 1 1 1 ...
data.eid.kap5 is the dataset from Chapter 5.
'data.frame': 499 obs. of 7 variables: $ sex : int 0 0 0 0 1 1 1 0 0 0 ... $ item_1: int 2 3 3 2 4 1 0 0 0 2 ... $ item_2: int 1 1 4 1 3 3 2 1 2 3 ... $ item_3: int 1 3 3 2 3 3 0 0 0 1 ... $ item_4: int 2 4 3 4 3 3 3 2 0 2 ... $ item_5: int 1 3 2 2 0 0 0 0 1 2 ... $ item_6: int 4 3 4 3 4 3 2 1 1 3 ...
data.eid.kap6 is the dataset from Chapter 6.
'data.frame': 238 obs. of 7 variables: $ geschl: int 1 1 0 0 0 1 0 1 1 0 ... $ item_1: int 3 3 3 3 2 0 1 4 3 3 ... $ item_2: int 2 2 2 2 2 0 2 3 1 3 ... $ item_3: int 2 2 1 3 2 0 0 3 1 3 ... $ item_4: int 2 3 3 3 3 0 2 4 3 4 ... $ item_5: int 1 2 1 2 2 0 1 2 2 2 ... $ item_6: int 2 2 2 2 2 0 1 2 1 2 ...
data.eid.kap7 is the dataset Emotionale Klarheit from Chapter 7.
'data.frame': 238 obs. of 9 variables: $ geschl : int 1 0 1 1 0 1 0 1 0 1 ... $ reakt_1: num 2.13 1.78 1.28 1.82 1.9 1.63 1.73 1.49 1.43 1.27 ... $ reakt_2: num 1.2 1.73 0.95 1.5 1.99 1.75 1.58 1.71 1.41 0.96 ... $ reakt_3: num 1.77 1.42 0.76 1.54 2.36 1.84 2.06 1.21 1.75 0.92 ... $ reakt_4: num 2.18 1.28 1.39 1.82 2.09 2.15 2.1 1.13 1.71 0.78 ... $ reakt_5: num 1.47 1.7 1.08 1.77 1.49 1.73 1.96 1.76 1.88 1.1 ... $ reakt_6: num 1.63 0.9 0.82 1.63 1.79 1.37 1.79 1.11 1.27 1.06 ... $ kla_th1: int 8 11 11 8 10 11 12 5 6 12 ... $ kla_th2: int 7 11 12 8 10 11 12 5 8 11 ...
The material and original datasets can be downloaded from http://www.hogrefe.de/buecher/lehrbuecher/psychlehrbuchplus/lehrbuecher/ testtheorie-und-testkonstruktion/zusatzmaterial/.
Eid, M., & Schmidt, K. (2014). Testtheorie und Testkonstruktion. Goettingen, Hogrefe.
Hosoya, G. (2014). Einfuehrung in die Analyse testtheoretischer Modelle mit R. Available at http://www.hogrefe.de/buecher/lehrbuecher/psychlehrbuchplus/lehrbuecher/testtheorie-und-testkonstruktion/zusatzmaterial/.
## Not run:
miceadds::library_install("foreign")
#---- load some IRT packages in R
miceadds::library_install("TAM") # package (a)
miceadds::library_install("mirt") # package (b)
miceadds::library_install("sirt") # package (c)
miceadds::library_install("eRm") # package (d)
miceadds::library_install("ltm") # package (e)
miceadds::library_install("psychomix") # package (f)
#############################################################################
# EXAMPLES Ch. 4: Unidimensional IRT models | dichotomous data
#############################################################################
data(data.eid.kap4)
data0 <- data.eid.kap4
# load data
data0 <- foreign::read.spss( linkname, to.data.frame=TRUE, use.value.labels=FALSE)
# extract items
dat <- data0[,2:11]
#*********************************************************
# Model 1: Rasch model
#*********************************************************
#-----------
#-- 1a: estimation with TAM package
# estimation with tam.mml
mod1a <- TAM::tam.mml(dat)
summary(mod1a)
# person parameters in TAM
pp1a <- TAM::tam.wle(mod1a)
# plot item response functions
plot(mod1a,export=FALSE,ask=TRUE)
# Infit and outfit in TAM
itemf1a <- TAM::tam.fit(mod1a)
itemf1a
# model fit
modf1a <- TAM::tam.modelfit(mod1a)
summary(modf1a)
#-----------
#-- 1b: estimation with mirt package
# estimation with mirt
mod1b <- mirt::mirt( dat, 1, itemtype="Rasch")
summary(mod1b)
print(mod1b)
# person parameters
pp1b <- mirt::fscores(mod1b, method="WLE")
# extract coefficients
sirt::mirt.wrapper.coef(mod1b)
# plot item response functions
plot(mod1b, type="trace" )
par(mfrow=c(1,1))
# item fit
itemf1b <- mirt::itemfit(mod1b)
itemf1b
# model fit
modf1b <- mirt::M2(mod1b)
modf1b
#-----------
#-- 1c: estimation with sirt package
# estimation with rasch.mml2
mod1c <- sirt::rasch.mml2(dat)
summary(mod1c)
# person parameters (EAP)
pp1c <- mod1c$person
# plot item response functions
plot(mod1c, ask=TRUE )
# model fit
modf1c <- sirt::modelfit.sirt(mod1c)
summary(modf1c)
#-----------
#-- 1d: estimation with eRm package
# estimation with RM
mod1d <- eRm::RM(dat)
summary(mod1d)
# estimation person parameters
pp1d <- eRm::person.parameter(mod1d)
summary(pp1d)
# plot item response functions
eRm::plotICC(mod1d)
# person-item map
eRm::plotPImap(mod1d)
# item fit
itemf1d <- eRm::itemfit(pp1d)
# person fit
persf1d <- eRm::personfit(pp1d)
#-----------
#-- 1e: estimation with ltm package
# estimation with rasch
mod1e <- ltm::rasch(dat)
summary(mod1e)
# estimation person parameters
pp1e <- ltm::factor.scores(mod1e)
# plot item response functions
plot(mod1e)
# item fit
itemf1e <- ltm::item.fit(mod1e)
# person fit
persf1e <- ltm::person.fit(mod1e)
# goodness of fit with Bootstrap
modf1e <- ltm::GoF.rasch(mod1e,B=20) # use more bootstrap samples
modf1e
#*********************************************************
# Model 2: 2PL model
#*********************************************************
#-----------
#-- 2a: estimation with TAM package
# estimation
mod2a <- TAM::tam.mml.2pl(dat)
summary(mod2a)
# model fit
modf2a <- TAM::tam.modelfit(mod2a)
summary(modf2a)
# item response functions
plot(mod2a, export=FALSE, ask=TRUE)
# model comparison
anova(mod1a,mod2a)
#-----------
#-- 2b: estimation with mirt package
# estimation
mod2b <- mirt::mirt(dat,1,itemtype="2PL")
summary(mod2b)
print(mod2b)
sirt::mirt.wrapper.coef(mod2b)
# model fit
modf2b <- mirt::M2(mod2b)
modf2b
#-----------
#-- 2c: estimation with sirt package
I <- ncol(dat)
# estimation
mod2c <- sirt::rasch.mml2(dat,est.a=1:I)
summary(mod2c)
# model fit
modf2c <- sirt::modelfit.sirt(mod2c)
summary(modf2c)
#-----------
#-- 2e: estimation with ltm package
# estimation
mod2e <- ltm::ltm(dat ~ z1 )
summary(mod2e)
# item response functions
plot(mod2e)
#*********************************************************
# Model 3: Mixture Rasch model
#*********************************************************
#-----------
#-- 3a: estimation with TAM package
# avoid "_" in column names if the "__" operator is used in
# the tamaan syntax
dat1 <- dat
colnames(dat1) <- gsub("_", "", colnames(dat1) )
# define tamaan model
tammodel <- "
ANALYSIS:
TYPE=MIXTURE ;
NCLASSES(2);
NSTARTS(20,25); # 20 random starts with 25 initial iterations each
LAVAAN MODEL:
F=~ Freude1__Freude2
F ~~ F
ITEM TYPE:
ALL(Rasch);
"
mod3a <- TAM::tamaan( tammodel, resp=dat1 )
summary(mod3a)
# extract item parameters
ipars <- mod2$itempartable_MIXTURE[ 1:10, ]
plot( 1:10, ipars[,3], type="o", ylim=range( ipars[,3:4] ), pch=16,
xlab="Item", ylab="Item difficulty")
lines( 1:10, ipars[,4], type="l", col=2, lty=2)
points( 1:10, ipars[,4], col=2, pch=2)
#-----------
#-- 3f: estimation with psychomix package
# estimation
mod3f <- psychomix::raschmix( as.matrix(dat), k=2, scores="meanvar")
summary(mod3f)
# plot class-specific item difficulties
plot(mod3f)
#############################################################################
# EXAMPLES Ch. 5: Unidimensional IRT models | polytomous data
#############################################################################
data(data.eid.kap5)
data0 <- data.eid.kap5
# extract items
dat <- data0[,2:7]
#*********************************************************
# Model 1: Partial credit model
#*********************************************************
#-----------
#-- 1a: estimation with TAM package
# estimation with tam.mml
mod1a <- TAM::tam.mml(dat)
summary(mod1a)
# person parameters in TAM
pp1a <- tam.wle(mod1a)
# plot item response functions
plot(mod1a,export=FALSE,ask=TRUE)
# Infit and outfit in TAM
itemf1a <- TAM::tam.fit(mod1a)
itemf1a
# model fit
modf1a <- TAM::tam.modelfit(mod1a)
summary(modf1a)
#-----------
#-- 1b: estimation with mirt package
# estimation with tam.mml
mod1b <- mirt::mirt( dat, 1, itemtype="Rasch")
summary(mod1b)
print(mod1b)
sirt::mirt.wrapper.coef(mod1b)
# plot item response functions
plot(mod1b, type="trace" )
par(mfrow=c(1,1))
# item fit
itemf1b <- mirt::itemfit(mod1b)
itemf1b
#-----------
#-- 1c: estimation with sirt package
# estimation with rm.facets
mod1c <- sirt::rm.facets(dat)
summary(mod1c)
summary(mod1a)
#-----------
#-- 1d: estimation with eRm package
# estimation
mod1d <- eRm::PCM(dat)
summary(mod1d)
# plot item response functions
eRm::plotICC(mod1d)
# person-item map
eRm::plotPImap(mod1d)
# item fit
itemf1d <- eRm::itemfit(pp1d)
#-----------
#-- 1e: estimation with ltm package
# estimation
mod1e <- ltm::gpcm(dat, constraint="1PL")
summary(mod1e)
# plot item response functions
plot(mod1e)
#*********************************************************
# Model 2: Generalized partial credit model
#*********************************************************
#-----------
#-- 2a: estimation with TAM package
# estimation with tam.mml
mod2a <- TAM::tam.mml.2pl(dat, irtmodel="GPCM")
summary(mod2a)
# model fit
modf2a <- TAM::tam.modelfit(mod2a)
summary(modf2a)
#-----------
#-- 2b: estimation with mirt package
# estimation
mod2b <- mirt::mirt( dat, 1, itemtype="gpcm")
summary(mod2b)
print(mod2b)
sirt::mirt.wrapper.coef(mod2b)
#-----------
#-- 2c: estimation with sirt package
# estimation with rm.facets
mod2c <- sirt::rm.facets(dat, est.a.item=TRUE)
summary(mod2c)
#-----------
#-- 2e: estimation with ltm package
# estimation
mod2e <- ltm::gpcm(dat)
summary(mod2e)
plot(mod2e)
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