sirt (version 4.1-15)

data.eid: Examples with Datasets from Eid and Schmidt (2014)

Description

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.

Usage

data(data.eid.kap4)
data(data.eid.kap5)
data(data.eid.kap6)
data(data.eid.kap7)

Format

• 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 ...
  

References

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/.

Examples

if (FALSE) {
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)
}