Package 'TAM'

Description

Includes marginal maximum likelihood estimation and joint maximum likelihood estimation for unidimensional and multidimensional item response models. The package functionality covers the Rasch model, 2PL model, 3PL model, generalized partial credit model, multi-faceted Rasch model, nominal item response model, structured latent class model, mixture distribution IRT models, and located latent class models. Latent regression models and plausible value imputation are also supported. For details see Adams, Wilson and Wang, 1997 <doi:10.1177/0146621697211001>, Adams, Wilson and Wu, 1997 <doi:10.3102/10769986022001047>, Formann, 1982 <doi:10.1002/bimj.4710240209>, Formann, 1992 <doi:10.1080/01621459.1992.10475229>.

Details

See http://www.edmeasurementsurveys.com/TAM/Tutorials/ for tutorials of the TAM package.

Author(s)

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>), Thomas Kiefer [aut], Margaret Wu [aut]

Maintainer: Alexander Robitzsch <[email protected]>

References

Adams, R. J., Wilson, M., & Wang, W. C. (1997). The multidimensional random coefficients multinomial logit model. Applied Psychological Measurement, 21(1), 1-23. doi:10.1177/0146621697211001

Adams, R. J., Wilson, M., & Wu, M. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22(1), 47-76. doi:10.3102/10769986022001047

Adams, R. J., & Wu, M. L. (2007). The mixed-coefficients multinomial logit model. A generalized form of the Rasch model. In M. von Davier & C. H. Carstensen (Eds.): Multivariate and mixture distribution Rasch models: Extensions and applications (pp. 55-76). New York: Springer. doi:10.1007/978-0-387-49839-3_4

Formann, A. K. (1982). Linear logistic latent class analysis. Biometrical Journal, 24(2), 171-190. doi:10.1002/bimj.4710240209

Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data. Journal of the American Statistical Association, 87(418), 476-486. doi:10.1080/01621459.1992.10475229

Description

The anova function compares two models estimated of class tam, tam.mml or tam.mml.3pl using a likelihood ratio test. The logLik function extracts the value of the log-Likelihood.

The function can be applied for values of tam.mml, tam.mml.2pl, tam.mml.mfr, tam.fa, tam.mml.3pl, tam.latreg or tamaan.

Usage

## S3 method for class 'tam'
anova(object, ...)
## S3 method for class 'tam'
logLik(object, ...)

## S3 method for class 'tam.mml'
anova(object, ...)
## S3 method for class 'tam.mml'
logLik(object, ...)

## S3 method for class 'tam.mml.3pl'
anova(object, ...)
## S3 method for class 'tam.mml.3pl'
logLik(object, ...)

## S3 method for class 'tamaan'
anova(object, ...)
## S3 method for class 'tamaan'
logLik(object, ...)

## S3 method for class 'tam.latreg'
anova(object, ...)
## S3 method for class 'tam.latreg'
logLik(object, ...)

## S3 method for class 'tam.np'
anova(object, ...)
## S3 method for class 'tam.np'
logLik(object, ...)

Arguments

Value

A data frame containing the likelihood ratio test statistic and information criteria.

Examples

#############################################################################
# EXAMPLE 1: Dichotomous data sim.rasch - 1PL vs. 2PL model
#############################################################################

data(data.sim.rasch)
# 1PL estimation
mod1 <- TAM::tam.mml(resp=data.sim.rasch)
logLik(mod1)
# 2PL estimation
mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch, irtmodel="2PL")
logLik(mod2)
# Model comparison
anova( mod1, mod2 )
  ##     Model   loglike Deviance Npars      AIC      BIC    Chisq df       p
  ##   1  mod1 -42077.88 84155.77    41 84278.77 84467.40 54.05078 39 0.05508
  ##   2  mod2 -42050.86 84101.72    80 84341.72 84709.79       NA NA      NA

## Not run: 
#############################################################################
# EXAMPLE 2: Dataset reading (sirt package): 1- vs. 2-dimensional model
#############################################################################

data(data.read, package="sirt")

# 1-dimensional model
mod1 <- TAM::tam.mml.2pl(resp=data.read )
# 2-dimensional model
mod2 <- TAM::tam.fa(resp=data.read, irtmodel="efa", nfactors=2,
             control=list(maxiter=150) )
# Model comparison
anova( mod1, mod2 )
  ##       Model   loglike Deviance Npars      AIC      BIC    Chisq df  p
  ##   1    mod1 -1954.888 3909.777    24 3957.777 4048.809 76.66491 11  0
  ##   2    mod2 -1916.556 3833.112    35 3903.112 4035.867       NA NA NA

## End(Not run)

Description

This function extract item parameters from a fitted lavaan::cfa object in lavaan. It extract item loadings, item intercepts and the mean and covariance matrix of latent variables in a confirmatory factor analysis model.

Usage

cfa.extract.itempars(object)

Arguments

Value

List with following entries

See Also

See IRTLikelihood.cfa for extracting the individual likelihood from fitted confirmatory factor analyses.

lavaan::cfa

Examples

#############################################################################
# EXAMPLE 1: CFA data.Students
#############################################################################

library(lavaan)
library(CDM)

data(data.Students, package="CDM")
dat <- data.Students

dat1 <- dat[, paste0( "mj", 1:4 ) ]

#*** Model 1: Unidimensional model scale mj
lavmodel <- "
   mj=~ mj1 + mj2 + mj3 + mj4
   mj ~~ mj
     "
mod1 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
summary(mod1, standardized=TRUE, rsquare=TRUE )
# extract parameters
res1 <- TAM::cfa.extract.itempars( mod1 )

## Not run: 
#*** Model 2: Scale mj - explicit modelling of item intercepts
lavmodel <- "
   mj=~ mj1 + mj2 + mj3 + mj4
   mj ~~ mj
   mj1 ~ 1
     "
mod2 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
summary(mod2, standardized=TRUE, rsquare=TRUE )
res2 <- TAM::cfa.extract.itempars( mod2 )

#*** Model 3: Tau-parallel measurements scale mj
lavmodel <- "
   mj=~ a*mj1 + a*mj2 + a*mj3 + a*mj4
   mj ~~ 1*mj
   mj1 ~ b*1
   mj2 ~ b*1
   mj3 ~ b*1
   mj4 ~ b*1
     "
mod3 <- lavaan::cfa( lavmodel, data=dat1, std.lv=TRUE )
summary(mod3, standardized=TRUE, rsquare=TRUE )
res3 <- TAM::cfa.extract.itempars( mod3 )

#*** Model 4: Two-dimensional CFA with scales mj and sc
dat2 <- dat[, c(paste0("mj",1:4), paste0("sc",1:4)) ]
# lavaan model with shortage "__" operator
lavmodel <- "
   mj=~ mj1__mj4
   sc=~ sc1__sc4
   mj ~~ sc
   mj ~~ 1*mj
   sc ~~ 1*sc
     "
lavmodel <- TAM::lavaanify.IRT( lavmodel, data=dat2 )$lavaan.syntax
cat(lavmodel)
mod4 <- lavaan::cfa( lavmodel, data=dat2, std.lv=TRUE )
summary(mod4, standardized=TRUE, rsquare=TRUE )
res4 <- TAM::cfa.extract.itempars( mod4 )

## End(Not run)

Description

Datasets and examples similar to the ones in the ConQuest manual (Wu, Adams, Wilson, & Haldane, 2007).

Usage

data(data.cqc01)
data(data.cqc02)
data(data.cqc03)
data(data.cqc04)
data(data.cqc05)

Format

• data.cqc01 contains 512 persons on 12 dichotomous items of following format

  'data.frame': 512 obs. of 12 variables:
$ BSMMA01: int 1 1 0 1 1 1 1 1 0 0 ...
$ BSMMA02: int 1 0 1 1 0 1 1 1 0 0 ...
$ BSMMA03: int 1 1 0 1 1 1 1 1 1 0 ...
[...]
$ BSMSA12: int 0 0 0 0 1 0 1 1 0 0 ...
  

• data.cqc02 contains 431 persons on 8 polytomous variables of following format

  'data.frame': 431 obs. of 8 variables:
$ It1: int 1 1 2 0 2 1 2 2 2 1 ...
$ It2: int 3 0 1 2 2 3 2 2 1 1 ...
$ It3: int 1 1 1 0 1 1 0 0 1 0 ...
[...]
$ It8: int 3 1 0 0 3 1 3 0 3 0 ...
  

• data.cqc03 contains 11200 observations for 5600 persons, 16 raters and 2 items (crit1 and crit2)

  'data.frame': 11200 obs. of 4 variables:
$ pid : num 10001 10001 10002 10002 10003 ...
$ rater: chr "R11" "R12" "R13" "R14" ...
$ crit1: int 2 2 2 1 3 2 2 1 1 1 ...
$ crit2: int 3 3 2 1 2 2 2 2 2 1 ...
  

• data.cqc04 contains 1452 observations for 363 persons, 4 raters, 4 topics and 5 items (spe, coh, str, gra, con)

  'data.frame': 1452 obs. of 8 variables:
$ pid : num 10010 10010 10010 10010 10016 ...
$ rater: chr "BE" "CO" "BE" "CO" ...
$ topic: chr "Spor" "Spor" "Spor" "Spor" ...
$ spe : int 2 0 2 1 3 3 3 3 3 2 ...
$ coh : int 1 1 2 0 3 3 3 3 3 3 ...
$ str : int 0 1 3 0 3 2 3 2 3 0 ...
$ gra : int 0 0 2 0 3 3 3 3 2 1 ...
$ con : int 0 0 0 0 3 1 2 2 3 0 ...
  

• data.cqc05 contains 1500 persons, 3 covariates and 157 items.

  'data.frame': 1500 obs. of 160 variables:
$ gender: int 1 0 1 0 0 0 0 1 0 1 ...
$ level : int 0 1 1 0 0 0 1 0 1 1 ...
$ gbyl : int 0 0 1 0 0 0 0 0 0 1 ...
$ A001 : num 0 0 0 1 0 1 1 1 0 1 ...
$ A002 : num 1 1 0 1 1 1 1 1 1 0 ...
$ A003 : num 0 0 0 0 1 1 1 0 0 1 ...
[...]
  

References

Wu, M. L., Adams, R. J., Wilson, M. R. & Haldane, S. (2007). ACER ConQuest Version 2.0. Mulgrave. https://shop.acer.edu.au/acer-shop/group/CON3.

See Also

See the sirt::R2conquest function for running ConQuest software from within R.

See the WrightMap package for functions connected to reading ConQuest files and creating Wright maps. ConQuest output files can be read into R with the help of the WrightMap::CQmodel function. See also the IRT.WrightMap function in TAM.

See also the eat package (https://r-forge.r-project.org/projects/eat/) for elaborate functionality for communication of ConQuest with R.

Examples

## Not run: 

library(sirt)
library(WrightMap)
# In the following, ConQuest will also be used for estimation.
path.conquest <- "C:/Conquest"             # path of the ConQuest console.exe
setwd( "p:/my_files/ConQuest_analyses" )  # working directory

#############################################################################
# EXAMPLE 01: Rasch model data.cqc01
#############################################################################

data(data.cqc01)
dat <- data.cqc01

#********************************************
#*** Model 01: Estimate Rasch model
mod01 <- TAM::tam.mml(dat)
summary(mod01)

#------- ConQuest

# estimate model
cmod01 <- sirt::R2conquest( dat, name="mod01", path.conquest=path.conquest)
summary(cmod01)   # summary output
# read shw file with some terms
shw01a <- sirt::read.show( "mod01.shw" )
cmod01$shw.itemparameter
# read person item maps
pi01a <- sirt::read.pimap( "mod01.shw" )
cmod01$shw.pimap
# read plausible values (npv=10 plausible values)
pv01a <- sirt::read.pv(pvfile="mod01.pv", npv=10)
cmod01$person

# read ConQuest model
res01a <- WrightMap::CQmodel(p.est="mod01.wle", show="mod01.shw", p.type="WLE" )
print(res01a)
# plot item fit
WrightMap::fitgraph(res01a)
# Wright map
plot(res01a, label.items.srt=90 )

#############################################################################
# EXAMPLE 02: Partial credit model and rating scale model data.cqc02
#############################################################################

data(data.cqc02)
dat <- data.cqc02

#********************************************
# Model 02a: Partial credit model in ConQuest parametrization 'item+item*step'
mod02a <- TAM::tam.mml( dat, irtmodel="PCM2" )
summary(mod02a, file="mod02a")
fit02a <- TAM::tam.fit(mod02a)
summary(fit02a)

#--- ConQuest
# estimate model
maxK <- max( dat, na.rm=TRUE )
cmod02a <- sirt::R2conquest( dat, itemcodes=0:maxK, model="item+item*step",
               name="mod02a", path.conquest=path.conquest)
summary(cmod02a)   # summary output

# read ConQuest model
res02a <- WrightMap::CQmodel(p.est="mod02a.wle", show="mod02a.shw", p.type="WLE" )
print(res02a)
# Wright map
plot(res02a, label.items.srt=90 )
plot(res02a, item.table="item")

#********************************************
# Model 02b: Rating scale model
mod02b <- TAM::tam.mml( dat, irtmodel="RSM" )
summary( mod02b )

#############################################################################
# EXAMPLE 03: Faceted Rasch model for rating data data.cqc03
#############################################################################

data(data.cqc03)
# select items
resp <- data.cqc03[, c("crit1","crit2") ]

#********************************************
# Model 03a: 'item+step+rater'
mod03a <- TAM::tam.mml.mfr( resp, facets=data.cqc03[,"rater",drop=FALSE],
            formulaA=~ item+step+rater, pid=data.cqc03$pid )
summary( mod03a )

#--- ConQuest
X <- data.cqc03[,"rater",drop=FALSE]
X$rater <- as.numeric(substring( X$rater, 2 )) # convert 'rater' in numeric format
maxK <- max( resp, na.rm=TRUE)
cmod03a <- sirt::R2conquest( resp,  X=X, regression="",  model="item+step+rater",
             name="mod03a", path.conquest=path.conquest, set.constraints="cases" )
summary(cmod03a)   # summary output

# read ConQuest model
res03a <- WrightMap::CQmodel(p.est="mod03a.wle", show="mod03a.shw", p.type="WLE" )
print(res03a)
# Wright map
plot(res03a)

#********************************************
# Model 03b: 'item:step+rater'
mod03b <- TAM::tam.mml.mfr( resp, facets=data.cqc03[,"rater",drop=FALSE],
            formulaA=~ item + item:step+rater, pid=data.cqc03$pid )
summary( mod03b )

#********************************************
# Model 03c: 'step+rater' for first item 'crit1'
# Restructuring the data is necessary.
# Define raters as items in the new dataset 'dat1'.
persons <- unique( data.cqc03$pid )
raters <- unique( data.cqc03$rater )
dat1 <- matrix( NA, nrow=length(persons), ncol=length(raters) + 1 )
dat1 <- as.data.frame(dat1)
colnames(dat1) <- c("pid", raters )
dat1$pid <- persons
for (rr in raters){
    dat1.rr <- data.cqc03[ data.cqc03$rater==rr, ]
    dat1[ match(dat1.rr$pid, persons),rr] <- dat1.rr$crit1
        }
  ##   > head(dat1)
  ##       pid R11 R12 R13 R14 R15 R16 R17 R18 R19 R20 R21 R22 R23 R24 R25 R26
  ##   1 10001   2   2  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  ##   2 10002  NA  NA   2   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  ##   3 10003  NA  NA   3   2  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  ##   4 10004  NA  NA   2   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  ##   5 10005  NA  NA   1   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
  ##   6 10006  NA  NA   1   1  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA  NA
# estimate model 03c
mod03c <- TAM::tam.mml( dat1[,-1], pid=dat1$pid )
summary( mod03c )

#############################################################################
# EXAMPLE 04: Faceted Rasch model for rating data data.cqc04
#############################################################################

data(data.cqc04)
resp <- data.cqc04[,4:8]
facets <- data.cqc04[, c("rater", "topic") ]

#********************************************
# Model 04a: 'item*step+rater+topic'
formulaA <- ~ item*step + rater + topic
mod04a <- TAM::tam.mml.mfr( resp, facets=facets,
            formulaA=formulaA, pid=data.cqc04$pid )
summary( mod04a )

#********************************************
# Model 04b: 'item*step+rater+topic+item*rater+item*topic'
formulaA <- ~ item*step + rater + topic + item*rater + item*topic
mod04b <- TAM::tam.mml.mfr( resp, facets=facets,
            formulaA=formulaA, pid=data.cqc04$pid )
summary( mod04b )

#********************************************
# Model 04c: 'item*step' with fixing rater and topic parameters to zero
formulaA <- ~ item*step + rater + topic
mod04c0 <- TAM::tam.mml.mfr( resp, facets=facets,
            formulaA=formulaA, pid=data.cqc04$pid, control=list(maxiter=4) )
summary( mod04c0 )
# fix rater and topic parameter to zero
xsi.est <- mod04c0$xsi
xsi.fixed <- cbind( seq(1,nrow(xsi.est)), xsi.est$xsi )
rownames(xsi.fixed) <- rownames(xsi.est)
xsi.fixed <- xsi.fixed[ c(8:13),]
xsi.fixed[,2] <- 0
  ##   > xsi.fixed
  ##             [,1] [,2]
  ##   raterAM      8    0
  ##   raterBE      9    0
  ##   raterCO     10    0
  ##   topicFami   11    0
  ##   topicScho   12    0
  ##   topicSpor   13    0
mod04c1 <- TAM::tam.mml.mfr( resp, facets=facets,
             formulaA=formulaA, pid=data.cqc04$pid, xsi.fixed=xsi.fixed )
summary( mod04c1 )

#############################################################################
# EXAMPLE 05: Partial credit model with latent regression and
#             plausible value imputation
#############################################################################

data(data.cqc05)
resp <- data.cqc05[, -c(1:3) ] # select item responses

#********************************************
# Model 05a: Partial credit model
mod05a <-tam.mml(resp=resp, irtmodel="PCM2" )

#********************************************
# Model 05b: Partial credit model with latent regressors
mod05b <-tam.mml(resp=resp, irtmodel="PCM2",  Y=data.cqc05[,1:3] )
# Plausible value imputation
pvmod05b <- TAM::tam.pv( mod05b )

## End(Not run)

Description

Some C-Test datasets.

Usage

data(data.ctest1)
data(data.ctest2)

Format

• The dataset data.ctest1 contains item responses of C-tests at two time points. The format is

  'data.frame': 1675 obs. of 42 variables:
$ idstud : num 100101 100102 100103 100104 100105 ...
$ idclass: num 1001 1001 1001 1001 1001 ...
$ A01T1 : int 0 1 0 1 1 NA 1 0 1 1 ...
$ A02T1 : int 0 1 0 1 0 NA 0 1 1 0 ...
$ A03T1 : int 0 1 1 1 0 NA 0 1 1 1 ...
$ A04T1 : int 1 0 0 0 0 NA 0 0 0 0 ...
$ A05T1 : int 0 0 0 1 1 NA 0 0 1 1 ...
$ B01T1 : int 1 1 0 1 1 NA 0 0 1 0 ...
$ B02T1 : int 0 0 0 1 0 NA 0 0 1 1 ...
[...]
$ C02T2 : int 0 1 1 1 1 0 1 0 1 1 ...
$ C03T2 : int 1 1 0 1 0 0 0 0 1 0 ...
$ C04T2 : int 0 0 1 0 0 0 0 1 0 0 ...
$ C05T2 : int 0 1 0 0 1 0 1 0 0 1 ...
$ D01T2 : int 0 1 1 1 0 1 1 1 1 1 ...
$ D02T2 : int 0 1 1 1 1 1 0 1 1 1 ...
$ D03T2 : int 1 0 0 0 1 0 0 0 0 0 ...
$ D04T2 : int 1 0 1 1 1 0 1 0 1 1 ...
$ D05T2 : int 1 0 1 1 1 1 1 1 1 1 ...
  

• The dataset data.ctest2 contains two datasets ($data1 containing item responses, $data2 containing sum scores of each C-test) and a data frame $ITEM with item informations.

  List of 3
$ data1:'data.frame': 933 obs. of 102 variables:
..$ idstud: num [1:933] 10001 10002 10003 10004 10005 ...
..$ female: num [1:933] 1 1 0 0 0 0 1 1 0 1 ...
..$ A101 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ A102 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ A103 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ A104 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ A105 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ A106 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ E115 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ E116 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ E117 : int [1:933] NA NA NA NA NA NA NA NA NA NA ...
.. [list output truncated]
$ data2:'data.frame': 933 obs. of 7 variables:
..$ idstud: num [1:933] 10001 10002 10003 10004 10005 ...
..$ female: num [1:933] 1 1 0 0 0 0 1 1 0 1 ...
..$ A : num [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ B : num [1:933] 16 14 15 13 17 11 11 18 19 13 ...
..$ C : num [1:933] 17 15 17 14 17 13 9 15 17 12 ...
..$ D : num [1:933] NA NA NA NA NA NA NA NA NA NA ...
..$ E : num [1:933] NA NA NA NA NA NA NA NA NA NA ...
$ ITEM :'data.frame': 100 obs. of 3 variables:
..$ item : chr [1:100] "A101" "A102" "A103" "A104" ...
..$ ctest : chr [1:100] "A" "A" "A" "A" ...
..$ testlet: int [1:100] 1 1 2 2 2 3 3 3 NA 4 ...
  

Description

Datasets included in the TAM package

Usage

data(data.ex08)
data(data.ex10)
data(data.ex11)
data(data.ex12)
data(data.ex14)
data(data.ex15)
data(data.exJ03)

Format

• Data data.ex08 for Example 8 in tam.mml has the following format:

  List of 2
$ facets:'data.frame': 1000 obs. of 1 variable:
..$ female: int [1:1000] 1 1 1 1 1 1 1 1 1 1 ...
$ resp : num [1:1000, 1:10] 1 1 1 0 1 0 1 1 0 1 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:10] "I0001" "I0002" "I0003" "I0004" ...
  

• Data data.ex10 for Example 10 in tam.mml has the following format:

  'data.frame': 675 obs. of 7 variables:
$ pid : int 1 1 1 2 2 3 3 4 4 5 ...
$ rater: int 1 2 3 2 3 1 2 1 3 1 ...
$ I0001: num 0 1 1 1 1 1 1 1 1 1 ...
$ I0002: num 1 1 1 1 1 0 1 1 1 1 ...
$ I0003: num 1 1 1 1 0 0 0 1 0 1 ...
$ I0004: num 0 1 0 0 1 0 1 0 1 0 ...
$ I0005: num 0 0 1 1 1 0 0 1 0 1 ...
  

• Data data.ex11 for Example 11 in tam.mml has the following format:

  'data.frame': 3400 obs. of 13 variables:
$ booklet: chr "B1" "B1" "B3" "B2" ...
$ M133 : int 1 1 NA 1 NA 1 NA 1 0 1 ...
$ M176 : int 1 0 1 NA 0 0 0 NA NA NA ...
$ M202 : int NA NA NA 0 NA NA NA 0 0 0 ...
$ M212 : int NA NA 1 0 0 NA 0 1 0 0 ...
$ M214 : int 1 0 1 1 0 0 0 0 1 0 ...
$ M259 : int NA NA 1 1 1 NA 1 1 1 1 ...
$ M303 : int NA NA 1 1 1 NA 1 1 1 0 ...
$ M353 : int NA NA NA 1 NA NA NA 1 1 9 ...
$ M355 : int NA NA NA 1 NA NA NA 1 1 0 ...
$ M444 : int 0 0 0 NA 0 0 0 NA NA NA ...
$ M446 : int 1 0 0 1 0 1 1 1 0 0 ...
$ M449 : int NA NA NA 1 NA NA NA 1 1 1 ...

  Missing responses by design are coded as NA, omitted responses are coded as 9.
  

• Data data.ex12 for Example 12 in tam.mml has the following format:

  num [1:100, 1:10] 1 1 1 1 1 1 1 1 1 1 ...
- attr(*, "dimnames")=List of 2
..$ : NULL
..$ : chr [1:10] "I0001" "I0002" "I0003" "I0004" ...
  

• Data data.ex14 for Example 14 in tam.mml has the following format:

  'data.frame': 1110 obs. of 11 variables:
$ pid : num 1001 1001 1001 1001 1001 ...
$ X1 : num 1 1 1 1 1 1 0 0 0 0 ...
$ X2 : int 1 1 1 1 1 1 1 1 1 1 ...
$ rater: int 4 4 4 4 4 4 4 4 4 4 ...
$ crit1: int 0 0 2 1 1 2 0 0 0 0 ...
$ crit2: int 0 0 0 0 0 0 0 0 0 0 ...
$ crit3: int 0 1 1 0 0 1 0 0 1 0 ...
$ crit4: int 0 0 0 1 0 0 0 0 0 0 ...
$ crit5: int 0 0 0 0 1 1 0 0 0 0 ...
$ crit6: int 0 0 0 0 1 0 0 0 0 0 ...
$ crit7: int 1 0 2 0 0 0 0 0 0 0 ...
  

• Data data.ex15 for Example 15 in tam.mml has the following format:

  'data.frame': 2155 obs. of 182 variables:
$ pid : num 10001 10002 10003 10004 10005 ...
$ group : num 1 1 0 0 1 0 1 0 1 1 ...
$ Item001: num 0 NA NA 0 NA NA NA 0 0 NA ...
$ Item002: num 1 NA NA 1 NA NA NA NA 1 NA ...
$ Item003: num NA NA NA NA 1 NA NA NA NA 1 ...
$ Item004: num NA NA 0 NA NA NA NA NA NA NA ...
$ Item005: num NA NA 1 NA NA NA NA NA NA NA ...
[...]

  This dataset shows an atypical convergence behavior. Look at Example 15 to fix convergence problems using arguments increment.factor and fac.oldxsi.
  

• Data data.exJ03 for Example 4 in tam.jml has the following format:

  List of 2
$ resp:'data.frame': 40 obs. of 20 variables:
..$ I104: int [1:40] 4 5 6 5 3 4 3 5 4 6 ...
..$ I118: int [1:40] 6 4 6 5 3 2 5 3 5 4 ...
[...] ..$ I326: int [1:40] 6 1 5 1 4 2 4 1 6 1 ...
..$ I338: int [1:40] 6 2 6 1 6 2 4 1 6 1 ...
$ X :'data.frame': 40 obs. of 4 variables:
..$ rater : int [1:40] 40 40 96 96 123 123 157 157 164 164 ...
..$ gender: int [1:40] 2 2 1 1 1 1 2 2 2 2 ...
..$ region: num [1:40] 1 1 1 1 2 2 1 1 1 1 ...
..$ leader: int [1:40] 1 2 1 2 1 2 1 2 1 2 ...

  It is a rating dataset (a subset of a dataset provided by Matt Barney).
  

• Data data.ex16 contains dichotomous item response data from three studies corresponding to three grades.

  'data.frame': 3235 obs. of 25 variables:
$ idstud: num 1e+05 1e+05 1e+05 1e+05 1e+05 ...
$ grade : num 1 1 1 1 1 1 1 1 1 1 ...
$ A1 : int 1 1 1 1 1 1 1 1 1 1 ...
$ B1 : int 1 1 1 1 1 1 1 1 1 1 ...
$ C1 : int 1 1 1 1 1 1 1 1 1 1 ...
$ D1 : int 1 1 1 1 1 1 1 1 1 1 ...
$ E1 : int 0 0 1 0 1 1 1 0 1 1 ...
$ E2 : int 1 1 1 1 1 1 1 0 1 1 ...
$ E3 : int 1 1 1 1 1 1 1 0 1 1 ...
$ F1 : int 1 0 1 1 0 0 1 0 1 1 ...
$ G1 : int 0 1 1 1 1 0 1 0 1 1 ...
$ G2 : int 1 1 1 1 1 0 0 0 1 1 ...
$ G3 : int 1 0 1 1 1 0 0 0 1 1 ...
$ H1 : int 1 0 1 1 1 0 0 0 1 1 ...
$ H2 : int 1 0 1 1 1 0 0 0 1 1 ...
$ I1 : int 1 0 1 0 1 0 0 0 1 1 ...
$ I2 : int 1 0 1 0 1 0 0 0 1 1 ...
$ J1 : int NA NA NA NA NA NA NA NA NA NA ...
$ K1 : int NA NA NA NA NA NA NA NA NA NA ...
$ L1 : int NA NA NA NA NA NA NA NA NA NA ...
$ L2 : int NA NA NA NA NA NA NA NA NA NA ...
$ L3 : int NA NA NA NA NA NA NA NA NA NA ...
$ M1 : int NA NA NA NA NA NA NA NA NA NA ...
$ M2 : int NA NA NA NA NA NA NA NA NA NA ...
$ M3 : int NA NA NA NA NA NA NA NA NA NA ...
  

• Data data.ex17 contains polytomous item response data from three studies corresponding to three grades.

  'data.frame': 3235 obs. of 15 variables:
$ idstud: num 1e+05 1e+05 1e+05 1e+05 1e+05 ...
$ grade : num 1 1 1 1 1 1 1 1 1 1 ...
$ A : int 1 1 1 1 1 1 1 1 1 1 ...
$ B : int 1 1 1 1 1 1 1 1 1 1 ...
$ C : int 1 1 1 1 1 1 1 1 1 1 ...
$ D : int 1 1 1 1 1 1 1 1 1 1 ...
$ E : num 2 2 3 2 3 3 3 0 3 3 ...
$ F : int 1 0 1 1 0 0 1 0 1 1 ...
$ G : num 2 2 3 3 3 0 1 0 3 3 ...
$ H : num 2 0 2 2 2 0 0 0 2 2 ...
$ I : num 2 0 2 0 2 0 0 0 2 2 ...
$ J : int NA NA NA NA NA NA NA NA NA NA ...
$ K : int NA NA NA NA NA NA NA NA NA NA ...
$ L : num NA NA NA NA NA NA NA NA NA NA ...
$ M : num NA NA NA NA NA NA NA NA NA NA ...
  

See Also

These examples are used in the tam.mml Examples.

Description

Dataset FIMS study with raw responses (data.fims.Aus.Jpn.raw) or scored responses (data.fims.Aus.Jpn.scored) of Australian and Japanese Students.

Usage

data(data.fims.Aus.Jpn.raw)
data(data.fims.Aus.Jpn.scored)

Format

A data frame with 6371 observations on the following 16 variables.

SEX

Gender: 1 – male, 2 – female

M1PTI1

A Mathematics item

M1PTI2

A Mathematics item

M1PTI3

A Mathematics item

M1PTI6

A Mathematics item

M1PTI7

A Mathematics item

M1PTI11

A Mathematics item

M1PTI12

A Mathematics item

M1PTI14

A Mathematics item

M1PTI17

A Mathematics item

M1PTI18

A Mathematics item

M1PTI19

A Mathematics item

M1PTI21

A Mathematics item

M1PTI22

A Mathematics item

M1PTI23

A Mathematics item

country

Country: 1 – Australia, 2 – Japan

See Also

http://www.edmeasurementsurveys.com/TAM/Tutorials/7DIF.htm

Examples

## Not run: 
data(data.fims.Aus.Jpn.scored)
#*****
# Model 1: Differential Item Functioning Gender for Australian students

# extract Australian students
scored <- data.fims.Aus.Jpn.scored[ data.fims.Aus.Jpn.scored$country==1, ]

# select items
items <- grep("M1", colnames(data.fims.Aus.Jpn.scored), value=TRUE)
##   > items
##    [1] "M1PTI1"  "M1PTI2"  "M1PTI3"  "M1PTI6"  "M1PTI7"  "M1PTI11" "M1PTI12"
##    [8] "M1PTI14" "M1PTI17" "M1PTI18" "M1PTI19" "M1PTI21" "M1PTI22" "M1PTI23"

# Run partial credit model
mod1 <- TAM::tam.mml(scored[,items])

# extract values of the gender variable into a variable called "gender".
gender <- scored[,"SEX"]
# computes the test score for each student by calculating the row sum
# of each student's scored responses.
raw_score <- rowSums(scored[,items] )

# compute the mean test score for each gender group: 1=male, and 2=female
stats::aggregate(raw_score,by=list(gender),FUN=mean)
# The mean test score is 6.12 for group 1 (males) and 6.27 for group 2 (females).
# That is, the two groups performed similarly, with girls having a slightly
# higher mean test score. The step of computing raw test scores is not necessary
# for the IRT analyses. But it's always a good practice to explore the data
# a little before delving into more complex analyses.

# Facets analysis
# To conduct a DIF analysis, we set up the variable "gender" as a facet and
# re-run the IRT analysis.
formulaA <- ~item+gender+item*gender    # define facets analysis
facets <- as.data.frame(gender)         # data frame with student covariates
# facets model for studying differential item functioning
mod2 <- TAM::tam.mml.mfr( resp=scored[,items], facets=facets, formulaA=formulaA )
summary(mod2)

## End(Not run)

Description

This is a subsample of the dataset used in Geiser et al. (2006) and Geiser and Eid (2010).

Usage

data(data.geiser)

Format

A data frame with 519 observations on the following 24 variables

'data.frame': 519 obs. of 24 variables:
$ mrt1 : num 0 0 0 0 0 0 0 0 0 0 ...
$ mrt2 : num 0 0 0 0 0 0 0 0 0 0 ...
$ mrt3 : num 0 0 0 0 0 0 0 0 1 0 ...
$ mrt4 : num 0 0 0 0 0 1 0 0 0 0 ...
[...]
$ mrt23: num 0 0 0 0 0 0 0 1 0 0 ...
$ mrt24: num 0 0 0 0 0 0 0 0 0 0 ...

References

Geiser, C., & Eid, M. (2010). Item-Response-Theorie. In C. Wolf & H. Best (Hrsg.). Handbuch der sozialwissenschaftlichen Datenanalyse (S. 311-332). VS Verlag fuer Sozialwissenschaften.

Geiser, C., Lehmann, W., & Eid, M. (2006). Separating rotators from nonrotators in the mental rotations test: A multigroup latent class analysis. Multivariate Behavioral Research, 41(3), 261-293. doi:10.1207/s15327906mbr4103_2

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Latent trait and latent class models (Geiser et al., 2006, MBR)
#############################################################################

data(data.geiser)
dat <- data.geiser

#**********************************************
# Model 1: Rasch model
tammodel <- "
  LAVAAN MODEL:
    F=~ 1*mrt1__mrt12
    F ~~ F
  ITEM TYPE:
    ALL(Rasch)
    "
mod1 <- TAM::tamaan( tammodel, dat)
summary(mod1)

#**********************************************
# Model 2: 2PL model
tammodel <- "
  LAVAAN MODEL:
    F=~ mrt1__mrt12
    F ~~ 1*F
    "
mod2 <- TAM::tamaan( tammodel, dat)
summary(mod2)

# model comparison Rasch vs. 2PL
anova(mod1,mod2)

#*********************************************************************
#*** Model 3: Latent class analysis with four classes

tammodel <- "
ANALYSIS:
  TYPE=LCA;
  NCLASSES(4);   # 4 classes
  NSTARTS(10,20); # 10 random starts with 20 iterations
LAVAAN MODEL:
  F=~ mrt1__mrt12
    "
mod3 <- TAM::tamaan( tammodel, resp=dat  )
summary(mod3)

# extract item response functions
imod2 <- IRT.irfprob(mod3)[,2,]
# plot class specific probabilities
matplot( imod2, type="o", pch=1:4, xlab="Item", ylab="Probability" )
legend( 10,1, paste0("Class",1:4), lty=1:4, col=1:4, pch=1:4 )

#*********************************************************************
#*** Model 4: Latent class analysis with five classes

tammodel <- "
ANALYSIS:
  TYPE=LCA;
  NCLASSES(5);
  NSTARTS(10,20);
LAVAAN MODEL:
  F=~ mrt1__mrt12
    "
mod4 <- TAM::tamaan( tammodel, resp=dat )
summary(mod4)

# compare different models
AIC(mod1); AIC(mod2); AIC(mod3); AIC(mod4)
BIC(mod1); BIC(mod2); BIC(mod3); BIC(mod4)
# more condensed form
IRT.compareModels(mod1, mod2, mod3, mod4)

#############################################################################
# EXAMPLE 2: Rasch model and mixture Rasch model (Geiser & Eid, 2010)
#############################################################################

data(data.geiser)
dat <- data.geiser

#*********************************************************************
#*** Model 1: Rasch model
tammodel <- "
LAVAAN MODEL:
  F=~ mrt1__mrt6
  F ~~ F
ITEM TYPE:
  ALL(Rasch);
    "
mod1 <- TAM::tamaan( tammodel, resp=dat  )
summary(mod1)

#*********************************************************************
#*** Model 2: Mixed Rasch model with two classes
tammodel <- "
ANALYSIS:
  TYPE=MIXTURE ;
  NCLASSES(2);
  NSTARTS(20,25);
LAVAAN MODEL:
  F=~ mrt1__mrt6
  F ~~ F
ITEM TYPE:
  ALL(Rasch);
    "
mod2 <- TAM::tamaan( tammodel, resp=dat  )
summary(mod2)

# plot item parameters
ipars <- mod2$itempartable_MIXTURE[ 1:6, ]
plot( 1:6, ipars[,3], type="o", ylim=c(-3,2), pch=16,
        xlab="Item", ylab="Item difficulty")
lines( 1:6, ipars[,4], type="l", col=2, lty=2)
points( 1:6, ipars[,4],  col=2, pch=2)

# extract individual posterior distribution
post2 <- IRT.posterior(mod2)
str(post2)
# num [1:519, 1:30] 0.000105 0.000105 0.000105 0.000105 0.000105 ...
# - attr(*, "theta")=num [1:30, 1:30] 1 0 0 0 0 0 0 0 0 0 ...
# - attr(*, "prob.theta")=num [1:30, 1] 1.21e-05 2.20e-04 2.29e-03 1.37e-02 4.68e-02 ...
# - attr(*, "G")=num 1

# There are 2 classes and 15 theta grid points for each class
# The loadings of the theta grid on items are as follows
mod2$E[1,2,,"mrt1_F_load_Cl1"]
mod2$E[1,2,,"mrt1_F_load_Cl2"]

# compute individual posterior probability for class 1 (first 15 columns)
round( rowSums( post2[, 1:15] ), 3 )
# columns 16 to 30 refer to class 2

#*********************************************************************
#*** Model 3: Mixed Rasch model with three classes
tammodel <- "
ANALYSIS:
  TYPE=MIXTURE ;
  NCLASSES(3);
  NSTARTS(20,25);
LAVAAN MODEL:
  F=~ mrt1__mrt6
  F ~~ F
ITEM TYPE:
  ALL(Rasch);
    "
mod3 <- TAM::tamaan( tammodel, resp=dat  )
summary(mod3)

# plot item parameters
ipars <- mod3$itempartable_MIXTURE[ 1:6, ]
plot( 1:6, ipars[,3], type="o", ylim=c(-3.7,2), pch=16,
        xlab="Item", ylab="Item difficulty")
lines( 1:6, ipars[,4], type="l", col=2, lty=2)
points( 1:6, ipars[,4],  col=2, pch=2)
lines( 1:6, ipars[,5], type="l", col=3, lty=3)
points( 1:6, ipars[,5],  col=3, pch=17)

# model comparison
IRT.compareModels( mod1, mod2, mod3 )

## End(Not run)

Description

Dataset with ordered values of 3 indicators

Usage

data(data.gpcm)

Format

A data frame with 392 observations on the following 3 items.

Comfort

a numeric vector

Work

a numeric vector

Benefit

a numeric vector

Source

The dataset is copied from the ltm package.

Examples

data(data.gpcm)
summary(data.gpcm)

Description

Dataset used in Janssen and Geiser (2010).

Usage

data(data.janssen)
data(data.janssen2)

Format

• data.janssen is a data frame with 346 observations on the 8 items of the following format

  'data.frame': 346 obs. of 8 variables:
$ PIS1 : num 1 1 1 0 0 1 1 1 0 1 ...
$ PIS3 : num 0 1 1 1 1 1 0 1 1 1 ...
$ PIS4 : num 1 1 1 1 1 1 1 1 1 1 ...
$ PIS5 : num 0 1 1 0 1 1 1 1 1 0 ...
$ SCR6 : num 1 1 1 1 1 1 1 1 1 0 ...
$ SCR9 : num 1 1 1 1 0 0 0 1 0 0 ...
$ SCR10: num 0 0 0 0 0 0 0 0 0 0 ...
$ SCR17: num 0 0 0 0 0 1 0 0 0 0 ...
  

• data.janssen2 contains 20 IST items:

  'data.frame': 346 obs. of 20 variables:
$ IST01 : num 1 1 1 0 0 1 1 1 0 1 ...
$ IST02 : num 1 0 1 0 1 1 1 1 0 1 ...
$ IST03 : num 0 1 1 1 1 1 0 1 1 1 ...
[...]
$ IST020: num 0 0 0 1 1 0 0 0 0 0 ...
  

References

Janssen, A. B., & Geiser, C. (2010). On the relationship between solution strategies in two mental rotation tasks. Learning and Individual Differences, 20(5), 473-478. doi:10.1016/j.lindif.2010.03.002

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: CCT data, Janssen and Geiser (2010, LID)
#            Latent class analysis based on data.janssen
#############################################################################

data(data.janssen)
dat <- data.janssen
colnames(dat)
  ##   [1] "PIS1"  "PIS3"  "PIS4"  "PIS5"  "SCR6"  "SCR9"  "SCR10" "SCR17"

#*********************************************************************
#*** Model 1: Latent class analysis with two classes

tammodel <- "
ANALYSIS:
  TYPE=LCA;
  NCLASSES(2);
  NSTARTS(10,20);
LAVAAN MODEL:
  # missing item numbers (e.g. PIS2) are ignored in the model
  F=~ PIS1__PIS5 + SCR6__SCR17
    "
mod3 <- TAM::tamaan( tammodel, resp=dat  )
summary(mod3)

# extract item response functions
imod2 <- IRT.irfprob(mod3)[,2,]
# plot class specific probabilities
ncl <- 2
matplot( imod2, type="o", pch=1:ncl, xlab="Item", ylab="Probability" )
legend( 1, .3, paste0("Class",1:ncl), lty=1:ncl, col=1:ncl, pch=1:ncl )

#*********************************************************************
#*** Model 2: Latent class analysis with three classes

tammodel <- "
ANALYSIS:
  TYPE=LCA;
  NCLASSES(3);
  NSTARTS(10,20);
LAVAAN MODEL:
  F=~ PIS1__PIS5 + SCR6__SCR17
    "
mod3 <- TAM::tamaan( tammodel, resp=dat  )
summary(mod3)

# extract item response functions
imod2 <- IRT.irfprob(mod3)[,2,]
# plot class specific probabilities
ncl <- 3
matplot( imod2, type="o", pch=1:ncl, xlab="Item", ylab="Probability" )
legend( 1, .3, paste0("Class",1:ncl), lty=1:ncl, col=1:ncl, pch=1:ncl )

# compare models
AIC(mod1); AIC(mod2)

## End(Not run)

Description

Dataset of responses from multiple choice items, containing 143 students on 30 items.

Usage

data(data.mc)

Format

The dataset is a list with two elements. The entry raw contains unscored (raw) item responses and the entry scored contains the scored (recoded) item responses. The format is:

List of 2
$ raw : chr [1:143, 1:30] "A" "A" "A" "A" ...
..- attr(*, "dimnames")=List of 2
.. ..$ : NULL
.. ..$ : chr [1:30] "I01" "I02" "I03" "I04" ...
$ scored:'data.frame':
..$ I01: num [1:143] 1 1 1 1 1 1 1 1 1 1 ...
..$ I02: num [1:143] 1 1 1 0 1 1 1 1 1 1 ...
..$ I03: num [1:143] 1 1 1 1 1 1 1 1 1 1 ...
[...]
..$ I29: num [1:143] NA 0 1 0 1 0 0 0 0 0 ...
..$ I30: num [1:143] NA NA 1 1 1 1 0 1 1 0 ...

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)

## Not run: 
#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 )

## End(Not run)

Description

Simulated data from multiple facets.

Usage

data(data.sim.mfr)
 data(data.sim.facets)

Format

The format of data.sim.mfr is:
num [1:100, 1:5] 3 2 1 1 0 1 0 1 0 0 ...
- attr(*, "dimnames")=List of 2
..$ : chr [1:100] "V1" "V1.1" "V1.2" "V1.3" ...
..$ : NULL

The format of data.sim.facets is:
'data.frame': 100 obs. of 3 variables:
$ rater : num 1 2 3 4 5 1 2 3 4 5 ...
$ topic : num 3 1 3 1 3 2 3 2 2 1 ...
$ female: num 2 2 1 2 1 1 2 1 2 1 ...

Source

Simulated

Examples

#######
# sim multi faceted Rasch model
data(data.sim.mfr)
data(data.sim.facets)

  # 1: A-matrix test_rater
  test_1_items <- TAM::.A.matrix( data.sim.mfr, formulaA=~rater,
            facets=data.sim.facets, constraint="items" )
  test_1_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~rater,
            facets=data.sim.facets, constraint="cases" )

  # 2: test_item+rater
  test_2_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater,
            facets=data.sim.facets, constraint="cases" )

  # 3: test_item+rater+topic+ratertopic
  test_3_items <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater*topic,
            facets=data.sim.facets, constraint="items" )
  # conquest uses a different way of ordering the rows
  # these are the first few rows of the conquest design matrix
  # test_3_items$A[grep("item1([[:print:]])*topic1", rownames(test_3_items)),]

  # 4: test_item+step
  test_4_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+step,
            facets=data.sim.facets, constraint="cases" )

  # 5: test_item+item:step
  test_5_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+item:step,
            facets=data.sim.facets, constraint="cases" )
  test_5_cases$A[, grep("item1", colnames(test_5_cases)) ]

  # 5+x: more
  #=> 6: is this even well defined in the conquest-design output
  #          (see test_item+topicstep_cases.cqc / .des)
  #        regardless of the meaning of such a formula;
  #        currently .A.matrix throws a warning
  # test_6_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+topic:step,
  #                 facets=data.sim.facets, constraint="cases" )
  test_7_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+topic+topic:step,
            facets=data.sim.facets, constraint="cases" )

## Not run: 
  #=> 8: same as with 6
  test_8_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+rater+item:rater:step,
            facets=data.sim.facets, constraint="cases" )
## [1] "Can't proceed the estimation: Lower-order term is missing."
  test_9_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+step+rater+item:step+item:rater,
            facets=data.sim.facets, constraint="cases" )
  test_10_cases <- TAM::.A.matrix( data.sim.mfr, formulaA=~item+female+item:female,
            facets=data.sim.facets, constraint="cases" )

  ### All Design matrices
  test_1_cases <- TAM::designMatrices.mfr( data.sim.mfr, formulaA=~rater,
            facets=data.sim.facets, constraint="cases" )
  test_4_cases <- TAM::designMatrices.mfr( data.sim.mfr, formulaA=~item+item:step,
            facets=data.sim.facets, constraint="cases" )

  ### TAM
  test_4_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~item+item:step )
  test_tam <- TAM::tam.mml( data.sim.mfr )

  test_1_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~rater,
            facets=data.sim.facets, constraint="cases" )
  test_2_cases <- TAM::tam.mml.mfr( data.sim.mfr, formulaA=~item+rater,
            facets=data.sim.facets, constraint="cases" )
## End(Not run)

Description

Simulated Rasch data under unidimensional trait distribution

Usage

data(data.sim.rasch)
 data(data.sim.rasch.pweights)
 data(data.sim.rasch.missing)

Format

The format is:

num [1:2000, 1:40] 1 0 1 1 1 1 1 1 1 1 ...
- attr(*, "dimnames")=List of 2
..$ : NULL
..$ : chr [1:40] "I1" "I2" "I3" "I4" ...

Details

N <- 2000
# simulate predictors
Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) )
theta <- stats::rnorm( N ) + .4 * Y[,1] + .2 * Y[,2] # latent regression model
# simulate item responses with missing data
I <- 40
resp[ theta < 0, c(1,seq(I/2+1, I)) ] <- NA
# define person weights
pweights <- c( rep(3,N/2), rep( 1, N/2 ) )

Source

Simulated data (see Details)

Examples

## Not run: 
data(data.sim.rasch)
N <- 2000
Y <- cbind( stats::rnorm( N, sd=1.5), stats::rnorm(N, sd=.3 ) )

# Loading Matrix
# B <- array( 0, dim=c( I, 2, 1 )  )
# B[1:(nrow(B)), 2, 1] <- 1
B <- TAM::designMatrices(resp=data.sim.rasch)[["B"]]

# estimate Rasch model
mod1_1 <- TAM::tam.mml(resp=data.sim.rasch, Y=Y)

# standard errors
res1 <- TAM::tam.se(mod1_1)

# Compute fit statistics
tam.fit(mod1_1)

# plausible value imputation
# PV imputation has to be adpated for multidimensional case!
pv1 <- TAM::tam.pv( mod1_1, nplausible=7, # 7 plausible values
               samp.regr=TRUE       # sampling of regression coefficients
              )

# item parameter constraints
xsi.fixed <- matrix( c( 1, -2,5, -.22,10, 2 ), nrow=3, ncol=2, byrow=TRUE)
xsi.fixed
mod1_4 <- TAM::tam.mml( resp=data.sim.rasch, xsi.fixed=xsi.fixed )

# missing value handling
data(data.sim.rasch.missing)
mod1_2 <- TAM::tam.mml(data.sim.rasch.missing, Y=Y)

# handling of sample (person) weights
data(data.sim.rasch.pweights)
N <- 1000
pweights <- c(  rep(3,N/2), rep( 1, N/2 ) )
mod1_3 <- TAM::tam.mml( data.sim.rasch.pweights, control=list(conv=.001),
               pweights=pweights )
  
## End(Not run)

Description

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.

Usage

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

## Not run: 
#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)

## End(Not run)

Description

S3 method for descriptive statistics of objects

Usage

DescribeBy(object, ...)

Arguments

See Also

psych::describe

Description

Generate design matrices, and display them at console.

Usage

designMatrices(modeltype=c("PCM", "RSM"), maxKi=NULL, resp=resp,
    ndim=1, A=NULL, B=NULL, Q=NULL, R=NULL, constraint="cases",...)

## S3 method for class 'designMatrices'
print(x, ...)

designMatrices.mfr(resp, formulaA=~ item + item:step, facets=NULL,
    constraint=c("cases", "items"), ndim=1, Q=NULL, A=NULL, B=NULL,
    progress=FALSE)
designMatrices.mfr2(resp, formulaA=~ item + item:step, facets=NULL,
    constraint=c("cases", "items"), ndim=1, Q=NULL, A=NULL, B=NULL,
    progress=FALSE)

.A.matrix(resp, formulaA=~ item + item*step, facets=NULL,
    constraint=c("cases", "items"), progress=FALSE, maxKi=NULL)
rownames.design(X)

.A.PCM2( resp, Kitem=NULL, constraint="cases", Q=NULL)
   # generates ConQuest parametrization of partial credit model

.A.PCM3( resp, Kitem=NULL ) # parametrization for A matrix in the dispersion model

Arguments

Details

The function .A.PCM2 generates the Conquest parametrization of the partial credit model.

The function .A.PCM3 generates the parametrization for the $A$ design matrix in the dispersion model for ordered data (Andrich, 1982).

Note

The function designMatrices.mfr2 handles multi-faceted design for items with differing number of response options.

References

Andrich, D. (1982). An extension of the Rasch model for ratings providing both location and dispersion parameters. Psychometrika, 47(1), 105-113. doi:10.1007/BF02293856

See Also

See data.sim.mfr for some examples for creating design matrices.

Examples

###########################################################
# different parametrizations for ordered data
data( data.gpcm )
resp <- data.gpcm

# parametrization for partial credit model
A1 <- TAM::designMatrices( resp=resp )$A
# item difficulty and threshold parametrization
A2 <- TAM::.A.PCM2( resp )
# dispersion model of Andrich (1982)
A3 <- TAM::.A.PCM3( resp )
# rating scale model
A4 <- TAM::designMatrices( resp=resp, modeltype="RSM" )$A

Description

This function parses a string and expands this string in case of DO statements which are shortcuts for writing loops. The statement DO(n,m,k) increments an index from n to m in steps of k. The index in the string model must be defined as %. For a nested loop within a loop, the DO2 statement can be used using %1 and %2 as indices. See Examples for hints on the specification. The loop in DO2 must not be explicitly crossed, e.g. in applications for specifying covariances or correlations. The formal syntax for
for (ii in 1:(K-1)){ for (jj in (ii+1):K) { ... } }
can be written as DO2(1,K-1,1,%1,K,1 ). See Example 2.

Usage

doparse(model)

Arguments

Value

Parsed string in which DO statements are expanded.

See Also

This function is also used in lavaanify.IRT and tamaanify.

Examples

#############################################################################
# EXAMPLE 1: doparse example
#############################################################################

# define model
model <- "
 # items I1,...,I10 load on G
 DO(1,10,1)
   G=~ lamg% * I%
 DOEND
 I2 | 0.75*t1
 v10 > 0 ;
 # The first index loops from 1 to 3 and the second index loops from 1 to 2
 DO2(1,3,1,  1,2,1)
   F%2=~ a%2%1 * A%2%1 ;
 DOEND
 # Loop from 1 to 9 with steps of 2
 DO(1,9,2)
   HA1=~ I%
   I% | beta% * t1
 DOEND
 "

# process string
out <- TAM::doparse(model)
cat(out)
  ##    # items I1,...,I10 load on G
  ##       G=~ lamg1 * I1
  ##       G=~ lamg2 * I2
  ##       G=~ lamg3 * I3
  ##       G=~ lamg4 * I4
  ##       G=~ lamg5 * I5
  ##       G=~ lamg6 * I6
  ##       G=~ lamg7 * I7
  ##       G=~ lamg8 * I8
  ##       G=~ lamg9 * I9
  ##       G=~ lamg10 * I10
  ##     I2 | 0.75*t1
  ##     v10 > 0
  ##       F1=~ a11 * A11
  ##       F2=~ a21 * A21
  ##       F1=~ a12 * A12
  ##       F2=~ a22 * A22
  ##       F1=~ a13 * A13
  ##       F2=~ a23 * A23
  ##       HA1=~ I1
  ##       HA1=~ I3
  ##       HA1=~ I5
  ##       HA1=~ I7
  ##       HA1=~ I9
  ##       I1 | beta1 * t1
  ##       I3 | beta3 * t1
  ##       I5 | beta5 * t1
  ##       I7 | beta7 * t1
  ##       I9 | beta9 * t1

#############################################################################
# EXAMPLE 2: doparse with nested loop example
#############################################################################

# define model
model <- "
 DO(1,4,1)
   G=~ lamg% * I%
 DOEND
 # specify some correlated residuals
 DO2(1,3,1,%1,4,1)
   I%1 ~~ I%2
 DOEND
 "
# process string
out <- TAM::doparse(model)
cat(out)
  ##       G=~ lamg1 * I1
  ##       G=~ lamg2 * I2
  ##       G=~ lamg3 * I3
  ##       G=~ lamg4 * I4
  ##     # specify some correlated residuals
  ##       I1 ~~ I2
  ##       I1 ~~ I3
  ##       I1 ~~ I4
  ##       I2 ~~ I3
  ##       I2 ~~ I4
  ##       I3 ~~ I4

Description

This S3 method performs a cross-validation of a fitted item response model.

Usage

IRT.cv(object, ...)

Arguments

Value

Numeric value: the cross-validated deviance value

Description

Extracts the used data set for models fitted in TAM. See CDM::IRT.data for more details.

Usage

## S3 method for class 'tam.mml'
IRT.data(object, ...)

## S3 method for class 'tam.mml.3pl'
IRT.data(object, ...)

## S3 method for class 'tamaan'
IRT.data(object, ...)

Arguments

Value

A dataset with item responses

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Dichotomous data data.sim.rasch
#############################################################################

data(data.sim.rasch)
dat <- data.sim.rasch

# estimate model
mod1 <- TAM::tam.mml(dat)
# extract dataset (and weights and group if available)
dmod1 <- IRT.data(mod1)
str(dmod1)

## End(Not run)

Description

This function draws plausible values of a continuous latent variable based on a fitted object for which the CDM::IRT.posterior method is defined.

Usage

IRT.drawPV(object,NPV=5)

Arguments

Value

Matrix with plausible values

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Plausible value imputation for Rasch model in sirt
#############################################################################

library(sirt)
data(data.read, package="sirt")
dat <- data.read

# fit Rasch model
mod <- rasch.mml2(dat)
# draw 10 plausible values
pv1 <- TAM::IRT.drawPV(mod, NPV=10)

## End(Not run)

Description

Extracts expected counts for models fitted in TAM. See CDM::IRT.expectedCounts for more details.

Usage

## S3 method for class 'tam'
IRT.expectedCounts(object, ...)

## S3 method for class 'tam.mml'
IRT.expectedCounts(object, ...)

## S3 method for class 'tam.mml.3pl'
IRT.expectedCounts(object, ...)

## S3 method for class 'tamaan'
IRT.expectedCounts(object, ...)

## S3 method for class 'tam.np'
IRT.expectedCounts(object, ...)

Arguments

Value

See CDM::IRT.expectedCounts.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Dichotomous data data.sim.rasch - extract expected counts
#############################################################################

data(data.sim.rasch)
# 1PL estimation
mod1 <- TAM::tam.mml(resp=data.sim.rasch)
# extract expected counts
IRT.expectedCounts(mod1)

## End(Not run)

Description

Extracts factor scores for models fitted in TAM. See CDM::IRT.factor.scores for more details.

Usage

## S3 method for class 'tam'
IRT.factor.scores(object, type="EAP", ...)

## S3 method for class 'tam.mml'
IRT.factor.scores(object, type="EAP", ...)

## S3 method for class 'tam.mml.3pl'
IRT.factor.scores(object, type="EAP", ...)

## S3 method for class 'tamaan'
IRT.factor.scores(object, type="EAP", ...)

Arguments

Value

See CDM::IRT.factor.scores.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: data.sim.rasch - Different factor scores in Rasch model
#############################################################################

data(data.sim.rasch)
# 1PL estimation
mod1 <- TAM::tam.mml(resp=data.sim.rasch)
# EAP
pmod1 <- IRT.factor.scores( mod1 )
# WLE
pmod1 <- IRT.factor.scores( mod1, type="WLE" )
# MLE
pmod1 <- IRT.factor.scores( mod1, type="MLE" )

## End(Not run)

Description

Computes observed and expected frequencies for univariate and bivariate distributions for models fitted in TAM. See CDM::IRT.frequencies for more details.

Usage

## S3 method for class 'tam.mml'
IRT.frequencies(object, ...)

## S3 method for class 'tam.mml.3pl'
IRT.frequencies(object, ...)

## S3 method for class 'tamaan'
IRT.frequencies(object, ...)

Arguments

Value

See CDM::IRT.frequencies.

See Also

CDM::IRT.frequencies

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Dichotomous data data.sim.rasch
#############################################################################

data(data.sim.rasch)
dat <- data.sim.rasch

# estimate model
mod1 <- TAM::tam.mml(dat)
# compute observed and expected frequencies
fmod1 <- IRT.frequencies(mod1)
str(fmod1)

## End(Not run)

Description

An S3 method which computes item and test information curves, see Muraki (1993).

Usage

IRT.informationCurves(object, ...)

## S3 method for class 'tam.mml'
IRT.informationCurves( object, h=.0001, iIndex=NULL,
          theta=NULL, ... )

## S3 method for class 'tam.mml.2pl'
IRT.informationCurves( object, h=.0001, iIndex=NULL,
          theta=NULL, ... )

## S3 method for class 'tam.mml.mfr'
IRT.informationCurves( object, h=.0001, iIndex=NULL,
          theta=NULL, ... )

## S3 method for class 'tam.mml.3pl'
IRT.informationCurves( object, h=.0001, iIndex=NULL,
          theta=NULL, ... )

## S3 method for class 'IRT.informationCurves'
plot(x, curve_type="test", ...)

Arguments

Value

List with following entries

References

Muraki, E. (1993). Information functions of the generalized partial credit model. Applied Psychological Measurement, 17(4), 351-363. doi:10.1177/014662169301700403

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Dichotomous data | data.read
#############################################################################

data(data.read, package="sirt")
dat <- data.read

# fit 2PL model
mod1 <- TAM::tam.mml.2pl( dat )
summary(mod1)

# compute information curves at grid seq(-5,5,length=100)
imod1 <- TAM::IRT.informationCurves( mod1, theta=seq(-5,5,len=100)  )
str(imod1)
# plot test information
plot( imod1 )
# plot standard error curve
plot( imod1, curve_type="se", xlim=c(-3,2) )
# cutomized plot
plot( imod1, curve_type="se", xlim=c(-3,2), ylim=c(0,2), lwd=2, lty=3)

#############################################################################
# EXAMPLE 2: Mixed dichotomous and polytomous data
#############################################################################

data(data.timssAusTwn.scored, package="TAM")
dat <- data.timssAusTwn.scored
# select item response data
items <- grep( "M0", colnames(dat), value=TRUE )
resp <- dat[, items ]

#*** Model 1: Partial credit model
mod1 <- TAM::tam.mml( resp )
summary(mod1)
# information curves
imod1 <- TAM::IRT.informationCurves( mod1, theta=seq(-3,3,len=20)  )

#*** Model 2: Generalized partial credit model
mod2 <- TAM::tam.mml.2pl( resp, irtmodel="GPCM")
summary(mod2)
imod2 <- TAM::IRT.informationCurves( mod2 )

#*** Model 3: Mixed 3PL and generalized partial credit model
psych::describe(resp)
maxK <- apply( resp, 2, max, na.rm=TRUE )
I <- ncol(resp)
# specify guessing parameters, including a prior distribution
est.guess <- 1:I
est.guess[ maxK > 1 ] <- 0
guess <- .2*(est.guess >0)
guess.prior <- matrix( 0, nrow=I, ncol=2 )
guess.prior[ est.guess  > 0, 1] <- 5
guess.prior[ est.guess  > 0, 2] <- 17

# fit model
mod3 <- TAM::tam.mml.3pl( resp, gammaslope.des="2PL", est.guess=est.guess, guess=guess,
           guess.prior=guess.prior,
           control=list( maxiter=100, Msteps=10, fac.oldxsi=0.1,
                        nodes=seq(-8,8,len=41) ),  est.variance=FALSE )
summary(mod3)

# information curves
imod3 <- TAM::IRT.informationCurves( mod3 )
imod3

#*** estimate model in mirt package
library(mirt)
itemtype <- rep("gpcm", I)
itemtype[ maxK==1] <- "3PL"
mod3b <- mirt::mirt(resp, 1, itemtype=itemtype, verbose=TRUE )
print(mod3b)

## End(Not run)

Description

Extracts item response functions for models fitted in TAM. See CDM::IRT.irfprob for more details.

Usage

## S3 method for class 'tam'
IRT.irfprob(object, ...)

## S3 method for class 'tam.mml'
IRT.irfprob(object, ...)

## S3 method for class 'tam.mml.3pl'
IRT.irfprob(object, ...)

## S3 method for class 'tamaan'
IRT.irfprob(object, ...)

## S3 method for class 'tam.np'
IRT.irfprob(object, ...)

Arguments

Value

See CDM::IRT.irfprob.

Examples

#############################################################################
# EXAMPLE 1: Dichotomous data data.sim.rasch - item response functions
#############################################################################

data(data.sim.rasch)
# 1PL estimation
mod1 <- TAM::tam.mml(resp=data.sim.rasch)
IRT.irfprob(mod1)

Description

Computes the RMSD item fit statistic (formerly labeled as RMSEA; Yamamoto, Khorramdel, & von Davier, 2013) for fitted objects in the TAM package, see CDM::IRT.itemfit and CDM::IRT.RMSD.

Usage

## S3 method for class 'tam.mml'
IRT.itemfit(object, method="RMSD", ...)

## S3 method for class 'tam.mml.2pl'
IRT.itemfit(object, method="RMSD", ...)

## S3 method for class 'tam.mml.mfr'
IRT.itemfit(object, method="RMSD", ...)

## S3 method for class 'tam.mml.3pl'
IRT.itemfit(object, method="RMSD", ...)

Arguments

References

Yamamoto, K., Khorramdel, L., & von Davier, M. (2013). Scaling PIAAC cognitive data. In OECD (Eds.). Technical Report of the Survey of Adults Skills (PIAAC) (Ch. 17). Paris: OECD.

See Also

CDM::IRT.itemfit, CDM::IRT.RMSD

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: RMSD item fit statistic data.read
#############################################################################

library(sirt)
data(data.read,package="sirt")
dat <- data.read

#*** fit 1PL model
mod1 <- TAM::tam.mml( dat )
summary(mod1)

#*** fit 2PL model
mod2 <- TAM::tam.mml.2pl( dat )
summary(mod2)

#*** assess RMSEA item fit
fmod1 <- IRT.itemfit(mod1)
fmod2 <- IRT.itemfit(mod2)
# summary of fit statistics
summary( fmod1 )
summary( fmod2 )

#############################################################################
# EXAMPLE 2: Simulated 2PL data and fit of 1PL model
#############################################################################

set.seed(987)
N <- 1000    # 1000 persons
I <- 10      # 10 items
# define item difficulties and item slopes
b <- seq(-2,2,len=I)
a <- rep(1,I)
a[c(3,8)] <- c( 1.7, .4 )
# simulate 2PL data
dat <- sirt::sim.raschtype( theta=rnorm(N), b=b, fixed.a=a)

# fit 1PL model
mod <- TAM::tam.mml( dat )

# RMSEA item fit
fmod <- IRT.itemfit(mod)
round( fmod, 3 )

## End(Not run)

Description

Extracts individual likelihood and posterior for models fitted in TAM. See CDM::IRT.likelihood for more details.

Usage

## S3 method for class 'tam'
IRT.likelihood(object, ...)
## S3 method for class 'tam'
IRT.posterior(object, ...)

## S3 method for class 'tam.mml'
IRT.likelihood(object, ...)
## S3 method for class 'tam.mml'
IRT.posterior(object, ...)

## S3 method for class 'tam.mml.3pl'
IRT.likelihood(object, ...)
## S3 method for class 'tam.mml.3pl'
IRT.posterior(object, ...)

## S3 method for class 'tamaan'
IRT.likelihood(object, ...)
## S3 method for class 'tamaan'
IRT.posterior(object, ...)

## S3 method for class 'tam.latreg'
IRT.likelihood(object, ...)
## S3 method for class 'tam.latreg'
IRT.posterior(object, ...)

## S3 method for class 'tam.np'
IRT.likelihood(object, ...)
## S3 method for class 'tam.np'
IRT.posterior(object, ...)

Arguments

Value

See CDM::IRT.likelihood.

Examples

#############################################################################
# EXAMPLE 1: Dichotomous data data.sim.rasch - extracting likelihood/posterior
#############################################################################

data(data.sim.rasch)
# 1PL estimation
mod1 <- TAM::tam.mml(resp=data.sim.rasch)
lmod1 <- IRT.likelihood(mod1)
str(lmod1)
pmod1 <- IRT.posterior(mod1)
str(pmod1)

Description

This function approximates a fitted item response model by a linear confirmatory factor analysis. I.e., given item response functions, the expectation $E(X_i | \theta_1, \ldots, \theta_D)$ is linearly approximated by $a_{i1} \theta _1 + \ldots + a_{iD} \theta_D$. See Vermunt and Magidson (2005) for details.

Usage

IRT.linearCFA( object, group=1)

## S3 method for class 'IRT.linearCFA'
summary(object,  ...)

Arguments

Value

A list with following entries

References

Vermunt, J. K., & Magidson, J. (2005). Factor Analysis with categorical indicators: A comparison between traditional and latent class approaches. In A. Van der Ark, M.A. Croon & K. Sijtsma (Eds.), New Developments in Categorical Data Analysis for the Social and Behavioral Sciences (pp. 41-62). Mahwah: Erlbaum

See Also

See tam.fa for confirmatory factor analysis in TAM.

Examples

## Not run: 
library(lavaan)

#############################################################################
# EXAMPLE 1: Two-dimensional confirmatory factor analysis data.Students
#############################################################################

data(data.Students, package="CDM")
# select variables
vars <- scan(nlines=1, what="character")
    sc1 sc2 sc3 sc4 mj1 mj2 mj3 mj4
dat <- data.Students[, vars]

# define Q-matrix
Q <- matrix( 0, nrow=8, ncol=2 )
Q[1:4,1] <- Q[5:8,2] <- 1

#*** Model 1: Two-dimensional 2PL model
mod1 <- TAM::tam.mml.2pl( dat, Q=Q, control=list( nodes=seq(-4,4,len=12) ) )
summary(mod1)

# linear approximation CFA
cfa1 <- TAM::IRT.linearCFA(mod1)
summary(cfa1)

# linear CFA in lavaan package
lavmodel <- "
    sc=~ sc1+sc2+sc3+sc4
    mj=~ mj1+mj2+mj3+mj4
    sc1 ~ 1
    sc ~~ mj
    "
mod1b <- lavaan::sem( lavmodel, data=dat, missing="fiml", std.lv=TRUE)
summary(mod1b, standardized=TRUE, fit.measures=TRUE )

#############################################################################
# EXAMPLE 2: Unidimensional confirmatory factor analysis data.Students
#############################################################################

data(data.Students, package="CDM")
# select variables
vars <- scan(nlines=1, what="character")
    sc1 sc2 sc3 sc4
dat <- data.Students[, vars]

#*** Model 1: 2PL model
mod1 <- TAM::tam.mml.2pl( dat )
summary(mod1)

# linear approximation CFA
cfa1 <- TAM::IRT.linearCFA(mod1)
summary(cfa1)

# linear CFA
lavmodel <- "
    sc=~ sc1+sc2+sc3+sc4
    "
mod1b <- lavaan::sem( lavmodel, data=dat, missing="fiml", std.lv=TRUE)
summary(mod1b, standardized=TRUE, fit.measures=TRUE )

## End(Not run)

Description

Defines an S3 method for the computation of observed residual values. The computation of residuals is based on weighted likelihood estimates as person parameters, see tam.wle. IRT.residuals can only be applied for unidimensional IRT models. The methods IRT.residuals and residuals are equivalent.

Usage

IRT.residuals(object, ...)

## S3 method for class 'tam.mml'
IRT.residuals(object, ...)
## S3 method for class 'tam.mml'
residuals(object, ...)

## S3 method for class 'tam.mml.2pl'
IRT.residuals(object, ...)
## S3 method for class 'tam.mml.2pl'
residuals(object, ...)

## S3 method for class 'tam.mml.mfr'
IRT.residuals(object, ...)
## S3 method for class 'tam.mml.mfr'
residuals(object, ...)

## S3 method for class 'tam.jml'
IRT.residuals(object, ...)
## S3 method for class 'tam.jml'
residuals(object, ...)

Arguments

Value

List with following entries

Note

Residuals can be used to inspect local dependencies in the item response data, for example using principle component analysis or factor analysis (see Example 1).

See Also

See also the eRm::residuals (eRm) or residuals (mirt) functions.

See also predict.tam.mml.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Residuals data.read
#############################################################################

library(sirt)
data(data.read, package="sirt")
dat <- data.read

# for Rasch model
mod <- TAM::tam.mml( dat )
# extract residuals
res <- TAM::IRT.residuals( mod )
str(res)

## End(Not run)

Description

Defines an S3 method for simulation of item response models.

Usage

IRT.simulate(object, ...)

## S3 method for class 'tam.mml'
IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

## S3 method for class 'tam.mml.2pl'
IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

## S3 method for class 'tam.mml.mfr'
IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

## S3 method for class 'tam.mml.3pl'
IRT.simulate(object, iIndex=NULL, theta=NULL, nobs=NULL, ...)

Arguments

Value

Data frame with simulated item responses

Examples

#############################################################################
# EXAMPLE 1: Simulating Rasch model
#############################################################################

data(data.sim.rasch)

#** (1) estimate model
mod1 <- TAM::tam.mml(resp=data.sim.rasch )

#** (2) simulate data
sim.dat <- TAM::IRT.simulate(mod1)

## Not run: 
#** (3) use a subset of items with the argument iIndex
set.seed(976)
iIndex <- sort(sample(ncol(data.sim.rasch), 15))  # randomly select 15 items
sim.dat <- TAM::IRT.simulate(mod1, iIndex=iIndex)
mod.sim.dat <- TAM::tam.mml(sim.dat)

#** (4) specify number of persons in addition
sim.dat <- TAM::IRT.simulate(mod1, nobs=1500, iIndex=iIndex)

# Rasch - constraint="items" ----
mod1 <- TAM::tam.mml(resp=data.sim.rasch,  constraint="items",
                control=list( xsi.start0=1, fac.oldxsi=.5) )

# provide abilities
theta0 <- matrix( rnorm(1500, mean=0.5, sd=sqrt(mod1$variance)), ncol=1 )
# simulate data
data <- TAM::IRT.simulate(mod1, theta=theta0 )
# estimate model based on simulated data
xsi.fixed <- cbind(1:nrow(mod1$item), mod1$item$xsi.item)
mod2 <- TAM::tam.mml(data, xsi.fixed=xsi.fixed )
summary(mod2)

#############################################################################
# EXAMPLE 2: Simulating 2PL model
#############################################################################

data(data.sim.rasch)
# estimate 2PL
mod2 <- TAM::tam.mml.2pl(resp=data.sim.rasch, irtmodel="2PL")
# simulate 2PL
sim.dat <- TAM::IRT.simulate(mod2)
mod.sim.dat <- TAM::tam.mml.2pl(resp=sim.dat, irtmodel="2PL")

#############################################################################
# EXAMPLE 3: Simulate multiple group model
#############################################################################

# Multi-Group ----
set.seed(6778)
N <- 3000
theta <- c( stats::rnorm(N/2,mean=0,sd=1.5), stats::rnorm(N/2,mean=.5,sd=1)  )
I <- 20
p1 <- stats::plogis( outer( theta, seq( -2, 2, len=I ), "-" ) )
resp <- 1 * ( p1 > matrix( stats::runif( N*I ), nrow=N, ncol=I ) )
colnames(resp) <- paste("I", 1:I, sep="")
group <- rep(1:2, each=N/2 )
mod3 <- TAM::tam.mml(resp, group=group)

# simulate data
sim.dat.g1 <- TAM::IRT.simulate(mod3,
                   theta=matrix( stats::rnorm(N/2, mean=0, sd=1.5), ncol=1) )
sim.dat.g2 <- TAM::IRT.simulate(mod3,
                   theta=matrix( stats::rnorm(N/2, mean=.5, sd=1), ncol=1) )
sim.dat <- rbind( sim.dat.g1, sim.dat.g2)
# estimate model
mod3s <- TAM::tam.mml( sim.dat, group=group)

#############################################################################
# EXAMPLE 4: Multidimensional model and latent regression
#############################################################################

set.seed(6778)
N <- 2000
Y <- cbind( stats::rnorm(N), stats::rnorm(N))
theta <- mvtnorm::rmvnorm(N, mean=c(0,0), sigma=matrix(c(1,.5,.5,1), 2, 2))
theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model
I <- 20
p1 <- stats::plogis(outer(theta[, 1], seq(-2, 2, len=I), "-"))
resp1 <- 1 * (p1 > matrix(stats::runif(N * I), nrow=N, ncol=I))
p1 <- stats::plogis(outer(theta[, 2], seq(-2, 2, len=I ), "-" ))
resp2 <- 1 * (p1 > matrix(stats::runif(N * I), nrow=N, ncol=I))
resp <- cbind(resp1, resp2)
colnames(resp) <- paste("I", 1 : (2 * I), sep="")

# (2) define loading Matrix
Q <- array(0, dim=c(2 * I, 2))
Q[cbind(1:(2*I), c(rep(1, I), rep(2, I)))] <- 1
Q

# (3) estimate models
mod4 <- TAM::tam.mml(resp=resp, Q=Q, Y=Y, control=list(  maxiter=15))

# simulate new item responses
theta <- mvtnorm::rmvnorm(N, mean=c(0,0), sigma=matrix(c(1,.5,.5,1), 2, 2))
theta[,1] <- theta[,1] + .4 * Y[,1] + .2 * Y[,2]  # latent regression model
theta[,2] <- theta[,2] + .8 * Y[,1] + .5 * Y[,2]  # latent regression model

sim.dat <- TAM::IRT.simulate(mod4, theta=theta)
mod.sim.dat <- TAM::tam.mml(resp=sim.dat, Q=Q, Y=Y, control=list( maxiter=15))

## End(Not run)

Description

The function IRT.threshold computes Thurstonian thresholds for item response models. It is only based on fitted models for which the IRT.irfprob does exist.

The function IRT.WrightMap creates a Wright map and works as a wrapper to the WrightMap::wrightMap function in the WrightMap package. Wright maps operate on objects of class IRT.threshold.

Usage

IRT.threshold(object, prob.lvl=.5, type="category")

## S3 method for class 'IRT.threshold'
print(x, ...)

IRT.WrightMap(object, ...)

## S3 method for class 'IRT.threshold'
IRT.WrightMap(object, label.items=NULL, ...)

Arguments

Value

Function IRT.threshold:
Matrix with Thurstonian thresholds

Function IRT.WrightMap:
A Wright map generated by the WrightMap package.

Author(s)

The IRT.WrightMap function is based on the WrightMap::wrightMap function in the WrightMap package.

References

Ali, U. S., Chang, H.-H., & Anderson, C. J. (2015). Location indices for ordinal polytomous items based on item response theory (Research Report No. RR-15-20). Princeton, NJ: Educational Testing Service. doi:10.1002/ets2.12065

See Also

See the WrightMap::wrightMap function in the WrightMap package.

Examples

## Not run: 
#############################################################################
# EXAMPLE 1: Fitted unidimensional model with gdm
#############################################################################

data(data.Students)
dat <- data.Students

# select part of the dataset
resp <- dat[, paste0("sc",1:4) ]
resp[ paste(resp[,1])==3,1] <-  2
psych::describe(resp)

# Model 1: Partial credit model in gdm
theta.k <- seq( -5, 5, len=21 )   # discretized ability
mod1 <- CDM::gdm( dat=resp, irtmodel="1PL", theta.k=theta.k, skillspace="normal",
              centered.latent=TRUE)

# compute thresholds
thresh1 <- TAM::IRT.threshold(mod1)
print(thresh1)
IRT.WrightMap(thresh1)

#############################################################################
# EXAMPLE 2: Fitted mutidimensional model with gdm
#############################################################################

data( data.fraction2 )
dat <- data.fraction2$data
Qmatrix <- data.fraction2$q.matrix3

# Model 1: 3-dimensional Rasch Model (normal distribution)
theta.k <- seq( -4, 4, len=11 )   # discretized ability
mod1 <- CDM::gdm( dat, irtmodel="1PL", theta.k=theta.k, Qmatrix=Qmatrix,
              centered.latent=TRUE, maxiter=10 )
summary(mod1)

# compute thresholds
thresh1 <- TAM::IRT.threshold(mod1)
print(thresh1)

#############################################################################
# EXAMPLE 3: Item-wise thresholds
#############################################################################

data(data.timssAusTwn.scored)
dat <- data.timssAusTwn.scored
dat <- dat[, grep("M03", colnames(dat) ) ]
summary(dat)

# fit partial credit model
mod <- TAM::tam.mml( dat )
# compute thresholds with tam.threshold function
t1mod <- TAM::tam.threshold( mod )
t1mod
# compute thresholds with IRT.threshold function
t2mod <- TAM::IRT.threshold( mod )
t2mod
# compute item-wise thresholds
t3mod <- TAM::IRT.threshold( mod, type="item")
t3mod

## End(Not run)

Description

Converts a $\theta$ score into an unweighted true score $\tau ( \theta)=\sum_i \sum_h h P_i ( \theta )$. In addition, a weighted true score $\tau ( \theta)=\sum_i \sum_h q_{ih} P_i ( \theta )$ can also be computed by specifying item-category weights $q_{ih}$ in the matrix Q.

Usage

IRT.truescore(object, iIndex=NULL, theta=NULL, Q=NULL)

Arguments

Value

Data frame containing $\theta$ values and corresponding true scores $\tau( \theta )$.

See Also

See also sirt::truescore.irt for a conversion function for generalized partial credit models.

Examples

#############################################################################
# EXAMPLE 1: True score conversion for a test with polytomous items
#############################################################################

data(data.Students, package="CDM")
dat <- data.Students[, paste0("mj",1:4) ]

# fit partial credit model
mod1 <- TAM::tam.mml( dat,control=list(maxiter=20) )
summary(mod1)

# true score conversion
tmod1 <- TAM::IRT.truescore( mod1 )
round( tmod1, 4 )
# true score conversion with user-defined theta grid
tmod1b <- TAM::IRT.truescore( mod1, theta=seq( -8,8, len=33 ) )
# plot results
plot( tmod1$theta, tmod1$truescore, type="l",
            xlab=expression(theta), ylab=expression(tau( theta ) ) )
points( tmod1b$theta, tmod1b$truescore, pch=16, col="brown" )

## Not run: 
#############################################################################
# EXAMPLE 2: True scores with different category weightings
#############################################################################

data(data.timssAusTwn.scored)
dat <- data.timssAusTwn.scored
# extract item response data
dat <- dat[, grep("M03", colnames(dat) ) ]
# select items with do have maximum score of 2 (polytomous items)
ind <- which( apply( dat,  2, max, na.rm=TRUE )==2 )
I <- ncol(dat)
# define Q-matrix with scoring variant
Q <- matrix( 1, nrow=I, ncol=1 )
Q[ ind, 1 ] <- .5    # score of 0.5 for polyomous items

# estimate model
mod1 <- TAM::tam.mml( dat, Q=Q, irtmodel="PCM2", control=list( nodes=seq(-10,10,len=61) ) )
summary(mod1)

# true score with scoring (0,1,2) which is the default of the function
tmod1 <- TAM::IRT.truescore(mod1)
# true score with user specified weighting matrix
Q <- mod1$B[,,1]
tmod2 <- TAM::IRT.truescore(mod1, Q=Q)

## End(Not run)

Description

This function creates a Wright map and works as a wrapper to the wrightMap function in the WrightMap package. The arguments thetas and thresholds are automatically generated from fitted objects in TAM.

Usage

## S3 method for class 'tam.mml'
IRT.WrightMap(object, prob.lvl=.5, type="PV", ...)

## S3 method for class 'tamaan'
IRT.WrightMap(object, prob.lvl=.5, type="PV", ...)

Arguments

Details

A Wright map is only created for models with an assumed normal distribution. Hence, not for all models of the tamaan functions Wright maps are created.

Value

A Wright map generated by the WrightMap package.

Author(s)

The IRT.WrightMap function is based on the WrightMap::wrightMap function in the WrightMap package.

See Also

See the WrightMap::wrightMap function in the WrightMap package.

Examples

## Not run: 
library(WrightMap)

#############################################################################
# EXAMPLE 1: Unidimensional models dichotomous data
#############################################################################

data(data.sim.rasch)
str(data.sim.rasch)
dat <- data.sim.rasch

# fit Rasch model
mod1 <- TAM::tam.mml(resp=dat)
# Wright map
IRT.WrightMap( mod1 )
# some customized plots
IRT.WrightMap( mod1, show.thr.lab=FALSE, label.items=c(1:40), label.items.rows=3)

IRT.WrightMap( mod1,  show.thr.sym=FALSE, thr.lab.text=paste0("I",1:ncol(dat)),
     label.items="", label.items.ticks=FALSE)

#--- direct specification with wrightMap function
theta <- TAM::tam.wle(mod1)$theta
thr <- TAM::tam.threshold(mod1)

# default wrightMap plots
WrightMap::wrightMap( theta, thr, label.items.srt=90)
WrightMap::wrightMap( theta, t(thr), label.items=c("items") )

# stack all items below each other
thr.lab.text <- matrix( "", 1, ncol(dat) )
thr.lab.text[1,] <- colnames(dat)
WrightMap::wrightMap( theta, t(thr), label.items=c("items"),
       thr.lab.text=thr.lab.text, show.thr.sym=FALSE )

#############################################################################
# EXAMPLE 2: Unidimensional model polytomous data
#############################################################################

data( data.Students, package="CDM")
dat <- data.Students

# fit generalized partial credit model using the tamaan function
tammodel <- "
LAVAAN MODEL:
  SC=~ sc1__sc4
  SC ~~ 1*SC
    "
mod1 <- TAM::tamaan( tammodel, dat )
# create item level colors
library(RColorBrewer)
ncat <- 3               # number of category parameters
I <- ncol(mod1$resp)    # number of items
itemlevelcolors <- matrix(rep( RColorBrewer::brewer.pal(ncat, "Set1"), I),
        byrow=TRUE, ncol=ncat)
# Wright map
IRT.WrightMap(mod1, prob.lvl=.625, thr.sym.col.fg=itemlevelcolors,
     thr.sym.col.bg=itemlevelcolors, label.items=colnames( mod1$resp) )

#############################################################################
# EXAMPLE 3: Multidimensional item response model
#############################################################################

data( data.read, package="sirt")
dat <- data.read

# fit three-dimensional Rasch model
Q <- matrix( 0, nrow=12, ncol=3 )
Q[1:4,1] <- Q[5:8,2] <- Q[9:12,3] <- 1
mod1 <- TAM::tam.mml( dat, Q=Q, control=list(maxiter=20, snodes=1000)  )
summary(mod1)
# define matrix with colors for thresholds
c1 <- matrix( c( rep(1,4), rep(2,4), rep(4,4)), ncol=1 )
# create Wright map using WLE
IRT.WrightMap( mod1, prob.lvl=.65, type="WLE", thr.lab.col=c1, thr.sym.col.fg=c1,
        thr.sym.col.bg=c1, label.items=colnames(dat) )
# Wright map using PV (the default)
IRT.WrightMap( mod1, prob.lvl=.65, type="PV" )
# Wright map using population distribution
IRT.WrightMap( mod1, prob.lvl=.65, type="Pop" )

#############################################################################
# EXAMPLE 4: Wright map for a multi-faceted Rasch model
#############################################################################

# This example is copied from
# http://wrightmap.org/post/107431190622/wrightmap-multifaceted-models

library(WrightMap)
data(data.ex10)
dat <- data.ex10

#--- fit multi-faceted Rasch model
facets <- dat[, "rater", drop=FALSE]  # define facet (rater)
pid <- dat$pid  # define person identifier (a person occurs multiple times)
resp <- dat[, -c(1:2)]  # item response data
formulaA <- ~item * rater  # formula
mod <- TAM::tam.mml.mfr(resp=resp, facets=facets, formulaA=formulaA, pid=dat$pid)

# person parameters
persons.mod <- TAM::tam.wle(mod)
theta <- persons.mod$theta
# thresholds
thr <- TAM::tam.threshold(mod)
item.labs <- c("I0001", "I0002", "I0003", "I0004", "I0005")
rater.labs <- c("rater1", "rater2", "rater3")

#--- Plot 1: Item specific
thr1 <- matrix(thr, nrow=5, byrow=TRUE)
WrightMap::wrightMap(theta, thr1, label.items=item.labs,
   thr.lab.text=rep(rater.labs, each=5))

#--- Plot 2: Rater specific
thr2 <- matrix(thr, nrow=3)
WrightMap::wrightMap(theta, thr2, label.items=rater.labs,
   thr.lab.text=rep(item.labs,  each=3), axis.items="Raters")

#--- Plot 3a: item, rater and item*rater parameters
pars <- mod$xsi.facets$xsi
facet <- mod$xsi.facets$facet

item.par <- pars[facet=="item"]
rater.par <- pars[facet=="rater"]
item_rat <- pars[facet=="item:rater"]

len <- length(item_rat)
item.long <- c(item.par, rep(NA, len - length(item.par)))
rater.long <- c(rater.par, rep(NA, len - length(rater.par)))
ir.labs <- mod$xsi.facets$parameter[facet=="item:rater"]

WrightMap::wrightMap(theta, rbind(item.long, rater.long, item_rat),
    label.items=c("Items",  "Raters", "Item*Raters"),
    thr.lab.text=rbind(item.labs, rater.labs, ir.labs), axis.items="")

#--- Plot 3b: item, rater and item*rater (separated by raters) parameters

# parameters item*rater
ir_rater <- matrix(item_rat, nrow=3, byrow=TRUE)
# define matrix of thresholds
thr <- rbind(item.par, c(rater.par, NA, NA), ir_rater)
# matrix with threshold labels
thr.lab.text <- rbind(item.labs, rater.labs,
           matrix(item.labs, nrow=3, ncol=5, byrow=TRUE))

WrightMap::wrightMap(theta, thresholds=thr,
      label.items=c("Items", "Raters", "Item*Raters (R1)",
                           "Item*Raters (R2)", "Item*Raters (R3)"),
      axis.items="", thr.lab.text=thr.lab.text )

#--- Plot 3c: item, rater and item*rater (separated by items) parameters

# thresholds
ir_item <- matrix(item_rat, nrow=5)
thr <- rbind(item.par, c(rater.par, NA, NA), cbind(ir_item, NA, NA))
# labels
label.items <- c("Items", "Raters", "Item*Raters\n (I1)", "Item*Raters \n(I2)",
     "Item*Raters \n(I3)", "Item*Raters \n (I4)", "Item*Raters \n(I5)")
thr.lab.text <- rbind(item.labs,
          matrix(c(rater.labs, NA, NA), nrow=6, ncol=5, byrow=TRUE))

WrightMap::wrightMap(theta, thr,  label.items=label.items,
      axis.items="", thr.lab.text=thr.lab.text  )

## End(Not run)