Calculation of Thurstonian Thresholds

This function estimates Thurstonian thresholds for item category parameters of (generalized) partial credit models (see Details).

tam.threshold(tamobj, prob.lvl=0.5)

Arguments

tamobj

Object of class tam

prob.lvl

A numeric specifying the probability level of the threshold. The default is prob.lvl=0.5.

Details

This function only works appropriately for unidimensional models or between item multidimensional models.

Value

A data frame with Thurstonian thresholds. Rows correspond to items and columns to item steps.

See also

See the WrightMap package and Example 3 for creating Wright maps with fitted models in TAM, see wrightMap.

Examples

#############################################################################
# EXAMPLE 1: ordered data - Partial credit model
#############################################################################
data( data.gpcm )

# Model 1: partial credit model
mod1 <- TAM::tam.mml( resp=data.gpcm,control=list( maxiter=200) )
summary(mod1)
  ##   Item Parameters -A*Xsi
  ##        item   N     M AXsi_.Cat1 AXsi_.Cat2 AXsi_.Cat3 B.Cat1.Dim1 B.Cat2.Dim1 B.Cat3.Dim1
  ##   1 Comfort 392 0.880     -1.302      1.154      3.881           1           2           3
  ##   2    Work 392 1.278     -1.706     -0.847      0.833           1           2           3
  ##   3 Benefit 392 1.163     -1.233     -0.404      1.806           1           2           3

# Calculation of Thurstonian thresholds
TAM::tam.threshold(mod1)
  ##                Cat1      Cat2     Cat3
  ##   Comfort -1.325226 2.0717468 3.139801
  ##   Work    -1.777679 0.6459045 1.971222
  ##   Benefit -1.343536 0.7491760 2.403168

if (FALSE) {
#############################################################################
# EXAMPLE 2: Multidimensional model data.math
#############################################################################

library(sirt)
data(data.math, package="sirt")
dat <- data.math$data
# select items
items1 <- grep("M[A-D]", colnames(dat), value=TRUE)
items2 <- grep("M[H-I]", colnames(dat), value=TRUE)
# select dataset
dat <- dat[ c(items1,items2)]
# create Q-matrix
Q <- matrix( 0, nrow=ncol(dat), ncol=2 )
Q[ seq(1,length(items1) ), 1 ] <- 1
Q[ length(items1) + seq(1,length(items2) ), 2 ] <- 1

# fit two-dimensional model
mod1 <- TAM::tam.mml( dat, Q=Q )
# compute thresholds (specify a probability level of .625)
tmod1 <- TAM::tam.threshold( mod1, prob.lvl=.625 )

#############################################################################
# EXAMPLE 3: Creating Wright maps with the WrightMap package
#############################################################################

library(WrightMap)
# For conducting Wright maps in combination with TAM, see
# http://wrightmap.org/post/100850738072/using-wrightmap-with-the-tam-package
data(sim.rasch)
dat <- sim.rasch

# estimate Rasch model in TAM
mod1 <- TAM::tam.mml(dat)
summary(mod1)

#--- A: creating a Wright map with WLEs

# compute WLE
wlemod1 <- TAM::tam.wle(mod1)$theta
# extract thresholds
tmod1 <- TAM::tam.threshold(mod1)
# create Wright map
WrightMap::wrightMap( thetas=wlemod1, thresholds=tmod1, label.items.srt=-90)

#--- B: creating a Wright Map with population distribution

# extract ability distribution and replicate observations
uni.proficiency <- rep( mod1$theta[,1], round( mod1$pi.k * mod1$ic$n) )
# draw WrightMap
WrightMap::wrightMap( thetas=uni.proficiency, thresholds=tmod1, label.items.rows=3)
}