TAM (version 2.13-15)

tam.threshold: Calculation of Thurstonian Thresholds

Description

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

Usage

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.

Value

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

Details

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

See Also

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

Examples

# NOT RUN {
#############################################################################
# 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

# }
# NOT RUN {
#############################################################################
# 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)
# }