sirt (version 1.5-0)

testlet.yen.q3: $Q_3$ Statistic of Yen (1984) for Testlets

Description

This function calculates the average $Q_3$ statistic (Yen, 1984) within and between testlets.

Usage

testlet.yen.q3(q3.res, testlet.matrix)

Arguments

q3.res

An object generated by yen.q3

testlet.matrix

A matrix with two columns. The first column contains names of the testlets and the second names of the items. See the examples for the definition of such matrices.

Value

• A list with following entries
• testlet.q3
  Data frame with average $Q_3$ statistics within testlets
• testlet.q3.korr
  Matrix of average $Q_3$ statistics within and between testlets

References

Yen, W. M. (1984). Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement, 8, 125-145.

See Also

For estimating all $Q_3$ statistics between item pairs use yen.q3.

Examples

#############################################################################
# EXAMPLE 1: data.read. The 12 items are arranged in 4 testlets
#############################################################################
data(data.read)

# estimate the Rasch model
mod <- rasch.mml2( data.read)
mod$item

# estmate WLEs
mod.wle <- wle.rasch( dat = data.read , b = mod$item$b )

# Yen's Q3 statistic
mod.q3 <- yen.q3( dat = data.read , theta = mod.wle$theta , b = mod$item$b )

# Yen's Q3 statistic with testlets
items <- colnames(data.read)
testlet.matrix <- cbind( substring(  items,1,1) , items )
mod.testletq3 <- testlet.yen.q3( q3.res=mod.q3,testlet.matrix=testlet.matrix)
mod.testletq3