sirt (version 0.36-30)

yen.q3: Estimation of the $Q_3$ Statistic (Yen, 1984)

Description

This function estimates the $Q_3$ statistic according to Yen (1984). The statistic $Q_3$ is calculated for every item pair $(i,j)$ which is the correlation between item residuals after fitting the Rasch model.

Usage

yen.q3(dat, theta, b, progress=TRUE)

Arguments

dat

An $N \times I$ data frame of dichotomous item responses

theta

Vector of length $N$ of person parameter estimates (e.g. obtained from wle.rasch)

b

Vector of length $I$ (e.g. obtained from rasch.mml2)

progress

Should iteration progress be displayed?

Value

• A list with following entries
• q3.matrix
  An $I \times I$ matrix of $Q_3$ statistics
• q3.long
  Just the q3.matrix in long matrix format where every row corresponds to an item pair
• expected
  An $N \times I$ matrix of expected probabilities by the Rasch model
• residual
  An $N \times I$ matrix of residuals obtained after fitting the Rasch model
• Q3.stat
  Vector with descriptive statistics of $Q_3$

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 the estimation of the average $Q_3$ statistic within testlets see testlet.yen.q3. For modelling testlet effects see mcmc.3pno.testlet. For handling local dependencies in IRT models see rasch.copula2, rasch.pml3 or rasch.pairwise.itemcluster.

Examples

########################
# use data.read
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 )