Weighted Likelihood Estimation of Person Abilities

This function computes weighted likelihood estimates for dichotomous responses based on the Rasch model (Warm, 1989).

Usage

wle.rasch(dat, dat.resp=NULL, b, itemweights=1 + 0 * b,
    theta=rep(0, nrow(dat)), conv=0.001, maxit=200,
    wle.adj=0, progress=FALSE)

Arguments

dat

An \(N \times I\) data frame of dichotomous item responses

dat.resp

Optional data frame with dichotomous response indicators

b

Vector of length \(I\) with fixed item difficulties

itemweights

Optional vector of fixed item discriminations

theta

Optional vector of initial person parameter estimates

conv

Convergence criterion

maxit

Maximal number of iterations

wle.adj

Constant for WLE adjustment

progress

Display progress?

Value

A list with following entries

theta

Estimated weighted likelihood estimate

dat.resp

Data frame with dichotomous response indicators. A one indicates an observed response, a zero a missing response. See also dat.resp in the list of arguments of this function.

p.ia

Matrix with expected item response, i.e. the probabilities \(P(X_{pi}=1|\theta_p )=invlogit( \theta_p - b_i )\).

wle

WLE reliability (Adams, 2005)

References

Adams, R. J. (2005). Reliability as a measurement design effect. Studies in Educational Evaluation, 31, 162-172.

Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450.

See also

For standard errors of weighted likelihood estimates estimated via jackknife see wle.rasch.jackknife.

For a joint estimation of item and person parameters see the joint maximum likelihood estimation method in rasch.jml.

Examples

#############################################################################
# EXAMPLE 1: Dataset Reading
#############################################################################
data(data.read)

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

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