wle.rasch: Weighted Likelihood Estimation of Person Abilities

Description

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

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
thetaEstimated weighted likelihood estimate
dat.respData 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.iaMatrix with expected item response, i.e. the probabilities $P(X_{pi}=1|\theta_p ) = invlogit( \theta_p - b_i )$.
wleWLE 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.

Examples

Run this code

#############################################################################
# EXAMPLE 1: Dataset Reading
#############################################################################
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 )