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)

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)

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?

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 <- sirt::rasch.mml2(data.read)
mod$item

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