wle.rasch: Weighted Likelihood Estimation of Person Abilities

In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

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
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 )

alexanderrobitzsch/sirt documentation built on Sept. 8, 2024, 2:45 a.m.