Weighted Likelihood Estimation of Person Abilities
This function computes weighted likelihood estimates for dichotomous responses based on the Rasch model (Warm, 1989).
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)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? |
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 |
p.ia |
Matrix with expected item response, i.e. the probabilities P(X_{pi}=1|θ_p )=invlogit( θ_p - b_i ). |
wle |
WLE reliability (Adams, 2005) |
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.
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.
############################################################################# # 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 )
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