wle.rasch.Rd
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
Estimated weighted likelihood estimate
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.
Matrix with expected item response, i.e. the probabilities \(P(X_{pi}=1|\theta_p )=invlogit( \theta_p - b_i )\).
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 )