TAM (version 0.04-43)

tam.wle: Weighted Likelihood Estimation and Maximum Likelihood Estimation of Person Parameters

Description

Compute weighted likelihood estimator for objects of classes tam, tam.mml and tam.jml, respectively.

Usage

tam.wle(tamobj, ...)
tam.mml.wle(tamobj, WLE=TRUE, adj=0.3, Msteps=20, convM=1e-04)
tam.jml.WLE(tamobj, resp, resp.ind, A, B, nstud, nitems, maxK, convM, 
    PersonScores, theta, xsi, Msteps, WLE=FALSE)

Arguments

tamobj

An object generated by tam.mml or tam.jml

WLE

A logical which indicates if the weighted likelihood estimate (WLE, WLE=TRUE) or the maximum likelihood estimate (MLE, WLE=FALSE) should be used.

adj

Adjustment in WLE estimation for extreme scores (i.e. all or none items were correctly solved)

Msteps

Maximum number of iterations

convM

Convergence criterion

resp

Data frame with item responses (only for tam.jml.WLE)

resp.ind

Data frame with response indicators (only for tam.jml.WLE)

A

Design matrix $A$ (only for tam.jml.WLE)

B

Design matrix $B$ (only for tam.jml.WLE)

nstud

...(only for tam.jml.WLE)

nitems

...(only for tam.jml.WLE)

maxK

...(only for tam.jml.WLE)

PersonScores

...(only for tam.jml.WLE)

theta

...(only for tam.jml.WLE)

xsi

...(only for tam.jml.WLE)

...

Further arguments to be passed

Value

• For tam.wle.mml it is a data frame with following columns:
• pid
  Person identifier
• PersonScores
  Score of each person
• PersonMax
  Maximum score of each person
• theta
  Weighted likelihood estimate (WLE) or MLE
• error
  Standard error of the WLE or MLE
• WLE.rel
  WLE reliability (same value for all persons)
• For tam.jml.WLE it is a list with following entries:
• theta
  Weighted likelihood estimate (WLE) or MLE
• errorWLE
  Standard error of the WLE or MLE
• meanChangeWLE
  Mean change between updated and previous ability estimates from last iteration

References

Warm, T. A. (1989). Weighted likelihood estimation of ability in item response theory. Psychometrika, 54, 427-450.

Examples

data(sim.rasch)
# estimate Rasch model
mod1 <- tam.mml(resp=sim.rasch) 
# WLE estimation
wle1 <- tam.wle( mod1 )
## ----
## WLE Reliability = 0.894