JOINT MAXIMUM LIKELIHOOD ESTIMATES ON ITEMS-EXAMINEES USING THE PROX METHOD: A STUDY ON THE READING SUBTEST OF TOEFL

Abstract

Item response theory (IRT) emerges as an accurate solution to the weaknesses of the classical test theory (CTT). IRT provides more advantages than CTT does. The advantages include the requirements of unidimension for items, local independence between examinees and items, and examinee-item parameter invariance. The requirements are needed in test construction. TOEFL is so far known as the test which meets the requirements in language testing. It however concerns IRT. In this case, the research deals with the reading subtest of TOEFL with regard to IRT. The research is designed to estimate examinee-item parameters. As a parameter logistic (1PL) model in IRT, the Prox method is employed to estimate the parameters jointly. This is named joint maximum likelihood estimates. The method requires dichotomous data. Therefore, TOEFL as a good test instrument is chosen. It includes 30 persons as the examinee measure θ parameter and 20 items as the item difficulty b parameter. Unlike CTT, IRT using Prox method is able to estimate the examinee-item parameters jointly. As a result, the values of θ and b prove the ranges as the model intended in IRT, which is commonly named as the item characteristic curve. Keywords : item response theory, one parameter logistic model, parameter estimates, the Prox method.