MARGIE: Marginal maximum likelihood estimation of the parameters of the one-, two-, and three-parameter logistic models

Abstract

Bock and Aitkin (1981) provided a powerful estima­ tion technique for use with item response theory. Margi­ nal maximum likelihood estimation (MMLE) treats the examinee ability parameter as a random nuisance parameter that is eliminated from the estimation process by specifying a form for the ability distribution, and in­ tegration over that distribution. Thus, item-parameter es­ timates are obtained by maximum likelihood estimation (MLE) in the marginal distribution. In this way, problems such as inconsistent parameter estimates which arise in joint MLE are avoided. The MARGIE program is designed to perform MMLE of the item parameters of the one-parameter logistic (1PL), two-parameter logistic (2PL), and three-parameter logistic (3PL) item response theory (IRT) models. In addition, ability estimates are produced using either MLE or Bayesian expected a posteriori estimation (EAPE). Also, a chi-square test of the goodness of fit of the IRT model to the data is performed, using the procedure described by Yen (1981). The Models. The program estimates the parameters of the IPL, 2PL, and 3PL IRT models. The IPL model is given by Cj: 0 k