MML and EAP Estimation in Testlet-based Adaptive Testing

Abstract

In the previous chapter, Wainer, Bradlow and Du (this volume) presented a generalization of the three-parameter item response model in which the dependencies generated by a testlet structure are explicitly taken into account. That chapter is an extension of their prior work that developed the generalization for the two-parameter model (Bradlow, Wainer, & Wang, 1999). Their approach is to use a fully Bayesian formulation of the problem, coupled with a Markov Chain Monte Carlo (MCMC) procedure to estimate the posterior distribution of the model parameters. They then use the estimated posterior distribution to compute interval and point estimates. In this chapter, we derive estimates for the parameters of the Wainer, Bradlow, and Du testlet model using more traditional estimation methodology; maximum marginal likelihood (MML) and expected a posteriori (EAP) estimates. We also show how the model might be used within a CAT environment. After deriving the estimation equations, we compare the results of MCMC and MML estimation procedures and we examine the extent to which ignoring the testlet structure affects the precision of item calibration and the estimation of ability within a CAT procedure.