Likelihood-Based Estimation Methods for Models for Concurrent Continuous and Discrete Responses With a Structure for the Item and Person Parameters (RR 06-03)
by Wim J. van der Linden and Cees A. W. Glas, University of Twente, Enschede, The Netherlands
Executive Summary
In an earlier research project, a hierarchical framework for modeling speed and accuracy of test-taker responses to test questions (items) in a computerized adaptive testing environment was presented. The goal of the current study is to apply a more traditional procedure (specifically, marginal maximum likelihood) to the estimation of the parameters of the model.
First, the equations necessary for estimating the parameters of the model were derived. Second, parallel versions of the tests of model assumptions were developed.
In a small parameter recovery study with simulated data, the parameter estimates were found to be within the confidence bands. In addition, we showed that the model assumption tests still function as desired if the items have not been calibrated with enough precision to ignore estimation error.