An item response model, similar to that in test theory, was proposed for multiple-choice questionaire data. In this model both subjects and item categories are represented as points in a multidimensional euclidean space. The probability of a particular subject choosing a particular item category is stated as a decreasing function of the distance between the subject point and the item category point. The subject point is assumed to follow a certain distribution, and is then integrated out to derive marginal probabilities of response patterns. A marginal maximum likelihood (MML) method was developed to estimate coordinates of the item category points as well as distributional properties of the subject point. Bock and Aitkin’s EM algorithm was adapted to the MML estimation of the proposed model. Examples were given to illustrate the method, which we call MAXMC.

The MAXMC method, adapted from Bock and Aitkin's EM algorithm, effectively estimates coordinates and distributional properties of item category points in multiple-choice questionaire data.

AN ITEM RESPONSE MODEL FOR MULTIDIMENSIONAL ANALYSIS OF MULTIPLE-CHOICE DATA

Key Takeaway: The MAXMC method, adapted from Bock and Aitkin's EM algorithm, effectively estimates coordinates and distributional properties of item category points in multiple-choice questionaire data.