Maximum Marginal Likelihood Estimation for Semiparametric Item Analysis

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Abstract
The item characteristic curve (ICC), defining the relation between ability and the probability of choosing a particular option for a test item, can be estimated by using polynomial regression splines. These provide a more flexible family of functions than is given by the three-parameter logistic family. The estimation of spline ICCs is described by maximizing the marginal likelihood formed by integrating ability over a beta prior distribution. Some simulation results compare this approach with the joint estimation of ability and item parameters.