Estimation of Item Response Models Using the EM Algorithm for Finite Mixtures.

This paper presents a detailed description of maximum parameter estimation for item response models using the general EM algorithm. In this paper the models are specified using a univariate discrete latent ability variable. When the latent ability variable is discrete the distribution of the observed item responses is a finite mixture, and the EM algorithm for finite mixtures can be used. Maximum likelihood estimates of the item parameters and of the discrete probabilities of the latent ability distribution are given using the EM algorithm for finite mixtures. Results are presented in general for both dichotomous and polytomous item response models. The relation between the EM estimates and the Bock Aitken marginal maximum likelihood estimates is discussed. Estimates for the item parameters will depend on the specific form of the item response functions, and will usually require iterative numerical procedures. The EM algorithm is the same as the Bock-Aitken algorithm (R. D. Bock and M. Aitken, 1981) for marginal maximum likelihood estimation of the item parameters. (Contains 28 references.) (Author/SLD)