## IRT Parameter Estimation using the EM Algorithm

Bradley A. Hanson

**Date**: October 28, 1998

**Revised**: September 27, 2000

**Summary**: These are notes to accompany a lecture I gave in a seminar at the University of Iowa taught by Mike Kolen. A detailed description is given of using the EM algorithm to compute maximum likelihood parameter estimates in IRT models for dichotomous items. An example of applying the procedures described is given using a generalized Guttman scale model. Brief descriptions of how to use the EM algorithm to compute Bayes modal parameter estimates and maximum likelihood parameter estimates for polytomous IRT models are given in the final section.

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**Links**: A paper I wrote with David Woodruff provides more details in regard to parameter estimation in IRT models for polytomous items. I have written a paper that describes using the EM algorithm to compute maximum likelihood or Bayes modal estimates of a discrete latent variable distribution.

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