## Estimating parametric continuous latent distributions with the EM Algorithm

Bradley A. Hanson

**Date**: October 1, 1996

**Summary**: This note describes using the EM algorithm to estimate continuous (possibly multivariate) parametric latent variable distributions in item response models. The general formula for expectation computed in the E step is given. The formula can be simplified when the sufficient statistics of the latent distribution can be written as the sum of statistics that only involve the latent variable for a single examinee (for example, when the latent variable distribution is assumed to be multivariate normal).

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**Links**: 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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