Item Parameter Estimation Via Marginal Maximum Likelihood and an EM Algorithm: A Didactic

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Abstract
The Bock and Aitkin (1981) Marginal Maximum Likelihood/EM approach to item parameter estimation is an alternative to the classical joint maximum likelihood procedure of item response theory. Unfortunately, the complexity of the underlying mathematics and the terse nature of the existing literature has made understanding of the approach difficult. To make the approach accessible to a wider audience, the present didactic paper provides the essential mathematical details of a marginal maximum likelihood/EM solution and shows how it can be used to obtain consistent item parameter estimates. For pedagogical purposes, a short BASIC computer program is used to illustrate the underlying simplicity of the method.