The use of prior distributions in marginalized Bayesian item parameter estimation: A didactic

The marginal maximum likelihood estimation(MMLE) procedure (Bock & Lieberman, 1970; Bock& Aitkin, 1981) has led to advances in the estimationof item parameters in item response theory.Mislevy (1986) extended this approach by employingthe hierarchical Bayesian estimation model ofLindley and Smith (1972). Mislevy’s procedureposits prior probability distributions for both abilityand item parameters, and is implemented in thePC-BILOG computer program. This paper extendsthe work of Harwell, Baker, and Zwarts (1988),who provided the mathematical and implementationdetails of MMLE in an earlier didactic paper,by encompassing Mislevy’s marginalized Bayesianestimation of item parameters. The purpose wasto communicate the essential conceptual and mathematicaldetails of Mislevy’s procedure to practitionersand to users of PC-BILOG, thus makingit more accessible. Index terms: Bayesian estimation,BILOG, item parameter estimation, item responsetheory.