The marginal maximum likelihood estimation (MMLE) procedure (Bock & Lieberman, 1970; Bock & Aitkin, 1981) has led to advances in the estima tion of item parameters in item response theory. Mislevy (1986) extended this approach by employ ing the hierarchical Bayesian estimation model of Lindley and Smith (1972). Mislevy's procedure posits prior probability distributions for both abili ty and item parameters, and is implemented in the PC-BILOG computer program. This paper extends the work of Harwell, Baker, and Zwarts (1988), who provided the mathematical and implemen tation details of MMLE in an earlier didactic paper, by encompassing Mislevy's marginalized Bayesian estimation of item parameters. The purpose was to communicate the essential conceptual and math ematical details of Mislevy's procedure to prac titioners and to users of PC-BILOG, thus making it more accessible.
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