The marginal maximum likelihood estimation
(MMLE) procedure (Bock & Lieberman, 1970; Bock
& Aitkin, 1981) has led to advances in the estimation
of item parameters in item response theory.
Mislevy (1986) extended this approach by employing
the hierarchical Bayesian estimation model of
Lindley and Smith (1972). Mislevy’s procedure
posits prior probability distributions for both ability
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 implementation
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 mathematical
details of Mislevy’s procedure to practitioners
and to users of PC-BILOG, thus making
it more accessible. Index terms: Bayesian estimation,
BILOG, item parameter estimation, item response
Harwell, Michael R.; Baker, Frank B..
The use of prior distributions in marginalized Bayesian item parameter estimation: A didactic.
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