Sujit K. Sahu
April 3, 2001
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SUMMARY

Item response models are essential tools for analyzing results from
many educational and psychological tests. Such models are used to quantify the
probability of correct response as a function of unobserved examinee
ability and other parameters explaining the difficulty and the
discriminatory power of the questions in the test. Some of
these models also incorporate a threshold parameter for the
probability of the correct response to account for the effect of
guessing the correct answer in multiple choice type tests.

In this article we consider fitting of such models using
the Gibbs sampler. A data augmentation method to analyze a
normal-ogive model incorporating a threshold guessing parameter
is introduced and compared with a Metropolis-Hastings sampling method.
The proposed method is an order of magnitude more efficient than the
existing method.
Another objective of this paper is to develop Bayesian model choice
techniques for model discrimination. A predictive approach based on
a variant of the Bayes factor is used and compared with another decision
theoretic method which
minimizes an expected loss function on the predictive space. A
classical model choice technique based on a modified likelihood ratio
test statistic is shown as one component of the second criterion. As
a consequence the Bayesian methods proposed in this paper are
contrasted with the classical approach based on the likelihood ratio
test. Several examples are given to illustrate the methods.

You can get the paper in postscript
or in pdf format.

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S.K.Sahu@maths.soton.ac.uk