Date of Award

2016

Document Type

Open Access Dissertation

Department

Statistics

Sub-Department

College of Arts and Sciences

First Advisor

Brian Habing

Abstract

Both the marginalized Bayesian modal estimation (MBME) and Metropolis-Hasting within Gibbs (MH/Gibbs) are the popular estimation methods for Item Response Theory (IRT). However, predictions from MBME and MH/Gibbs are not directly comparable because of two problems. First, the examinees with the same response pattern do not produce the same ability estimates from MH/Gibbs while MBME provides identical estimates. This problem can be handled by updating each response pattern instead of updating each examinee. Second, standard errors from MBME are smaller than standard error estimates from MH/Gibbs. This pattern occurs because of two speculated reasons; correlation between item parameter estimations and ability estimations even after thinning and the absence of a procedure which centers ability for every iteration which existed in MBME. In-chain centered MCMC mitigates the correlation by using a linking procedure to adjust candidates of item parameters at the middle of every iteration and can provide item parameter estimations which are closer the item parameter estimations from MBME. Two methods of in-chain centered MCMC are introduced - one using extra sets of abilities simulated in the proposal step, and one using the abilities generated previously. The simulation results demonstrate that both in-chain centered MCMC using extra simulated sets of abilities and in-chain centered MCMC with previous abilities can generate item parameter estimations with comparable standard errors without losing the accuracy of the point estimates. Therefore, in-chained MCMC can generate whole posterior distributions for item parameters which are comparable to the point estimates and standard errors from MBME.

Rights

© 2016, Han Kil Lee

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