Date of Award

2011

Document Type

Campus Access Dissertation

Department

Statistics

First Advisor

Brian T Habing

Abstract

DISS_abstract>

Estimation of the parameters in item response theory (IRT) models is routinely accomplished using marginalized Bayes modal estimation (MBME) as implemented through standard IRT software, such as BILOG-MG. However, checking IRT model fit is an on-going area of research, with no one method in wide use. One routine that has recently become popular for this is posterior predictive model checking (PPMC). This is commonly implemented using the joint posterior distribution of the item parameters as estimated through Markov chain Monte Carlo (MCMC). MCMC estimation is typically very computationally intensive for IRT models and does not result in the same parameter estimates as the MBME method. It is thus not currently used operationally. The goal of this research is to propose a computationally fast method of approximating the posterior distribution by using many of the ideas underlying the MBME algorithm. This fast posterior approximation is called the expectation maximization plus expectation (EM+E) method. A simulation study demonstrates the EM+E method as an excellent alternative to using MCMC by offering samples from (approximately) the same posterior distribution of item parameters, but with a significant time savings. In addition, the EM+E method for obtaining posterior samples circumvents well known issues associated with implementing MCMC, offering samples with no autocorrelation or convergence issues. The resulting posterior distribution from EM+E is compared to that from an MCMC. Applications demonstrated include: using the posterior sample to carry out PPMC model fit diagnostics.

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