Document Type


Date of Degree

Summer 2015

Degree Name

PhD (Doctor of Philosophy)

Degree In

Psychological and Quantitative Foundations

First Advisor

Timothy N. Ansley

First Committee Member

Stephen B Dunbar

Second Committee Member

Michael J Kolen

Third Committee Member

Catherine J Welch

Fourth Committee Member

Mary K Cowles


Item response theory (IRT) uses a family of statistical models for estimating stable characteristics of items and examinees and defining how these characteristics interact in describing item and test performance. With a focus on the three-parameter logistic IRT (Birnbaum, 1968; Lord, 1980) model, the current study examines the accuracy and variability of the item parameter estimates from the marginal maximum a posteriori estimation via an expectation-maximization algorithm (MMAP/EM) and the Markov chain Monte Carlo Gibbs sampling (MCMC/GS) approach.

In the study, the various factors which have an impact on the accuracy and variability of the item parameter estimates are discussed, and then further evaluated through a large scale simulation. The factors of interest include the composition and length of tests, the distribution of underlying latent traits, the size of samples, and the prior distributions of discrimination, difficulty, and pseudo-guessing parameters.

The results of the two estimation methods are compared to determine the lower limit--in terms of test length, sample size, test characteristics, and prior distributions of item parameters--at which the methods can satisfactorily recover item parameters and efficiently function in reality. For practitioners, the results help to define limits on the appropriate use of the BILOG-MG (which implements MMAP/EM) and also, to assist in deciding the utility of OpenBUGS (which carries out MCMC/GS) for item parameter estimation in practice.


Gibbs sampling, item parameter estimation, item response theory, marginal maximum A posteriori estimation, Marko chain Monte Carlo


xvi, 332 pages


Includes bibliographical references (pages 243-252).


Copyright © 2015 Yi-Fang Wu