About this Journal Submit a Manuscript Table of Contents
ISRN Computational Mathematics
Volume 2012 (2012), Article ID 264040, 9 pages
http://dx.doi.org/10.5402/2012/264040
Research Article

High Performance Gibbs Sampling for IRT Models Using Row-Wise Decomposition

1Educational Measurement and Statistics, Department of Educational Psychology & Special Education, Southern Illinois University Carbondale, Carbondale, IL 62901-4618, USA
2Department of Computer Science, Southern Illinois University Carbondale, Carbondale, IL 62901, USA

Received 15 October 2012; Accepted 4 November 2012

Academic Editors: L. S. Heath, R. Tuzun, and P. B. Vasconcelos

Copyright © 2012 Yanyan Sheng and Mona Rahimi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Item response theory (IRT) is a popular approach used for addressing statistical problems in psychometrics as well as in other fields. The fully Bayesian approach for estimating IRT models is computationally expensive. This limits the use of the procedure in real applications. In an effort to reduce the execution time, a previous study shows that high performance computing provides a solution by achieving a considerable speedup via the use of multiple processors. Given the high data dependencies in a single Markov chain for IRT models, it is not possible to avoid communication overhead among processors. This study is to reduce communication overhead via the use of a row-wise decomposition scheme. The results suggest that the proposed approach increased the speedup and the efficiency for each implementation while minimizing the cost and the total overhead. This further sheds light on developing high performance Gibbs samplers for more complicated IRT models.