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

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. 1. Introduction Item response theory (IRT) is a popular approach used for describing probabilistic relationships between correct responses on a set of test items and continuous latent traits (see [1–4]). In addition to educational and psychological measurement, IRT models have been used in other areas of applied mathematics and statistical research, including US Supreme Court decision-making processes [5], alcohol disorder analysis [6–9], nicotine dependency [10–12], multiple-recapture population estimation [13], and psychiatric epidemiology [14–16], to name a few. IRT has the advantage of allowing the inference of what the items and persons have on the responses to be modeled by distinct sets of parameters. As a result, a primary concern associated with IRT research has been on parameter estimation, which offers the basis for the theoretical advantages of IRT. Specifically, of concern are the statistical complexities that can often arise when item and person parameters are simultaneously estimated (see [1, 17–19]). More recent attention has focused on the fully Bayesian estimation where Markov chain Monte Carlo (MCMC, [20, 21]) simulation techniques are used. In spite of the many advantages, the fully Bayesian estimation is computationally expensive, which further limits its actual applications. It is hence important to seek ways to reduce the execution time. A suitable solution is to use high performance computing via the Message Passing Interface (MPI) standard, which employs supercomputers and computer clusters to tackle problems with complex computations. The implementation of parallel computing