Abstract
Bayesian item response models have been used in modeling educational testing and Internet ratings data. Typically, the statistical analysis is carried out using Markov Chain Monte Carlo methods. However, these may not be computationally feasible when real-time data continuously arrive and online parameter estimation is needed. We develop an efficient algorithm based on a deterministic moment-matching method to adjust the parameters in real-time. The proposed online algorithm works well for two real datasets, achieving good accuracy but with considerably less computational time.
Highlights
Markov Chain Monte Carlo (MCMC) methods have revolutionized statistical computing in the past two decades
The developments in MCMC algorithms and software have enabled the use of Bayesian inference for item response theory (IRT) models in psychological and educational studies
Johnson and Albert (1999) described Gibbs sampling methods for Normal Ogive IRT models; Patz and Junker (1999) developed a Metropolis-Hastings sampling method and illustrated it using the two-parameter logistic (2PL) IRT model; Fox and Glas (2001) proposed Gibbs sampling for multilevel IRT models; Ho and Quinn (2008a) fit a Bayesian ordinal item response theory (IRT) model via MCMC techniques for Internet ratings data, where the data are typically ordinal measurements on the quality of all kinds of items such as movies, consumer products, and so on; and Martin and Quinn (2002) and Wang et al (2013) presented the MCMC strategy for dynamic item response models
Summary
Markov Chain Monte Carlo (MCMC) methods have revolutionized statistical computing in the past two decades. Take the ordinal IRT model in Ho and Quinn (2008a) for illustration: this model has advantages over traditional average ratings by accounting for the rater bias and item quality, but fitting the model by MCMC methods may not be feasible for large-scale real-time data For such a scenario, Ho and Quinn (2008a, Section 5) commented on the possible use of efficient deterministic approximation algorithms. Weng and Lin (2011) proposed a new deterministic moment-matching approach based on a version of Stein’s identity and exact calculation of certain integrals When applying it for online ranking of players, the accuracy is comparable to TrueSkillTM, but the running time as well as the code are much shorter.
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