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PSYCHOMETRIKAVOL. 76, NO. 2, 360362
APRIL 2011
DOI: 10.1007/S11336-011-9205-9
BOOK REVIEW
J.-P. FOX (2010) Bayesian Item Response Modeling: Theory and Applications. New York: Springer. 313 pages. US$69.95. ISBN: 978-1441907417
Item response theory (IRT) models have been widely applied to address measurement issues in education, psychology, surveys, and health. An IRT model relates the probability of an item response to item and person characteristics with strong assumptions. However, the real measurement world is much more complicated than the standard IRT models can deal with. The complications due to such factors as multidimensionality, local dependence, and complex sampling design call for extended IRT models. The Bayesian Markov Chain Monte Carlo (MCMC) methods prove to be a viable and exible solution in parameter estimation of extended IRT models like multidimensional IRT models (Beguin & Glas, 2001; Segall, 2002; Yao, 2003), test-let models (Bradlow, Wainer, & Wang, 1999), and multilevel IRT models (Fox & Glas, 2001; Maier, 2001). The estimation of extended IRT models using MCMC requires knowledge in IRT models, Bayesian framework, mathematics, and computer programming skills. A reference book which provides a comprehensive synthesis of the related knowledge and skills is needed for researchers who wish to attempt to develop an extended IRT model to solve a specic measurement problem and estimate model parameters. The book Bayesian Item Response Modeling by Fox (2010) fullls this need.
This book covers the parameter estimation of standard and extended IRT models using the Bayesian simulation based MCMC method. There are many Bayesian data analysis books, but this is the rst book purely devoted to the Bayesian estimation of IRT models. The rst ve chapters provide the basics for IRT models, Bayesian theorem, and the MCMC estimation of IRT models. The last four chapters focus on parameter estimation related to extended IRT models, the multilevel IRT (MLIRT) models, mixture MLIRT models, MLIRT models for random DIF analysis, multivariate MLIRT models, random item response models, and extended models with covariates at different nested levels in modeling response data related to sensitive topics in survey research. In general, the models elaborated in each of the last four chapters are somewhat related to MLIRT.
The author should be rst credited for the clarity in introducing the IRT models. An introduction to standard IRT models...