An Investigation of Parameter Recovery in MCMC Estimation for the Additive IRT Model

The article aims at evaluating the parameter recovery for the multidimensional additive IRT model (Sheng, 2005 Sheng , Y. ( 2005 ). Bayesian Analysis of Hierarchical IRT Models: Comparing and Combining the Unidimensional & Multi-Unidimensional IRT Models. PhD thesis , Faculty of the Graduate SchoolUniversity of Missouri-Columbia . [Google Scholar]; Sheng and Wikle, 2009 Sheng , Y. , Wikle , C. K. ( 2009 ). Bayesian IRT models incorporating general and specific abilities . Behaviormetrika 36 : 27 – 48 .[Crossref] , [Google Scholar]). By estimating the model parameters via Gibbs sampler, a simulation study is conducted under different testing conditions, e.g., dimensionality, test and subtest lengths, correlation matrices, and different values of discrimination parameters. The results show that, especially when the test length is short and the abilities are highly correlated, the accuracy of the parameter estimates is reduced and more iterations are required to convergence. An application in educational testing is also described to show the effectiveness of the model in use.