Bayesian Model Assessment Under the Joint IRT and Generalized Odds-Rate Hazards Model for Response and Response Time Data in Computerized Testing

Recently, a new Bayesian model assessment criterion ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:math> ) has been proposed to separately assess the contributions of different sources of data in the joint model. In order to evaluate the performance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="normal">Δ</mml:mi> </mml:mrow> </mml:math> with a more complex response time model by jointly modeling with accuracy, we develop efficient computational algorithms to calculate the assessment criterion based on the decomposition of the deviance information criterion and the logarithm of the pseudo-marginal likelihood under the joint IRT and generalized odds-rate hazards model for accuracy and response time data. Extensive simulation studies are conducted to examine the empirical performance of the proposed methodology, and a detailed analysis of empirical data is carried out to demonstrate the usefulness of the assessment criterion.