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Psychometrika
12, 2022;87 (4): 1290-1317.

Bayesian Model Assessment for Jointly Modeling Multidimensional Response Data with Application to Computerized Testing.

Fang Liu, Xiaojing Wang, Roeland Hancock, Ming-Hui Chen
Author Information
  1. Fang Liu: Northeast Normal University, Changchun, China.
  2. Xiaojing Wang: University of Connecticut, Storrs, , CT, 06250, USA. xiaojing.wang@uconn.edu. ORCID
  3. Roeland Hancock: University of Connecticut, Storrs, , CT, 06250, USA.
  4. Ming-Hui Chen: University of Connecticut, Storrs, , CT, 06250, USA.
PMID: 35349031 DOI: 10.1007/s11336-022-09845-x

Abstract

Computerized assessment provides rich multidimensional data including trial-by-trial accuracy and response time (RT) measures. A key question in modeling this type of data is how to incorporate RT data, for example, in aid of ability estimation in item response theory (IRT) models. To address this, we propose a joint model consisting of a two-parameter IRT model for the dichotomous item response data, a log-normal model for the continuous RT data, and a normal model for corresponding paper-and-pencil scores. Then, we reformulate and reparameterize the model to capture the relationship between the model parameters, to facilitate the prior specification, and to make the Bayesian computation more efficient. Further, we propose several new model assessment criteria based on the decomposition of deviance information criterion (DIC) the logarithm of the pseudo-marginal likelihood (LPML). The proposed criteria can quantify the improvement in the fit of one part of the multidimensional data given the other parts. Finally, we have conducted several simulation studies to examine the empirical performance of the proposed model assessment criteria and have illustrated the application of these criteria using a real dataset from a computerized educational assessment program.

Keywords

DIC decomposition IRT models LPML decomposition computerized tests paper-and-pencil tests response times

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MeSH Term

Bayes Theorem
Psychometrics
Models, Statistical
Computer Simulation
Probability
Journal Article Research Support, U.S. Gov't, Non-P.H.S. Research Support, Non-U.S. Gov't

Word Cloud

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