Modeling Dependence Structures for Response Times in a Bayesian Framework.

Area of Science:

• Psychometrics
• Statistical Modeling
• Bayesian Inference

Background:

• Traditional log-normal models for response times struggle with complex dependencies.
• Existing Bayesian frameworks often rely on random-effect variables, which can complicate modeling.

Purpose of the Study:

• To propose a novel Bayesian Covariance Structure Model (BCSM) for multivariate response times.
• To model complex dependencies directly through an additive covariance structure, avoiding explicit random effects.
• To develop conjugate priors for variance parameters that facilitate model testing and accurate estimation.

Main Methods:

• Developed a Bayesian Covariance Structure Model (BCSM) with an additive covariance structure.
• Proposed a class of conjugate priors for random-effect variance parameters.
• Utilized Markov Chain Monte Carlo (MCMC) algorithms for posterior computation.
• Employed Bayes factors and Bayesian Information Criterion for model selection.

Main Results:

• The BCSM effectively models complex dependencies in response times, such as those arising from testlets or time limits.
• Conjugate priors support testing for random effects and allow for non-positive (co)variance parameters, reducing boundary issues.
• The MCMC algorithm and Bayes factor demonstrated satisfactory performance in simulation studies.
• Estimates of near-zero variance parameters were unbiased, and credible interval undercoverage was avoided compared to alternative methods.

Conclusions:

• The proposed BCSM offers a flexible and efficient framework for analyzing multivariate response times, particularly in digitally based assessments.
• The novel conjugate priors enhance the practical utility of the BCSM for statistical inference and model selection.
• An empirical example confirmed the BCSM's ability to assess the impact of item presentation formats on student test performance.