Modeling Dependence Structures for Response Times in a Bayesian Framework

Konrad Klotzke*, Jean Paul Fox

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    6 Citations (Scopus)
    81 Downloads (Pure)


    A multivariate generalization of the log-normal model for response times is proposed within an innovative Bayesian modeling framework. A novel Bayesian Covariance Structure Model (BCSM) is proposed, where the inclusion of random-effect variables is avoided, while their implied dependencies are modeled directly through an additive covariance structure. This makes it possible to jointly model complex dependencies due to for instance the test format (e.g., testlets, complex constructs), time limits, or features of digitally based assessments. A class of conjugate priors is proposed for the random-effect variance parameters in the BCSM framework. They give support to testing the presence of random effects, reduce boundary effects by allowing non-positive (co)variance parameters, and support accurate estimation even for very small true variance parameters. The conjugate priors under the BCSM lead to efficient posterior computation. Bayes factors and the Bayesian Information Criterion are discussed for the purpose of model selection in the new framework. In two simulation studies, a satisfying performance of the MCMC algorithm and of the Bayes factor is shown. In comparison with parameter expansion through a half-Cauchy prior, estimates of variance parameters close to zero show no bias and undercoverage of credible intervals is avoided. An empirical example showcases the utility of the BCSM for response times to test the influence of item presentation formats on the test performance of students in a Latin square experimental design.

    Original languageEnglish
    Pages (from-to)649-672
    Number of pages24
    Issue number3
    Early online date16 May 2019
    Publication statusPublished - 15 Sept 2019


    • Bayesian marginal modeling
    • conditional independence
    • local dependence
    • non-informative prior distribution
    • response time modeling
    • testlets


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