Improving precision of ability estimation: Getting more from response times

Maria Bolsinova*, J. Tijmstra

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

12 Citations (Scopus)

Abstract

By considering information about response time (RT) in addition to response accuracy (RA), joint models for RA and RT such as the hierarchical model (van der Linden, 2007) can improve the precision with which ability is estimated over models that only consider RA. The hierarchical model, however, assumes that only the person's speed is informative of ability. This assumption of conditional independence between RT and ability given speed may be violated in practice, and ignores collateral information about ability that may be present in the residual RTs. We propose a posterior predictive check for evaluating the assumption of conditional independence between RT and ability given speed. Furthermore, we propose an extension of the hierarchical model that contains cross‐loadings between ability and RT, which enables one to take additional collateral information about ability into account beyond what is possible in the standard hierarchical model. A Bayesian estimation procedure is proposed for the model. Using simulation studies, the performance of the model is evaluated in terms of parameter recovery, and the possible gain in precision over the standard hierarchical model and an RA‐only model is considered. The model is applied to data from a high‐stakes educational test.
Original languageEnglish
Pages (from-to)13-38
JournalBritish Journal of Mathematical and Statistical Psychology
Volume71
Issue number1
DOIs
Publication statusPublished - 2018

Keywords

  • ACCURACY
  • CONDITIONAL-INDEPENDENCE
  • DISTRIBUTIONS
  • FIT
  • FRAMEWORK
  • TESTS
  • THEORY MODELS
  • collateral information
  • hierarchical model
  • item response theory
  • measurement precision
  • response times

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