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Multimodal Likelihoods in Educational Assessment

Author

Listed:
  • Werner Wothke

    (The American Institutes for Research)

  • George Burket

    (Retired)

  • Li-Sue Chen

    (eBay)

  • Furong Gao

    (CTB/McGraw-Hill)

  • Lianghua Shu

    (CTB/McGraw-Hill)

  • Mike Chia

    (Consultant)

Abstract

It has been known for some time that item response theory (IRT) models may exhibit a likelihood function of a respondent’s ability which may have multiple modes, flat modes, or both. These conditions, often associated with guessing of multiple-choice (MC) questions, can introduce uncertainty and bias to ability estimation by maximum likelihood (ML) when standard Newton solutions are used. This article evaluates the performance of several maximization methods, including initial (grid) searches probing the function slopes, simulated annealing, exhaustive likelihood evaluation, and the standard Newton algorithm. In extensive studies, involving several million records of both generated and real data, the algorithms were evaluated with respect to precision and speed. Two methods, exhaustive search and grid search, followed by Newton steps, all yielded ML estimates at the required precision. At today’s computer speeds, either of these algorithms may be considered for high-volume response pattern scoring.

Suggested Citation

  • Werner Wothke & George Burket & Li-Sue Chen & Furong Gao & Lianghua Shu & Mike Chia, 2011. "Multimodal Likelihoods in Educational Assessment," Journal of Educational and Behavioral Statistics, , vol. 36(6), pages 736-754, December.
    • Handle: RePEc:sae:jedbes:v:36:y:2011:i:6:p:736-754
    DOI: 10.3102/1076998610381400
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    References listed on IDEAS

    as
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    2. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
    3. Wendy Yen & George Burket & Robert Sykes, 1991. "Nonunique solutions to the likelihood equation for the three-parameter logistic model," Psychometrika, Springer;The Psychometric Society, vol. 56(1), pages 39-54, March.
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