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A New Extension of the Binomial Error Model for Responses to Items of Varying Difficulty in Educational Testing and Attitude Surveys

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  • James A Wiley
  • John Levi Martin
  • Stephen J Herschkorn
  • Jason Bond

Abstract

We put forward a new item response model which is an extension of the binomial error model first introduced by Keats and Lord. Like the binomial error model, the basic latent variable can be interpreted as a probability of responding in a certain way to an arbitrarily specified item. For a set of dichotomous items, this model gives predictions that are similar to other single parameter IRT models (such as the Rasch model) but has certain advantages in more complex cases. The first is that in specifying a flexible two-parameter Beta distribution for the latent variable, it is easy to formulate models for randomized experiments in which there is no reason to believe that either the latent variable or its distribution vary over randomly composed experimental groups. Second, the elementary response function is such that extensions to more complex cases (e.g., polychotomous responses, unfolding scales) are straightforward. Third, the probability metric of the latent trait allows tractable extensions to cover a wide variety of stochastic response processes.

Suggested Citation

  • James A Wiley & John Levi Martin & Stephen J Herschkorn & Jason Bond, 2015. "A New Extension of the Binomial Error Model for Responses to Items of Varying Difficulty in Educational Testing and Attitude Surveys," PLOS ONE, Public Library of Science, vol. 10(11), pages 1-16, November.
    • Handle: RePEc:plo:pone00:0141981
    DOI: 10.1371/journal.pone.0141981
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    References listed on IDEAS

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    1. John Keats, 1964. "Some generalizations of a theoretical distribution of mental test scores," Psychometrika, Springer;The Psychometric Society, vol. 29(3), pages 215-231, September.
    2. J. Keats & Frederic Lord, 1962. "A theoretical distribution for mental test scores," Psychometrika, Springer;The Psychometric Society, vol. 27(1), pages 59-72, March.
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    Cited by:

    1. Alexander Robitzsch, 2021. "About the Equivalence of the Latent D-Scoring Model and the Two-Parameter Logistic Item Response Model," Mathematics, MDPI, vol. 9(13), pages 1-17, June.

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