IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0141981.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0141981
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0141981&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0141981?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. J. Keats & Frederic Lord, 1962. "A theoretical distribution for mental test scores," Psychometrika, Springer;The Psychometric Society, vol. 27(1), pages 59-72, March.
    2. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Jarjoura, 1986. "Probability-of-coverage tolerance intervals for the beta binomial," Psychometrika, Springer;The Psychometric Society, vol. 51(1), pages 137-141, March.
    2. Donald Morrison & George Brockway, 1979. "A modified beta binomial model with applications to multiple choice and taste tests," Psychometrika, Springer;The Psychometric Society, vol. 44(4), pages 427-442, December.
    3. Huynh Huynh, 1976. "Statistical consideration of mastery scores," Psychometrika, Springer;The Psychometric Society, vol. 41(1), pages 65-78, March.
    4. Rand Wilcox, 1979. "Comparing examinees to a control," Psychometrika, Springer;The Psychometric Society, vol. 44(1), pages 55-68, March.
    5. Rand Wilcox, 1978. "Estimating true score in the compound binomial error model," Psychometrika, Springer;The Psychometric Society, vol. 43(2), pages 245-258, June.
    6. Alan Gross, 1990. "A maximum likelihood approach to test validation with missing and censored dependent variables," Psychometrika, Springer;The Psychometric Society, vol. 55(3), pages 533-549, September.
    7. Miao-Hsiang Lin & Chao Hsiung, 1992. "Four bootstrap confidence intervals for the binomial-error model," Psychometrika, Springer;The Psychometric Society, vol. 57(4), pages 499-520, December.
    8. William Meredith & Jack Kearns, 1973. "Empirical bayes point estimates of latent trait scores without knowledge of the trait distribution," Psychometrika, Springer;The Psychometric Society, vol. 38(4), pages 533-554, December.
    9. Jack Kearns & William Meredith, 1975. "Methods for evaluating empirical bayes point estimates of latent trait scores," Psychometrika, Springer;The Psychometric Society, vol. 40(3), pages 373-394, September.
    10. Miao-Hsiang Lin & Chao Hsiung, 1994. "Empirical bayes estimates of domain scores under binomial and hypergeometric distributions for test scores," Psychometrika, Springer;The Psychometric Society, vol. 59(3), pages 331-359, September.
    11. Rand Wilcox, 1979. "A lower bound to the probability of choosing the optimal passing score for a mastery test when there is an external criterion," Psychometrika, Springer;The Psychometric Society, vol. 44(2), pages 245-249, June.
    12. Huynh Huynh, 1980. "Statistical inference for false positive and false negative error rates in mastery testing," Psychometrika, Springer;The Psychometric Society, vol. 45(1), pages 107-120, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0141981. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.