Item Information in the Rasch Model

Ron J.H. Engelen, Willem J. van der Linden, Sebe J. Oosterloo

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Abstract

Fisher's information measure for the item difficulty parameter in the Rasch model and its marginal and conditional formulations are investigated. It is shown that expected item information in the unconditional model equals information in the marginal model, provided the assumption of sampling examinees from an ability distribution is made. For the logistic ability distribution considered in this paper, item information in the two models can be expressed in a closed form. Also, it is shown that for a random examinee expected item information in the conditional model is always less than that in the other two models, albeit the difference quickly decreases with an increase in test length. If the distribution of the item difficulties in the test deviates more and more from the ability distribution, item information in all three models takes smaller and smaller values. Results from a simulation study of tests with 5 and 20 items demonstrate these features numerically. Six tables present the results of the simulation study, and one graph illustrates item information in the marginal model.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Faculty Educational Science and Technology
Publication statusPublished - 1988

Publication series

NameOMD research report
PublisherUniversity of Twente, Faculty of Educational Science and Technology
No.88-8

Keywords

  • Mathematical Models
  • Statistical Analysis
  • IR-104173
  • Latent Trait Theory
  • Foreign Countries
  • Test Items
  • Ability
  • Difficulty Level
  • Simulation

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