Estimation of the Operating Characteristics of Item Response Categories I: Introduction to the Two-Parameter Beta Method.

Abstract

Following the Normal Approximation Method, in this study, the Two-Parameter Beta Method is developed and introduced, as a method of estimating the operating characteristics of a test without assuming any prior model. The maximum likelihood estimation, Theta-bar, and its asymptotic property such that its conditional distribution, given ability Theta, is N(Theta, 1/I(theta), where I(Theta) is the test information function, are fully utilized. An approximation is made for the conditional distribution of Theta, given Theta-bar, by a Beta distribution using the method of moments, with two a priori set parameters and the other two estimated parameters from the first two conditional moments of Theta, given Theta-bar. The least square principle is adopted in estimating two parameters in the normal ogive model for each item.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1977
Accession Number
ADA049618

Entities

People

  • Fumiko Samejima

Organizations

  • University of Tennessee

Tags

Communities of Interest

  • Biomedical

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  • Air Force
  • Behavioral Sciences
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  • Cognition
  • Education
  • Educational Psychology
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  • Operating Systems
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  • Students
  • Tennessee
  • Training
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Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Statistical inference.