An Introduction to Multilinear Formula Score Theory.

Abstract

Formula score theory associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating ability distributions from sequences of item responses can be reformulated as maximizing a convex index of goodness of fit defined on a convex set. A major simplification of several theoretical problems has been obtained because the linear mathematics used by the theory has a well-developed generalization to problems involving many variables. For example, a battery of tests measuring several related variables and one test measuring one trait can be analyzed with essentially the same theory. An elementary outline of the basic theory is presented along with a discussion of several illustrative applications. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Aug 28, 1984
Accession Number
ADA145696

Entities

People

  • M. V. Levine

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Air Force
  • Behavioral Sciences
  • Cognition
  • Education
  • Educational Psychology
  • Estimators
  • Human Resources
  • Military Research
  • Personnel Management
  • Probability
  • Probability Distributions
  • Psychology
  • Random Variables
  • Social Sciences
  • Statistics
  • Two Dimensional
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Operations Research
  • Psychometric Testing or Psychological Assessment.