The Least-Squares Estimation of Latent Trait Variables by a Hilbert Space Approach.

Abstract

This research developed a new method for estimating a given latent trait variable Theta by the least-squares approach. The notion of multiple regression equation was reinterpreted in terms of properties of a Hilbert space and the calculation formula for beta weights that can be obtained recursively in the form of Fourier series was derived. The Theta values estimated by this method and the maximum likelihood method were compared using live data. It was shown that Theta values estimated by the least-squares method was just as good as Theta by the maximum likelihood method. The advantage of using this method as against the traditional method is that values of Theta are always obtainable even for a small number of items. The maximum likelihood method, on the other hand, often fails to converge in such cases. Author

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1979
Accession Number
ADA067279

Entities

People

  • Kikumi Tatsuoka

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Biomedical

DTIC Thesaurus Topics

  • Accuracy
  • Data Science
  • Education
  • Errors
  • Hilbert Space
  • Illinois
  • Information Science
  • Least Squares Method
  • Manpower Utilization
  • Military Research
  • New York
  • Psychology
  • Schools
  • Standards
  • Students
  • United States
  • Universities

Readers

  • Approximation Theory.
  • Regression Analysis.

Technology Areas

  • Space