Accession Number:

ADA067279

Title:

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

Descriptive Note:

Rept. for 1 Oct-31 Dec 79,

Corporate Author:

ILLINOIS UNIV AT URBANA-CHAMPAIGN COMPUTER-BASED EDUCATION RESEARCH LAB

Personal Author(s):

• Tatsuoka,Kikumi

Report Date:

1979-01-01

Pagination or Media Count:

40.0

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

Descriptors:

• *REGRESSION ANALYSIS
• *LEAST SQUARES METHOD
• *HILBERT SPACE
• OPERATORS(MATHEMATICS)
• COMPUTER AIDED INSTRUCTION
• FOURIER SERIES
• ADAPTIVE TRAINING
• PROJECTIVE TECHNIQUES

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE