University of Illinois Urbana-Champaign

Stability of Canonical Weights: A Monte Carlo Study

Sa'ad, Farouk Fayez

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Description

Title
Stability of Canonical Weights: A Monte Carlo Study
Author(s)
Sa'ad, Farouk Fayez
Issue Date
1980
Department of Study
Psychology
Discipline
Psychology
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
  • The primary aim of this research was to investigate the stability of the canonical weights and the canonical subspace. This investigation was carried out over four different population structures encompassing five different battery sizes. Two important and concrete notions were fully treated, the Tucker canonical subspace and its stability, and the derivation for the variance of the first canonical weight of the one-factor model.
  • The Tucker canonical subspace's stability was investigated in a thorough manner for the two population structures where (a) the first two canonical correlations were equal to one and the rest are zero and (b) the first two canonical correlations are very high and close and the rest are very small. A variance minimizing transformation T(,s) was developed. Trace (u(,s)) following the minimization process characterized the stability of the subspace which led to a quantitative evidence of the stability of the simple structure configuration.
  • The exact and asymptotic distributions were derived for the variance of the first canonical weight of the one-factor model. Variances for each one of the sample sizes were computed and compared with the Monte Carlo results.
Graduation Semester
1980
Type of Resource
text
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http://hdl.handle.net/2142/66591

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