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|Title:||Stability of Canonical Weights: A Monte Carlo Study|
|Author(s):||Sa'ad, Farouk Fayez|
|Department / Program:||Psychology|
|Degree Granting Institution:||University of Illinois at Urbana-Champaign|
|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.
Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980.
|Date Available in IDEALS:||2014-12-13|