{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/66591"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/66591","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Stability of Canonical Weights: A Monte Carlo Study","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Sa'ad, Farouk Fayez"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Psychology","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2014,"date_issued":"2014-12-13T18:22:28Z","date_published":"2014-12-13T18:22:28Z","updated_at":"2026-07-22T22:25:56Z","subjects":["Statistics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(UMI)AAI8108647"],"render_values":[{"text":"(UMI)AAI8108647","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/66591","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Sa'ad, Farouk Fayez"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2014-12-13T18:22:28Z","10000-01-01","1980"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Psychology"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Statistics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/66591","(UMI)AAI8108647"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2014-12-13T18:22:28Z (GMT). No. of bitstreams: 1 8108647.pdf: 1670858 bytes, checksum: 7cfee2d9ec99fcaa2d22c1706585aa76 (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 66769 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","57 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."]},{"key":"dc:title","label":"Title","values":["Stability of Canonical Weights: A Monte Carlo Study"]}]}],"canonical_facts":{"dc:creator":["Sa'ad, Farouk Fayez"],"dc:date":["2014-12-13T18:22:28Z","10000-01-01","1980"],"dc:description":["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.","Made available in DSpace on 2014-12-13T18:22:28Z (GMT). No. of bitstreams: 1 8108647.pdf: 1670858 bytes, checksum: 7cfee2d9ec99fcaa2d22c1706585aa76 (MD5) Previous issue date: 1980","Embargo set by: Seth Robbins for item 66769 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","57 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1980."],"dc:identifier":["http://hdl.handle.net/2142/66591","(UMI)AAI8108647"],"dc:language":["eng"],"dc:subject":["Statistics"],"dc:title":["Stability of Canonical Weights: A Monte Carlo Study"],"dc:type":["text"],"thesis:degree_discipline":["Psychology"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:25:56Z"}