{"id":{"repo_id":"buffalo","oai_identifier":"oai:ubir.buffalo.edu:10477/84031"},"canonical_url":"https://search.dev.ndltd.org/etd/buffalo/oai:ubir.buffalo.edu:10477/84031","repository":{"repo_id":"buffalo","name":"Buffalo","base_url":"https://ubir.buffalo.edu/oai/request"},"display":{"title":"The Impacts of the Modifiable Areal Unit Problem (MAUP) on Linear Regression","abstract":"Ph.D.","abstract_html":"Ph.D.","abstract_has_math":false,"creators":["Ye, Xiang; 0000-0002-2283-2591"],"institution":"State University of New York at Buffalo","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Rogerson, Peter","Geography"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-06-21T15:47:13Z","date_published":"2022-06-21T15:47:13Z","updated_at":"2026-07-27T19:05:30Z","subjects":["geography","statistics"],"languages":["eng"],"rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10477/84031","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Rogerson, Peter","Geography"]},{"key":"dc:creator","label":"Author","values":["Ye, Xiang; 0000-0002-2283-2591"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-06-21T15:47:13Z","2020"]},{"key":"dc:publisher","label":"Institution","values":["State University of New York at Buffalo"]},{"key":"dc:type","label":"Dc Type","values":["Text","Dissertation"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["geography","statistics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/10477/84031"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Ph.D.","The modifiable areal unit problem (MAUP) is the sensitivity or the inconsistency of the results of spatial analyses in the same study area with different spatial configurations. Along with spatial autocorrelation and spatial heterogeneity, it is one of the three fundamental issues that exert considerable effects in and beyond the discipline of geography. The issue has been noticed and formally recognized fairly early, and many empirical studies have focused on the multiple facets of the issue. Nevertheless, despite much research, a clear, concise and complete solution has not been achieved. The MAUP does not happen alone; its appearance and severity always hinge on the spatial phenomena being investigated and the analysis methods being implemented. In this research, the understanding of the MAUP will be focused on its interactions with statistical tools, leading to a systematic study on the impacts of the MAUP on linear regression, which is one of the most frequently adopted statistical tools when only observational data is available. By proposing the merging matrix M and incorporating it in the linear regression models, the research adopted a methodology of 'construct, calculate, and contrast' to discover the impacts of the MAUP on linear regression. Results suggest that for the classical linear regression model (CLRM) at the aggregate level (i.e. under the impact of the MAUP), the ordinary least square (OLS) estimator of β is still unbiased, just less efficient; but the OLS estimator of σ2 is no longer available without knowing M, and the traditional OLS estimator of σ2 at the individual level becomes downward biased at the aggregate level. If M is known, a best linear unbiased estimator (BLUE) of β can be acquired via the general least square (GLS) method. A GLS estimator of σ2 is available, too, and it is unbiased. For the generalized linear regression model (GLRM) at the aggregate level, the GLS estimator of β is best linear unbiased (BLU), and the GLS estimator of σ2 is unbiased. For both the CLRM and the GLRM at the aggregate level, their Cramér-Rao lower bounds for estimators are altered by the MAUP. The situation deteriorates if a model specification error appears simultaneously with the presence of the MAUP. In particular, the joint presence of both the MAUP and omission error will distort the expectations of coefficient estimations indefinitely for both the CLRM and the GLRM at the aggregate level, which is the most significant finding of this research.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["The Impacts of the Modifiable Areal Unit Problem (MAUP) on Linear Regression"]}]}],"canonical_facts":{"dc:contributor":["Rogerson, Peter","Geography"],"dc:creator":["Ye, Xiang; 0000-0002-2283-2591"],"dc:date":["2022-06-21T15:47:13Z","2020"],"dc:description":["Ph.D.","The modifiable areal unit problem (MAUP) is the sensitivity or the inconsistency of the results of spatial analyses in the same study area with different spatial configurations. Along with spatial autocorrelation and spatial heterogeneity, it is one of the three fundamental issues that exert considerable effects in and beyond the discipline of geography. The issue has been noticed and formally recognized fairly early, and many empirical studies have focused on the multiple facets of the issue. Nevertheless, despite much research, a clear, concise and complete solution has not been achieved. The MAUP does not happen alone; its appearance and severity always hinge on the spatial phenomena being investigated and the analysis methods being implemented. In this research, the understanding of the MAUP will be focused on its interactions with statistical tools, leading to a systematic study on the impacts of the MAUP on linear regression, which is one of the most frequently adopted statistical tools when only observational data is available. By proposing the merging matrix M and incorporating it in the linear regression models, the research adopted a methodology of 'construct, calculate, and contrast' to discover the impacts of the MAUP on linear regression. Results suggest that for the classical linear regression model (CLRM) at the aggregate level (i.e. under the impact of the MAUP), the ordinary least square (OLS) estimator of β is still unbiased, just less efficient; but the OLS estimator of σ2 is no longer available without knowing M, and the traditional OLS estimator of σ2 at the individual level becomes downward biased at the aggregate level. If M is known, a best linear unbiased estimator (BLUE) of β can be acquired via the general least square (GLS) method. A GLS estimator of σ2 is available, too, and it is unbiased. For the generalized linear regression model (GLRM) at the aggregate level, the GLS estimator of β is best linear unbiased (BLU), and the GLS estimator of σ2 is unbiased. For both the CLRM and the GLRM at the aggregate level, their Cramér-Rao lower bounds for estimators are altered by the MAUP. The situation deteriorates if a model specification error appears simultaneously with the presence of the MAUP. In particular, the joint presence of both the MAUP and omission error will distort the expectations of coefficient estimations indefinitely for both the CLRM and the GLRM at the aggregate level, which is the most significant finding of this research.","**To request an accessible version of the file(s) associated with this item, contact library@buffalo.edu. Please include the item's persistent URL [http://hdl.handle.net/. . .] in your request.**"],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/10477/84031"],"dc:language":["eng"],"dc:publisher":["State University of New York at Buffalo"],"dc:rights":["Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.","Copyright retained by author."],"dc:subject":["geography","statistics"],"dc:title":["The Impacts of the Modifiable Areal Unit Problem (MAUP) on Linear Regression"],"dc:type":["Text","Dissertation"]},"updated_at":"2026-07-27T19:05:30Z"}