{"id":"https://openalex.org/W4401722078","doi":"https://doi.org/10.1080/13658816.2024.2391412","title":"A backfitting maximum likelihood estimator for hierarchical and geographically weighted regression modelling, with a case study of house prices in Beijing","display_name":"A backfitting maximum likelihood estimator for hierarchical and geographically weighted regression modelling, with a case study of house prices in Beijing","publication_year":2024,"publication_date":"2024-08-21","ids":{"openalex":"https://openalex.org/W4401722078","doi":"https://doi.org/10.1080/13658816.2024.2391412"},"language":"en","primary_location":{"id":"doi:10.1080/13658816.2024.2391412","is_oa":true,"landing_page_url":"https://doi.org/10.1080/13658816.2024.2391412","pdf_url":null,"source":{"id":"https://openalex.org/S4210181446","display_name":"International Journal of Geographical Information Systems","issn_l":"0269-3798","issn":["0269-3798","1362-3087"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geographical Information Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1080/13658816.2024.2391412","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056564874","display_name":"Yigong Hu","orcid":"https://orcid.org/0000-0002-9553-6275"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Yigong Hu","raw_affiliation_strings":["School of Geographical Sciences, University of Bristol, Bristol, UK"],"raw_orcid":"https://orcid.org/0000-0002-9553-6275","affiliations":[{"raw_affiliation_string":"School of Geographical Sciences, University of Bristol, Bristol, UK","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002757843","display_name":"Richard Harris","orcid":"https://orcid.org/0000-0001-7943-9005"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Richard Harris","raw_affiliation_strings":["School of Geographical Sciences, University of Bristol, Bristol, UK"],"raw_orcid":"https://orcid.org/0000-0001-7943-9005","affiliations":[{"raw_affiliation_string":"School of Geographical Sciences, University of Bristol, Bristol, UK","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058894704","display_name":"Richard Timmerman","orcid":"https://orcid.org/0000-0002-7305-7804"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Richard Timmerman","raw_affiliation_strings":["School of Geographical Sciences, University of Bristol, Bristol, UK"],"raw_orcid":"https://orcid.org/0000-0002-7305-7804","affiliations":[{"raw_affiliation_string":"School of Geographical Sciences, University of Bristol, Bristol, UK","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023127879","display_name":"Binbin Lu","orcid":"https://orcid.org/0000-0001-7847-7560"},"institutions":[{"id":"https://openalex.org/I37461747","display_name":"Wuhan University","ror":"https://ror.org/033vjfk17","country_code":"CN","type":"education","lineage":["https://openalex.org/I37461747"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Binbin Lu","raw_affiliation_strings":["School of Remote Sensing and Information Engineering, Wuhan University, Wuhan, China"],"raw_orcid":"https://orcid.org/0000-0001-7847-7560","affiliations":[{"raw_affiliation_string":"School of Remote Sensing and Information Engineering, Wuhan University, Wuhan, China","institution_ids":["https://openalex.org/I37461747"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5056564874"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":null,"apc_paid":null,"fwci":8.0232,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.9691944,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"38","issue":"12","first_page":"2458","last_page":"2491"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T11911","display_name":"Spatial and Panel Data Analysis","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10298","display_name":"Urban Transport and Accessibility","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/3313","display_name":"Transportation"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11014","display_name":"Regional Economics and Spatial Analysis","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/2002","display_name":"Economics and Econometrics"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/beijing","display_name":"Beijing","score":0.7390190362930298},{"id":"https://openalex.org/keywords/multilevel-model","display_name":"Multilevel model","score":0.674780011177063},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.671637773513794},{"id":"https://openalex.org/keywords/geographically-weighted-regression","display_name":"Geographically Weighted Regression","score":0.6673623919487},{"id":"https://openalex.org/keywords/spatial-analysis","display_name":"Spatial analysis","score":0.5114938020706177},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4921726584434509},{"id":"https://openalex.org/keywords/hierarchical-database-model","display_name":"Hierarchical database model","score":0.4677676558494568},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.4668087959289551},{"id":"https://openalex.org/keywords/econometrics","display_name":"Econometrics","score":0.45933592319488525},{"id":"https://openalex.org/keywords/random-effects-model","display_name":"Random effects model","score":0.4552461504936218},{"id":"https://openalex.org/keywords/regression","display_name":"Regression","score":0.43537747859954834},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.43411290645599365},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.4202845096588135},{"id":"https://openalex.org/keywords/regression-analysis","display_name":"Regression analysis","score":0.41519081592559814},{"id":"https://openalex.org/keywords/geography","display_name":"Geography","score":0.4065099060535431},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3169761896133423},{"id":"https://openalex.org/keywords/china","display_name":"China","score":0.13866624236106873}],"concepts":[{"id":"https://openalex.org/C2778304055","wikidata":"https://www.wikidata.org/wiki/Q657474","display_name":"Beijing","level":3,"score":0.7390190362930298},{"id":"https://openalex.org/C53059260","wikidata":"https://www.wikidata.org/wiki/Q374758","display_name":"Multilevel model","level":2,"score":0.674780011177063},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.671637773513794},{"id":"https://openalex.org/C2910321205","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Geographically Weighted Regression","level":2,"score":0.6673623919487},{"id":"https://openalex.org/C159620131","wikidata":"https://www.wikidata.org/wiki/Q1938983","display_name":"Spatial analysis","level":2,"score":0.5114938020706177},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4921726584434509},{"id":"https://openalex.org/C144986985","wikidata":"https://www.wikidata.org/wiki/Q871236","display_name":"Hierarchical database model","level":2,"score":0.4677676558494568},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.4668087959289551},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.45933592319488525},{"id":"https://openalex.org/C168743327","wikidata":"https://www.wikidata.org/wiki/Q1826427","display_name":"Random effects model","level":3,"score":0.4552461504936218},{"id":"https://openalex.org/C83546350","wikidata":"https://www.wikidata.org/wiki/Q1139051","display_name":"Regression","level":2,"score":0.43537747859954834},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.43411290645599365},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.4202845096588135},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.41519081592559814},{"id":"https://openalex.org/C205649164","wikidata":"https://www.wikidata.org/wiki/Q1071","display_name":"Geography","level":0,"score":0.4065099060535431},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3169761896133423},{"id":"https://openalex.org/C191935318","wikidata":"https://www.wikidata.org/wiki/Q148","display_name":"China","level":2,"score":0.13866624236106873},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C95190672","wikidata":"https://www.wikidata.org/wiki/Q815382","display_name":"Meta-analysis","level":2,"score":0.0},{"id":"https://openalex.org/C43617362","wikidata":"https://www.wikidata.org/wiki/Q170050","display_name":"Chromatography","level":1,"score":0.0},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/13658816.2024.2391412","is_oa":true,"landing_page_url":"https://doi.org/10.1080/13658816.2024.2391412","pdf_url":null,"source":{"id":"https://openalex.org/S4210181446","display_name":"International Journal of Geographical Information Systems","issn_l":"0269-3798","issn":["0269-3798","1362-3087"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geographical Information Science","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire/0e05d0d6-5b34-4e19-b8ed-ff52564024ea","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/0e05d0d6-5b34-4e19-b8ed-ff52564024ea","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Hu, Y, Harris , R J, Timmerman, R M & Lu, B 2024, 'A backfitting maximum likelihood estimator for hierarchical and geographically weighted regression modelling, with a case study of house prices in Beijing', International Journal of Geographical Information Systems, vol. 38, no. 12, pp. 2458-2491. https://doi.org/10.1080/13658816.2024.2391412","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"doi:10.1080/13658816.2024.2391412","is_oa":true,"landing_page_url":"https://doi.org/10.1080/13658816.2024.2391412","pdf_url":null,"source":{"id":"https://openalex.org/S4210181446","display_name":"International Journal of Geographical Information Systems","issn_l":"0269-3798","issn":["0269-3798","1362-3087"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Geographical Information Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":71,"referenced_works":["https://openalex.org/W1598151839","https://openalex.org/W1599043334","https://openalex.org/W1600727626","https://openalex.org/W1886279074","https://openalex.org/W1910242272","https://openalex.org/W1943341549","https://openalex.org/W1951724000","https://openalex.org/W1973749534","https://openalex.org/W1976840258","https://openalex.org/W1978769039","https://openalex.org/W1980398988","https://openalex.org/W1985949711","https://openalex.org/W1989314352","https://openalex.org/W1989575639","https://openalex.org/W2004524716","https://openalex.org/W2012231377","https://openalex.org/W2015885089","https://openalex.org/W2028226037","https://openalex.org/W2045066934","https://openalex.org/W2045405291","https://openalex.org/W2047120335","https://openalex.org/W2053414100","https://openalex.org/W2055819169","https://openalex.org/W2059757885","https://openalex.org/W2063143131","https://openalex.org/W2063617810","https://openalex.org/W2069167028","https://openalex.org/W2069435832","https://openalex.org/W2071936897","https://openalex.org/W2081283602","https://openalex.org/W2083336903","https://openalex.org/W2084005892","https://openalex.org/W2089743085","https://openalex.org/W2090685952","https://openalex.org/W2109861390","https://openalex.org/W2116199388","https://openalex.org/W2121284273","https://openalex.org/W2147279463","https://openalex.org/W2163493657","https://openalex.org/W2184950388","https://openalex.org/W2261195128","https://openalex.org/W2312602772","https://openalex.org/W2317107098","https://openalex.org/W2388851236","https://openalex.org/W2500845915","https://openalex.org/W2507058334","https://openalex.org/W2526424534","https://openalex.org/W2559688945","https://openalex.org/W2580294918","https://openalex.org/W2599875474","https://openalex.org/W2605661896","https://openalex.org/W2747207142","https://openalex.org/W2901615696","https://openalex.org/W2977350438","https://openalex.org/W2981089230","https://openalex.org/W3005470619","https://openalex.org/W3014404004","https://openalex.org/W3016631355","https://openalex.org/W3020942403","https://openalex.org/W3088180712","https://openalex.org/W3116630953","https://openalex.org/W3152900914","https://openalex.org/W3165442031","https://openalex.org/W3175727668","https://openalex.org/W3216454795","https://openalex.org/W4206962063","https://openalex.org/W4239870817","https://openalex.org/W4313478272","https://openalex.org/W4313582660","https://openalex.org/W4386967839","https://openalex.org/W6634015478"],"related_works":["https://openalex.org/W2276173774","https://openalex.org/W2801157135","https://openalex.org/W1484328682","https://openalex.org/W1590597190","https://openalex.org/W1970241727","https://openalex.org/W2401588063","https://openalex.org/W2183628556","https://openalex.org/W2553612126","https://openalex.org/W53217798","https://openalex.org/W2898956632"],"abstract_inverted_index":{"Geographically":[0],"weighted":[1,85,105],"regression":[2,17,86],"(GWR)":[3],"and":[4,83,102,132,145,166],"its":[5,171],"extensions":[6],"are":[7,139],"important":[8],"local":[9],"modelling":[10,75,177],"techniques":[11],"for":[12,29,179],"exploring":[13],"spatial":[14,23,67,134,165],"heterogeneity":[15,135,168],"in":[16,155],"relationships.":[18],"However,":[19],"when":[20,31],"dealing":[21],"with":[22,63,77,184],"data":[24,62,176,183],"of":[25,46,152,160],"overlapping":[26],"samples":[27],"\u2013":[28,50],"example,":[30],"precise":[32],"locational":[33],"information":[34],"is":[35,125],"aggregated":[36],"to":[37,41,79,114,128,162],"a":[38,81,110,118,146,174],"shared":[39],"neighbourhood":[40],"avoid":[42],"revealing":[43],"the":[44,116,133],"addresses":[45],"individual":[47],"survey":[48],"respondents":[49],"GWR-based":[51],"models":[52],"can":[53],"encounter":[54],"several":[55],"problems,":[56],"including":[57],"obtaining":[58],"reliable":[59],"bandwidths.":[60],"Because":[61],"this":[64],"characteristic":[65],"exhibit":[66],"hierarchical":[68,73,82,186],"structures,":[69],"we":[70],"propose":[71],"combining":[72],"linear":[74],"(HLM)":[76],"GWR":[78,143],"give":[80],"geographically":[84],"(HGWR)":[87],"model":[88],"that":[89,121,123],"divides":[90],"coefficients":[91],"into":[92],"sample-level":[93,99],"fixed":[94,97],"effects,":[95,98,101],"group-level":[96,103,167],"random":[100],"spatially":[104,185],"effects.":[106],"This":[107],"paper":[108],"presents":[109],"back-fitting":[111],"likelihood":[112],"estimator":[113],"fit":[115],"model,":[117],"simulation":[119],"experiment":[120],"suggests":[122,170],"HGWR":[124,161],"better":[126],"able":[127],"capture":[129],"these":[130],"effects":[131],"within":[136],"them":[137],"than":[138],"traditional":[140],"HLM":[141],"or":[142],"models,":[144],"case":[147],"study":[148],"looking":[149],"at":[150],"predictors":[151],"housing":[153],"price":[154],"Beijing,":[156],"China.":[157],"The":[158],"ability":[159],"tackle":[163],"both":[164],"simultaneously":[169],"potential":[172],"as":[173],"promising":[175],"tool":[178],"handling":[180],"spatio-temporal":[181],"big":[182],"structures.":[187]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6}],"updated_date":"2026-06-25T08:15:23.626066","created_date":"2025-10-10T00:00:00"}
