{"id":"https://openalex.org/W2009444695","doi":"https://doi.org/10.3390/e10040776","title":"Generalized Measure of Departure from No Three-Factor Interaction Model for 2 x 2 x K Contingency Tables","display_name":"Generalized Measure of Departure from No Three-Factor Interaction Model for 2 x 2 x K Contingency Tables","publication_year":2008,"publication_date":"2008-12-21","ids":{"openalex":"https://openalex.org/W2009444695","doi":"https://doi.org/10.3390/e10040776","mag":"2009444695"},"language":"en","primary_location":{"id":"doi:10.3390/e10040776","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e10040776","pdf_url":"https://www.mdpi.com/1099-4300/10/4/776/pdf?version=1424784660","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1099-4300/10/4/776/pdf?version=1424784660","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101628756","display_name":"Kouji Yamamoto","orcid":"https://orcid.org/0000-0003-0696-9659"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kouji Yamamoto","raw_affiliation_strings":["Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040938244","display_name":"Yohei Ban","orcid":null},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Yohei Ban","raw_affiliation_strings":["Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan","institution_ids":["https://openalex.org/I161296585"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5049149402","display_name":"Sadao Tomizawa","orcid":"https://orcid.org/0000-0002-2819-827X"},"institutions":[{"id":"https://openalex.org/I161296585","display_name":"Tokyo University of Science","ror":"https://ror.org/05sj3n476","country_code":"JP","type":"education","lineage":["https://openalex.org/I161296585"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Sadao Tomizawa","raw_affiliation_strings":["Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Sciences, Faculty of Science and Technology, Tokyo University of Science, Noda City, Chiba, 278-8510, Japan","institution_ids":["https://openalex.org/I161296585"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5049149402"],"corresponding_institution_ids":["https://openalex.org/I161296585"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3094,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63050146,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"10","issue":"4","first_page":"776","last_page":"785"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10845","display_name":"Advanced Causal Inference Techniques","score":0.9674000144004822,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10845","display_name":"Advanced Causal Inference Techniques","score":0.9674000144004822,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11303","display_name":"Bayesian Modeling and Causal Inference","score":0.9649999737739563,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10410","display_name":"COVID-19 epidemiological studies","score":0.9455999732017517,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/contingency-table","display_name":"Contingency table","score":0.8646924495697021},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.8426765203475952},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6276938319206238},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.5611575245857239},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5603255033493042},{"id":"https://openalex.org/keywords/log-linear-model","display_name":"Log-linear model","score":0.44140705466270447},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.4354178309440613},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3837010860443115},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3589029908180237},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3564258813858032},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3362997770309448},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27158981561660767},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20188406109809875},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.18115991353988647},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.14181944727897644},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10388562083244324}],"concepts":[{"id":"https://openalex.org/C91998498","wikidata":"https://www.wikidata.org/wiki/Q1541178","display_name":"Contingency table","level":2,"score":0.8646924495697021},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.8426765203475952},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6276938319206238},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5611575245857239},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5603255033493042},{"id":"https://openalex.org/C70519679","wikidata":"https://www.wikidata.org/wiki/Q6666755","display_name":"Log-linear model","level":3,"score":0.44140705466270447},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.4354178309440613},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3837010860443115},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3589029908180237},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3564258813858032},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3362997770309448},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27158981561660767},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20188406109809875},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.18115991353988647},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.14181944727897644},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10388562083244324},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/e10040776","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e10040776","pdf_url":"https://www.mdpi.com/1099-4300/10/4/776/pdf?version=1424784660","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:07cd438ccf4f430292495eb695d5fdde","is_oa":true,"landing_page_url":"https://doaj.org/article/07cd438ccf4f430292495eb695d5fdde","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy, Vol 10, Iss 4, Pp 776-785 (2008)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/1099-4300/10/4/776/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/e10040776","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Entropy","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/e10040776","is_oa":true,"landing_page_url":"https://doi.org/10.3390/e10040776","pdf_url":"https://www.mdpi.com/1099-4300/10/4/776/pdf?version=1424784660","source":{"id":"https://openalex.org/S195231649","display_name":"Entropy","issn_l":"1099-4300","issn":["1099-4300"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Entropy","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2009444695.pdf","grobid_xml":"https://content.openalex.org/works/W2009444695.grobid-xml"},"referenced_works_count":7,"referenced_works":["https://openalex.org/W1493790738","https://openalex.org/W1516900628","https://openalex.org/W1988625484","https://openalex.org/W2074673068","https://openalex.org/W2081985429","https://openalex.org/W2135157209","https://openalex.org/W4294841944"],"related_works":["https://openalex.org/W1535388096","https://openalex.org/W1587989507","https://openalex.org/W2568690444","https://openalex.org/W2386609324","https://openalex.org/W1493790738","https://openalex.org/W2089046099","https://openalex.org/W2119308551","https://openalex.org/W2358237009","https://openalex.org/W79940031","https://openalex.org/W4212958385"],"abstract_inverted_index":{"For":[0],"2":[1,3,41,43],"x":[2,4,42,44],"K":[5,45],"contingency":[6],"tables,":[7],"Tomizawa":[8],"considered":[9],"a":[10,22,35],"Shannon":[11],"entropy":[12],"type":[13],"measure":[14,39,48,66,72],"to":[15],"represent":[16],"the":[17,64,78,83],"degree":[18],"of":[19,25,37,63,80],"departure":[20,81],"from":[21,82],"log-linear":[23],"model":[24,85],"no":[26],"three-factor":[27],"interaction":[28],"(the":[29],"NOTFI":[30,84],"model).":[31],"This":[32],"paper":[33],"proposes":[34],"generalization":[36],"Tomizawa's":[38,68],"for":[40,76],"tables.":[46,88],"The":[47,70],"proposed":[49,65,71],"is":[50],"expressed":[51],"by":[52],"using":[53],"Patil-Taillie":[54],"diversity":[55],"index":[56],"or":[57],"Cressie-Read":[58],"power-divergence.":[59],"A":[60],"special":[61],"case":[62],"includes":[67],"measure.":[69],"would":[73],"be":[74],"useful":[75],"comparing":[77],"degrees":[79],"in":[86],"several":[87]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
