{"id":"https://openalex.org/W2053818243","doi":"https://doi.org/10.1901/jeab.1989.52-65","title":"THE EFFECT OF LOGARITHMIC TRANSFORMATION ON ESTIMATING THE PARAMETERS OF THE GENERALIZED MATCHING LAW","display_name":"THE EFFECT OF LOGARITHMIC TRANSFORMATION ON ESTIMATING THE PARAMETERS OF THE GENERALIZED MATCHING LAW","publication_year":1989,"publication_date":"1989-07-01","ids":{"openalex":"https://openalex.org/W2053818243","doi":"https://doi.org/10.1901/jeab.1989.52-65","mag":"2053818243","pmid":"https://pubmed.ncbi.nlm.nih.gov/16812591","pmcid":"https://www.ncbi.nlm.nih.gov/pmc/articles/1338945"},"language":"en","primary_location":{"id":"doi:10.1901/jeab.1989.52-65","doi":"https://doi.org/10.1901/jeab.1989.52-65","is_oa":true,"landing_page_url":"https://doi.org/10.1901/jeab.1989.52-65","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1901/jeab.1989.52-65","source":{"id":"https://openalex.org/S168850678","display_name":"Journal of the Experimental Analysis of Behavior","issn_l":"0022-5002","issn":["0022-5002","1938-3711"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","erih-plus","jufo-1","medline","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Experimental Analysis of Behavior","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1901/jeab.1989.52-65","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015014560","display_name":"C. Donald Heth","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"C. Donald Heth","raw_affiliation_strings":["University of Alberta Edmonton"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta Edmonton","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047693364","display_name":"W. David Pierce","orcid":"https://orcid.org/0000-0001-9396-8763","observed_orcids":["https://orcid.org/0000-0001-9396-8763"]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"W. David Pierce","raw_affiliation_strings":["University of Alberta Edmonton"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta Edmonton","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089907107","display_name":"Terry W. Belke","orcid":"https://orcid.org/0000-0002-3430-6695","observed_orcids":["https://orcid.org/0000-0002-3430-6695"]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Terry W. Belke","raw_affiliation_strings":["University of Alberta Edmonton"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta Edmonton","institution_ids":["https://openalex.org/I154425047"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5034580414","display_name":"S. A. Hensch","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I154425047","display_name":"University of Alberta","ror":"https://ror.org/0160cpw27","country_code":"CA","type":"education","lineage":["https://openalex.org/I154425047"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"S. A. Hensch","raw_affiliation_strings":["University of Alberta Edmonton"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Alberta Edmonton","institution_ids":["https://openalex.org/I154425047"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015014560"],"corresponding_institution_ids":["https://openalex.org/I154425047"],"apc_list":{"value":3150,"currency":"USD","value_usd":3150},"apc_paid":null,"fwci":17.6817,"has_fulltext":true,"cited_by_count":38,"citation_normalized_percentile":{"value":0.99301459,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":94},"biblio":{"volume":"52","issue":"1","first_page":"65","last_page":"76"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10826","display_name":"Behavioral and Psychological Studies","score":0.6064000129699707,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10826","display_name":"Behavioral and Psychological Studies","score":0.6064000129699707,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10315","display_name":"Decision-Making and Behavioral Economics","score":0.22550000250339508,"subfield":{"id":"https://openalex.org/subfields/1800","display_name":"General Decision Sciences"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10467","display_name":"Psychometric Methodologies and Testing","score":0.03799999877810478,"subfield":{"id":"https://openalex.org/subfields/1803","display_name":"Management Science and Operations Research"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalized-matching-law","display_name":"generalized matching law","score":0.996999979019165},{"id":"https://openalex.org/keywords/logarithmic-transformation","display_name":"logarithmic transformation","score":0.949999988079071},{"id":"https://openalex.org/keywords/parameter-estimation-bias","display_name":"parameter estimation bias","score":0.8330000042915344},{"id":"https://openalex.org/keywords/least-squares-regression","display_name":"least squares regression","score":0.8050000071525574},{"id":"https://openalex.org/keywords/goodness-of-fit","display_name":"goodness of fit","score":0.902999997138977},{"id":"https://openalex.org/keywords/prediction-accuracy","display_name":"prediction accuracy","score":0.6349999904632568},{"id":"https://openalex.org/keywords/monte-carlo-simulation","display_name":"Monte Carlo simulation","score":0.5170000195503235}],"concepts":[{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.7501463294029236},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6594666242599487},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5823291540145874},{"id":"https://openalex.org/C45923927","wikidata":"https://www.wikidata.org/wiki/Q3319230","display_name":"Non-linear least squares","level":3,"score":0.5469581484794617},{"id":"https://openalex.org/C46889948","wikidata":"https://www.wikidata.org/wiki/Q2755024","display_name":"Nonlinear regression","level":3,"score":0.5371765494346619},{"id":"https://openalex.org/C132480984","wikidata":"https://www.wikidata.org/wiki/Q2034239","display_name":"Goodness of fit","level":2,"score":0.529047429561615},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5073818564414978},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.46550968289375305},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4518522620201111},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4483366310596466},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4280087947845459},{"id":"https://openalex.org/C152877465","wikidata":"https://www.wikidata.org/wiki/Q208042","display_name":"Regression analysis","level":2,"score":0.4197050929069519},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3710242509841919},{"id":"https://openalex.org/C49847556","wikidata":"https://www.wikidata.org/wiki/Q3964631","display_name":"Explained sum of squares","level":2,"score":0.25346237421035767},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1151873767375946},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1901/jeab.1989.52-65","doi":"https://doi.org/10.1901/jeab.1989.52-65","is_oa":true,"landing_page_url":"https://doi.org/10.1901/jeab.1989.52-65","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1901/jeab.1989.52-65","source":{"id":"https://openalex.org/S168850678","display_name":"Journal of the Experimental Analysis of Behavior","issn_l":"0022-5002","issn":["0022-5002","1938-3711"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","erih-plus","jufo-1","medline","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Experimental Analysis of Behavior","raw_type":"journal-article"},{"id":"pmh:oai:pubmedcentral.nih.gov:1338945","doi":null,"is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/1338945","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"J Exp Anal Behav","raw_type":"Text"},{"id":"pmid:16812591","doi":null,"is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/16812591","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the experimental analysis of behavior","raw_type":"Journal Article"}],"best_oa_location":{"id":"doi:10.1901/jeab.1989.52-65","doi":"https://doi.org/10.1901/jeab.1989.52-65","is_oa":true,"landing_page_url":"https://doi.org/10.1901/jeab.1989.52-65","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1901/jeab.1989.52-65","source":{"id":"https://openalex.org/S168850678","display_name":"Journal of the Experimental Analysis of Behavior","issn_l":"0022-5002","issn":["0022-5002","1938-3711"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","erih-plus","jufo-1","medline","norway-2","poland-100","russia-white-list-2","vabb-shw"],"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of the Experimental Analysis of Behavior","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2053818243.pdf","grobid_xml":"https://content.openalex.org/works/W2053818243.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W248108529","https://openalex.org/W279210805","https://openalex.org/W1989325827","https://openalex.org/W1989835373","https://openalex.org/W2036320532","https://openalex.org/W2057327562","https://openalex.org/W2062896473","https://openalex.org/W2064235439","https://openalex.org/W2072181866","https://openalex.org/W2074072839","https://openalex.org/W2074647637","https://openalex.org/W2082367324","https://openalex.org/W2082430497","https://openalex.org/W2082461441","https://openalex.org/W2093910548","https://openalex.org/W2105859139","https://openalex.org/W2106286455","https://openalex.org/W2325850497","https://openalex.org/W2797588280","https://openalex.org/W4233914190","https://openalex.org/W4236679173"],"related_works":["https://openalex.org/W4239602792","https://openalex.org/W2057609489","https://openalex.org/W1547508602","https://openalex.org/W4322721541","https://openalex.org/W2072181866","https://openalex.org/W2312752958","https://openalex.org/W2112157501","https://openalex.org/W1990753066","https://openalex.org/W4399347687","https://openalex.org/W7026701513"],"abstract_inverted_index":{"The":[0],"generalized":[1,100],"matching":[2,47,101],"law":[3,22,48,56,102],"was":[4],"initially":[5],"stated":[6],"as":[7],"a":[8,50,71],"nonlinear":[9],"relation":[10],"between":[11],"reinforcement-rate":[12],"ratios":[13],"and":[14,115],"response-rate":[15],"ratios.":[16],"Often,":[17],"the":[18,21,28,36,42,46,55,60,64,80,89,96,99,106,120],"variables":[19],"of":[20,45,54,79,82,91,95,98,108,110],"are":[23,32,103,123,130],"transformed":[24],"logarithmically":[25],"to":[26,35,67,127,132],"remove":[27],"nonlinearity;":[29],"empirical":[30],"results":[31],"then":[33],"fit":[34,111],"model":[37],"through":[38],"least-squares":[39,72],"regression.":[40],"However,":[41],"logarithmic":[43,61,128],"expression":[44],"is":[49,113],"biased":[51],"statistical":[52],"representation":[53],"itself.":[57],"In":[58],"particular,":[59],"transformation":[62],"alters":[63],"quantitative":[65],"conclusions":[66],"be":[68],"drawn":[69],"from":[70],"regression":[73],"analysis.":[74],"A":[75],"Monte":[76],"Carlo":[77],"study":[78],"effect":[81],"transforming":[83],"matching-law":[84],"data":[85],"demonstrated":[86],"that":[87],"(a)":[88],"estimates":[90],"one":[92],"or":[93],"both":[94],"parameters":[97,122],"biased,":[104],"(b)":[105],"measure":[107],"goodness":[109],"(R(2))":[112],"inaccurate,":[114],"(c)":[116],"predictions":[117],"generated":[118],"by":[119],"fitted":[121],"incorrect.":[124],"Alternative":[125],"approaches":[126],"transformations":[129],"shown":[131],"alleviate":[133],"these":[134],"problems.":[135]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-10-30T12:39:25.321706","created_date":"2016-06-24T00:00:00"}