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基于多维名义模型的加权似然估计方法(英文).docx

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基于多维名义模型的加权似然估计方法(英文) Introduction: Multi-dimensionalnominalmodelshavebeenwidelyusedinvariousfieldsofresearch,suchassocialsciences,psychology,economics,andmarketing.Thesemodelsaimtoestimatetherelationshipbetweennominalvariablesbytakingintoaccountvariousdimensionsorattributesofthevariables.Inthispaper,wewilldiscusstheweightedlikelihoodestimationmethodformulti-dimensionalnominalmodels,whichiswidelyusedinstatisticalanalysis. Multi-dimensionalNominalModels: Multi-dimensionalnominalmodelsareusedwhenthereisaneedtoanalyzetheassociationbetweennominalvariables.Thesemodelsinvolvetwoormorenominalvariablesthathaveoneormoreattributesordimensions.Forinstance,inasurvey,wemayaskrespondentstoratevariousbrandsofacoffeebasedonattributessuchasaroma,taste,packaging,andprice.Insuchacase,themulti-dimensionalnominalmodelwouldallowustoanalyzetherelationshipbetweenthebrandofcoffeeandtheseattributes. Thevariablesinamulti-dimensionalnominalmodelarerepresentedbycontingencytables.Thesetablesshowthedistributionofthevariablesacrossthedimensions.Forexample,inthecaseofthecoffeesurvey,thecontingencytablewouldshowthenumberofrespondentswhoratedeachbrandofcoffeebasedoneachoftheattributes. WeightedLikelihoodEstimation: Weightedlikelihoodestimationisapopularmethodusedtoestimatetheparametersofmulti-dimensionalnominalmodels.Themethodinvolvesassigningweightstotheobservationsinthecontingencytablebasedontheirfrequency.Themorefrequentlyanobservationoccurs,thehighertheweightassignedtoit. Theweightedlikelihoodestimationmethodprovidesanefficientwaytoestimatetheparametersofthemodel.Thismethodtakesintoaccounttheweightoftheobservations,whichincreasestheaccuracyoftheestimation.Themethodalsoaccountsfortheuncertaintyintheestimation,whichmakesitmorereliable. Applications: Theweightedlikelihoodestimationmethodformulti-dimensionalnominalmodelshasseveralapplicationsinstatisticalanalysis.Oneapplicationisinthefieldofmarketingresearch.Marketersoftenusemulti-dimensionalnominalmodelstoanalyzeconsumerpreferencesforproducts.Byusin