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Poisson-Lindley回归模型基于EM算法的诊断分析(英文).docx

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Poisson-Lindley回归模型基于EM算法的诊断分析(英文) Title:DiagnosticAnalysisofPoisson-LindleyRegressionModelbasedonEMAlgorithm Abstract: ThePoisson-Lindleyregressionmodelisanimportantstatisticaltoolusedinvariousfieldsformodelingcountdatawithover-dispersion.TheEM(Expectation-Maximization)algorithmiscommonlyemployedforestimatingtheparametersofthismodel.However,accuratediagnosisofthemodel'sgoodness-of-fitandtheidentificationofpotentialinfluentialoutliersarecrucialforensuringreliableinference.Inthispaper,weexplorethediagnosticanalysisofthePoisson-LindleyregressionmodelbasedontheEMalgorithm. 1.Introduction: Countdataoftenexhibitover-dispersion,meaningthatthevarianceislargerthanthemean,violatingtheassumptionsoftheclassicalPoissonregressionmodel.ThePoisson-Lindleyregressionmodelisaflexiblealternativethatincorporatesanadditionalcomponenttoaccountforover-dispersion.TheEMalgorithmiswidelyusedforparameterestimationinthismodel.However,itisimportanttoassessthemodel'sadequacyandidentifyinfluentialoutliersbeforedrawinganyconclusionsfromtheanalysis. 2.ThePoisson-LindleyRegressionModel: ThePoisson-LindleyregressionmodelisdefinedbyincorporatingaLindleycomponentwithameanparameterintothePoissonmodel.Itcanbewrittenasatwo-partmodel,wherethefirstpartmodelstheprobabilityofobservingazerocount,andthesecondpartmodelsthecountdistributionofpositiveobservations.TheEMalgorithmisusedtoestimatetheparametersofthismodelbyiterativelymaximizingthelikelihoodfunction. 3.DiagnosticAnalysis: 3.1.Goodness-of-fitTest: ToassesstheadequacyofthePoisson-Lindleyregressionmodel,variousgoodness-of-fittestscanbeemployed.ThemostcommonlyusedtestsincludethePearsonchi-squaretest,thedeviancetest,andthelikelihoodratiotest.Thesetestscomparetheobservedandexpectedcountstoevaluateifthemodelfitsthedatawell. 3.2.ResidualAnalysis: Residualanalysisisapowerfultoolfordetectingpotentialoutliersandassessingthemodel'sassumptions.Differenttypesofresidualscanbecalculated,suchasPearsonresiduals,devianceresiduals,andstandardizedresiduals.Theseresidualsare