分层回归分析

分层回归分析2007-12-0814:55:16|分类：专业补充|标签：|字号大中小订阅HierarchicalRegressionAnalysisInahierarchicalmultipleregression,theresearcherdecidesnotonlyhowmanypredictorstoenterbutalsotheorderinwhichtheyenter.Usually,theorderofentryisbasedonlogicalortheoreticalconsiderations.Therearethreepredictorvariablesandonecriterionvariableinthefollowingdataset.AresearcherdecidedtheorderofentryisX1,X2,andX3.SPSSforWindows1.EnterData.2.ChooseAnalyze/Regression/Linear.Dependent:SelectyandmoveittotheDependentvariablelist.First,clickonthevariabley.Next,clickontherightarrow.Block1of1Independent(s):Choosethefirstpredictorvariablex1andmoveittotheIndependent(s)box.Next,clicktheNextbuttonasshownbelow.Block2of2Clickthepredictorvariablex2andmoveittotheIndependent(s)box.Next,clicktheNextbuttonasshownbelow.Block3of3Clickthepredictorvariablex3andmoveittotheIndependent(s)box.3.ClicktheStatisticsbutton.CheckRsquaredchange.ClickContinueandOK.SPSSOutput1.RsquareChangeRSquareandRSquareChangeOrderofEntryModel1:EnterX1Model1:Rsquare=.25ThepredictorX1aloneaccountsfor25%ofthevarianceinY.R2=.25Model2:EnterX2next.Model2:Rsquare=.582TheIncreaseinRsquare:.582-.25=.332ThepredictorX2accountsfor33%ofthevarianceinYaftercontrollingforX1.R2=.25+.332=.582ModelThree:EnterX3thirdModel3:Rsquare=.835TheIncreaseinRsquare:.835-.582=.253ThepredictorX3accountsfor25%ofthevarianceinY,afterX1andX2werepartialedoutfromX3.R2=.25+.332+.253=.835About84%ofthevarianceinthecriterionvariablewasexplainedbythefirst(25%),second(33%)andthird(25%)predictorvariables.2.AdjustedRSquareForourexample,thereareonlyfivesubjects.However,therearethreepredictors.RecallthatRsquaremaybeoverestimatedwhenthedatasetshavefewcases(n)relativetonumberofpredictors(k).DatasetswithasmallsamplesizeandalargenumberofpredictorswillhaveagreaterdifferencebetweentheobtainedandadjustedRsquare(.25vs..000,.582vs..165,and.835vs..338).3.FChangeandSig.FChangeIftheRsquarechangeassociatedwithapredictorvariableinquestionislarge,itmeansthatthepredictorvariableisagoodpredictorofthecriterionvariable.Inthefirststep,enterthepredictorvariablex1first.ThisresultedinanRsquareof.25,whichwasnotstatisticallysignificant(FChange=1.00,p.05).Inthesecondstep,weaddx2.ThisincreasedtheRsquareby33%,whichwasnotstatisticallysignificant(FChange=1.592,p.05).Inthethirdstep,weaddx3.ThisincreasedtheRsquarebyanadditional25%,whichwasnotstatisticallysignificant(FChange=1.592,p.05).4.ANOVATableModel1:About25%(2.5/10=.25)ofthevarianceinthecriterionvariable(Y)canbeaccountedforbyX1.Thefirstmodel,whichincludesonepredictorvariable(X1),resultedinanFratioof1.000withap.05.Model2About58%(5.82/10=.58)ofthevarianceinthecriterionvariable(Y)canbeaccountedforbyX1andX2.Thesecondmodel,whichincludestwopredictors(X1andX2),resultedinanFratioof1.395withap.05.Model3:About84%(8.346/10=.84)ofthevarianceinthecriterionvariable(Y)canbeaccountedforbyallthreepredictors(X1,X2andX3).Thethirdmodel,whichincludesallthreepredictors,resultedinanFratioof1.681withap.05.wherekisthenumberofpredictorvariablesandNisthesamplesize.