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1、Chapter9GroupDifferencesinGeneralizedLinearModelsTimF.LiaoAbstractThischapterdealswithmakingcomparisonsbetweenÞxedgroupsintheframeworkofgeneralizedlinearmodels.First,webrießyintroducegeneralizedlinearmodels,themostcommontypeofregressionmodels.Next,wediscus
2、sasimplesystemforanalyzinggroupdifferencesinregression.WeprimarilyfocusontwotypesofcomparisonsÑanalyzingdifferencesintheparametervectorsofthelinearpredictoranddifferencesintheunderlyingdistributionsforthegroupsinthemodel.Toillustratesuchcomparativemethodsf
3、orgroupdifferences,weperformanalysesusingreal-worlddata.Theoretically,groupdifferencesinregressionestimatescanbeviewedasanexampleofconditionalcausality.Practically,testinggroupdifferencesinregressionmayseemanyusefulapplicationsinsocialscienceresearch.Intro
4、ductionThischapterdealswiththetopicofmakinggroupcomparisonsinregressionanalysis.ByÒgroupcom-parisons,ÓwemeanexaminingthedifferencesincertainstatisticalpropertiesbetweenÞxedgroups.ÒRegressionanalysisÓreferstoanalysisapplyinganymemberofthefamilyofstatistical
5、modelsknownasgeneralizedlinearmodelsortheirextensions.Forcomparingunderlyingdistributions,theframeworkofgeneralizedlinearmodelsisconvenientbecausecertainmodelsmayassumedifferentstatisticaldistributions.Makingpropercomparisonsisfundamentallyimportantincondu
6、ctingempiricalsociologicalresearch,becauseÒvirtuallyalltheorieswithempiricalramiÞcationsimplysomeformoranotherofcomparisonÓ(Lieberson1985:45).ThischapterpresentsasystematicmethodformakingcomparisonsbetweenÞxedgroupsintheregressionsetting,followingtheprinci
7、plesforsuchpurposesinLiao(2002).Wedo,however,gobeyondtheearliertreatmentbyexaminingmorecloselydistributionaldifferencesbetweengroupsandbetweenlinkfunctionsaswellaseffectsdecompositioninthesystematiccomponent.Mostoften,dataanalystsseektocompareparametersacr
8、ossÞxedsocialgroupssuchasgender,race,andnationalitybytestingtheirhypothesizedequality.This,however,representsonlyone,albeitarguablythemostcommon,typeofcomparison.Inaddition,onemaybeinterestedincomparingacross
