资源描述：
《maximum likelihood in concept and practice在理念和实践的最大似然》由会员上传分享，免费在线阅读，更多相关内容在应用文档-天天文库。
1、MaximumLikelihoodinConceptandPractice(cribbedmostlyfromGaryKing’sUnifyingPoliticalMethodology)Tuesday,September28:TheGoalsandFoundationsofMaximumLikelihoodI.DefinitionsandNotationII.TheLinearModelinaGeneralFormIII.WhyInverseProbabilityDoesn’tWorkIV.WhytheLikelihood
2、ModelofInferenceWorksI.DefinitionsandNotationA.DevelopedbystatisticianR.A.Fisherinthe1920s,borrowedfirstbyeconomists,andfinallyimportedintopoliticalscience,maximumlikelihoodprovidesafundamentalrationaleforusingappropriateestimatorsandgivesuslotsofflexibilitytomatch
3、ourstatisticalmodelstotheprocessthatwethinkgeneratedourdata.Thereareanumberoroverarchingapproachesdesignedtounifystatisticalmethodologies,butthisisbyfarthemostfamiliartopoliticalscientists.Itrequiresyoutomakeexplicitchoicesabouthowyouthinkyourdependentvariableisdis
4、tributed(themodel’sstochasticcomponent)andwhattherelationshipisbetweenyourindependentanddependentvariables(themodel’ssystematiccomponent).Then,basedonsomebasicrulesofprobability,itteachesyouhowtowriteoutalikelihoodfunctionandfindthesetofparametersmostlikelytohavege
5、neratedobserveddata,givenyourassumedmodel.Beforewelearnthestep-by-stepprocessofgettingmaximumlikelihoodestimate,weneedtolearnabitofnotation.B.LetYibea“randomvariable.”Itisrandominthatthereisstochasticvariationinitacrossmanyexperimentsforasingleobservation,andavaria
6、bleinthatitvariesacrossobservationsinasingleexperiment.Letyibeonedrawfromtherandomvariable.Letxibeonedraw(consistingofoneormoreexplanatoryfactors)fromthesocialsystemX.C.HypothesizesomemodelMabouthowthesocialsystemproducestherandomvariable.Wecanpartitionthismodelint
7、oM,thepartofthemodelthatwewillassume,andθ,thepartofthemodelcomposedofparametersthatwewillestimate.Afully“restrictive”modelhasallofitsassumptionsspecified(itisallMandnoθ);itisthemostparsimoniousmodelandomitsallofthevariables.An“unrestrictive”modelestimateseverything
8、,isallθandnoM,andismoreinterestingbutdemandsmorefromthedata.Inhypothesistesting,wewilloftencompareafairlyunrestrictivemodeltoaslightlymorerestric
