the r book mixedeffects models

《the r book mixedeffects models》由会员上传分享，免费在线阅读，更多相关内容在工程资料-天天文库。

1、19Mixed-EffectsModelsUptothispoint,wehavetreatedallcategoricalexplanatoryvariablesasiftheywerethesame.ThisiscertainlywhatR.A.Fisherhadinmindwhenheinventedtheanalysisofvarianceinthe1920sand1930s.ItwasEisenhart(1947)whorealizedthattherewereactuallytwofundamentallydifferentsortsofcategoricalexplan

2、atoryvariables:hecalledthesefixedeffectsandrandomeffects.Itwilltakeagooddealofpracticebeforeyouareconfidentindecidingwhetheraparticularcategoricalexplanatoryvariableshouldbetreatedasafixedeffectorarandomeffect,butinessence:
fixedeffectsinfluenceonlythemeanofy;
randomeffectsinfluenceonlythevarianceofy

3、.Fixedeffectsareunknownconstantstobeestimatedfromthedata.Randomeffectsgovernthevariance–covariancestructureoftheresponsevariable(seep.519).Nesting(orhierarchicalstructure)ofrandomeffectsisaclassicsourceofpseudoreplication,soitimportantthatyouareabletorecognizeitandhencenotfallintoitstrap.Random

4、effectsthatcomefromthesamegroupwillbecorrelated,andthiscontravenesoneofthefundamentalassumptionsofstandardstatisticalmodels:independenceoferrors.Randomeffectsoccurintwocontrastingkindsofcircumstances:
observationalstudieswithhierarchicalstructure;
designedexperimentswithdifferentspatialortempor

5、alscales.Fixedeffectshaveinformativefactorlevels,whilerandomeffectsoftenhaveuninformativefactorlevels.Thedistinctionisbestseenbyanexample.Inmostmammalspeciesthecategoricalvariablesexhastwolevels:maleandfemale.Foranyindividualthatyoufind,theknowledgethatitis,say,femaleconveysagreatdealofinformati

6、onabouttheindividual,andthisinformationdrawsonexperiencegleanedfrommanyotherindividualsthatwerefemale.Afemalewillhaveawholesetofattributes(associatedwithherbeingfemale)nomatterwhatpopulationthatindividualwasdrawnfrom.Takeadifferentcategoricalvariablelikegenotype.Ifwehavetwogenotypesinapopulatio

7、nwemightlabelthemAandB.IfwetaketwomoregenotypesfromadifferentpopulationwemightlabelthemAandBaswell.Inacaselikethis,thelabelAdoesnotconveyanyinformationatallaboutthegenotype,otherthanthatitisprobablydifferentfromgenotypeB.Inthecase