资源描述：
《canonical correlation：典型相关分析》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。
1、CanonicalCorrelationOverviewAcanonicalcorrelationisthecorrelationoftwocanonical(latent)variables,onerepresentingasetofindependentvariables,theotherasetofdependentvariables.Eachsetmaybeconsideredalatentvariablebasedonmeasuredindicatorvariablesinitsset.Thecanonicalcorre
2、lationisoptimizedsuchthatthelinearcorrelationbetweenthetwolatentvariablesismaximized.Whereasmultipleregressionisusedformany-to-onerelationships,canonicalcorrelationisusedformany-to-manyrelationships.Theremaybemorethanonesuchlinearcorrelationrelatingthetwosetsofvariabl
3、es,witheachsuchcorrelationrepresentingadifferentdimensionbywhichtheindependentsetofvariablesisrelatedtothedependentset.Thepurposeofcanonicalcorrelationistoexplaintherelationofthetwosetsofvariables,nottomodeltheindividualvariables.Foreachcanonicalvariatewecanalsoassess
4、howstronglyitisrelatedtomeasuredvariablesinitsownset,orthesetfortheothercanonicalvariate.Wilks'slambdaiscommonlyusedtotestthesignificanceofcanonicalcorrelation.Analogouswithordinarycorrelation,canonicalcorrelationsquaredisthepercentofvarianceinthedependentsetexplained
5、bytheindependentsetofvariablesalongagivendimension(theremaybemorethanone).Inadditiontoaskinghowstrongtherelationshipisbetweentwolatentvariables,canonicalcorrelationisusefulindetermininghowmanydimensionsareneededtoaccountforthatrelationship.Canonicalcorrelationfindsthe
6、linearcombinationofvariablesthatproducesthelargestcorrelationwiththesecondsetofvariables.Thislinearcombination,or"root,"isextractedandtheprocessisrepeatedfortheresidualdata,withtheconstraintthatthesecondlinearcombinationofvariablesmustnotcorrelatewiththefirstone.Thepr
7、ocessisrepeateduntilasuccessivelinearcombinationisnolongersignificant.Canonicalcorrelationisamemberofthemultiplegenerallinearhypothesis(MLGH)familyandsharesmanyoftheassumptionsofmutlipleregressionsuchaslinearityofrelationships,homoscedasticity(samelevelofrelationshipf
8、orthefullrangeofthedata),intervalornear-intervaldata,untruncatedvariables,properspecificationofthemodel,lackofhighmulticolli
