StephenParry

FitStatisticscommonlyreportedforCFAandSEMTherearemorethanadozendifferentfitstatisticsresearchersusetoassesstheirconfirmatoryfactoranalysesandstructuralequationmodels.Herewehaveassembledalistofthemostpopularfitstatisticsusedandrecommendedcut-offsthatindicateagoodfit.Measure Name Description Cut-offfor

goodfitΧ2 ModelChi-

SquareAssessoverallfitandthediscrepancybetweenthesampleandfittedcovariancematrices.Sensitivetosamplesize.H0:Themodelfitsperfectly.

p-value>0.05

(A)GFI (Adjusted)GoodnessofFit

GFIistheproportionofvarianceaccountedforbytheestimatedpopulationcovariance.AnalogoustoR2.AGFIfavorsparsimony.

GFI≥0.95AGFI≥0.90

(N)NFITLI

(Non)Normed-FitIndexTuckerLewisindex

AnNFIof.95,indicatesthemodelofinterestimprovesthefitby95%relativetothenullmodel.NNFIispreferableforsmallersamples.SometimestheNNFIiscalledtheTuckerLewisindex(TLI)

NFI≥0.95NNFI≥0.95

CFI ComparativeFitIndex

ArevisedformofNFI.Notverysensitivetosamplesize.Comparesthefitofatargetmodeltothefitofanindependent,ornull,model.

CFI≥.90

RMSEA RootMeanSquareErrorofApproximation

Aparsimony-adjustedindex.Valuescloserto0representagoodfit.

RMSEA<0.08

(S)RMR (Standardized)RootMeanSquareResidual

Thesquare-rootofthedifferencebetweentheresidualsofthesamplecovariancematrixandthehypothesizedmodel.Ifitemsvaryinrange(i.e.someitemsare1-5,others1-7)thenRMRishardtointerpret,bettertouseSRMR.

SRMR<0.08

AVE(CFAonly)

AverageValueExplained

TheaverageoftheR2sforitemswithinafactor

AVE>.5

StephenParry

Klinesuggeststhatataminimumthefollowingindicesshouldbereported:1) Themodelchi-square2) RMSEA3) CFI4) SRMR

Howtoestimatethesefitindices:

• InR,usetheFitMeasuresfunctionfromthelavaanpackage.• InSAS’sProcCalis,specifythefitindexoptionwiththeparticularindicesyouwant.• InStata,afterexecutingaCFAorSEM,usethecommand:estatgof,stats(all)

References:PrinciplesandPracticeofStructuralEquationModeling.RexB.Kline.2005.StructuralEquationModelling:GuidelinesforDeterminingModelFit.DaireHooper,etal.2008.