How is the g-factor of intelligence calculated?

PCA or EFA: A standard approach to calculating a g factor would be to use principal components analysis (PCA) or exploratory factor analysis ... Psychology&NeuroscienceStackExchangeisaquestionandanswersiteforpractitioners,researchers,andstudentsincognitivescience,psychology,neuroscience,andpsychiatry.Itonlytakesaminutetosignup. Signuptojointhiscommunity Anybodycanaskaquestion Anybodycananswer Thebestanswersarevotedupandrisetothetop Home Public Questions Tags Users Unanswered Teams StackOverflowforTeams –Startcollaboratingandsharingorganizationalknowledge. CreateafreeTeam WhyTeams? Teams CreatefreeTeam Teams Q&Aforwork Connectandshareknowledgewithinasinglelocationthatisstructuredandeasytosearch. LearnmoreaboutTeams Howistheg-factorofintelligencecalculated? AskQuestion Asked 4years,4monthsago Modified 4years,4monthsago Viewed 4ktimes 8 1 $\begingroup$ IamcurrentlyreadingDr.RichardHaier'sbookTheNeuroscienceofIntelligenceandIamalittleconfusedabouttheg-factor.NotethatIhavenoeducationinpsychologyoutsideofgeneraledcoursesatuniversity. Ihavetwoquestionsregardingtheg-factor.Whatconfusesmeisforone,hedoesnotgointotechnicaldetailabouthowtheg-factoriscalculated. Hedoesincludethisillustration: Hereweseethat15mentaltestsaretakeningroupsof3,whereeachgroupiscorrelatedtoacertainfactor.Sotests1-3areforreasoning,4-6forspatialability,andsoon.Thesefactorsthencorrelatetotheg-factor. Iamwonderingwhatisthemethodologyusedtofindthecorrelationsbetweenthetestsandfactors/factorsandtheg-factor?Forexample,Idon'tquiteunderstandhowtheymeasurethecorrelationbetweenthetestandthefactorgiventhatthefactorisabstract(ie.reasoning).IhopewhatIamaskingmakessense.IamnotaskinghowtoperformlinearregressionorcalculatePearson'sr. Mysecondquestionisaboutthestatementinthebook: "Differentmentalabilitiesarenotindependent.Theyareallrelatedtoeachotherandthecorrelationsamongmentaltestsarealwayspositive....Itstronglyimpliesthatallthefactorsderivedfromindividualtestshavesomethingincommon,andthiscommonfactoriscalledthegeneralfactorofintelligence." Wouldn'tthisimplythatallofthefactorsaremulticollinearandmakeitdifficulttodistinguishwhichfactorsaremostsignificant? neuroscienceintelligencecorrelation Share Improvethisquestion Follow editedApr12,2018at7:47 JeromyAnglim 30.4k1111goldbadges8989silverbadges218218bronzebadges askedApr12,2018at6:47 thevengefulcothevengefulco 22722silverbadges55bronzebadges $\endgroup$ 1 $\begingroup$ Ifinditconfusingthat"g"and"g-factor"areusedinterchangeablyintheliteraturetorefertosharedvariance(avaluebetwen0-1),ortowhatIQteststrytomeasure(averaging100withastandarddeviationof15).Ibelievetheversionof"g"askedabouthereismorepreciselyreferredtoas"psychometricg"or"Spearman'sg". $\endgroup$ – ArnonWeinberg ♦ Oct12,2021at17:41 Addacomment  |  1Answer 1 Sortedby: Resettodefault Highestscore(default) Datemodified(newestfirst) Datecreated(oldestfirst) 7 $\begingroup$ PCAorEFA:Astandardapproachtocalculatingagfactorwouldbetouseprincipalcomponentsanalysis(PCA)orexploratoryfactoranalysis(EFA).Basically,youadministerabroadbatteryofcognitiveabilitymeasures.ThenyouusethesetestsasvariablesinaPCAorEFA.Thiswillpartitionthevarianceinthetestsintoasetofuncorrelatedfactors.Thefirstfactorwillbethefactorthatexplainsthemostvarianceinthetests.Itisthisfirstfactorthatrepresents"g".Typically,eachtestwill"load"(orcorrelate)withthisfirstfactor,sometestsmorethanothers.Thefirstfactorwillcapturesomethingthatiscommonacrossmostorallofthetests.I.e.,itisg,forgeneralfactor,thatmeasurescognitiveability. Anempiricalfindingisthatalmostalltestsofspecificcognitiveabilitiescorrelatewiththegeneralfactor.Andtypically,theloadingsarefairlysubstantial.I.e.,thefirstfactorisquitesubstantialrelativetosecondandsubsequentfactors. Confirmatoryfactoranalysis:Itseemsthatwhatyoupresentisaconfirmatoryfactoranalysis.Thisisavariantonexploratoryfactoranalysis.Basically,youspecifywhichobservedvariablesloadonlatentfactorsandallotherpossibleloadingsareconstrainedtozero.Morespecifically,thisisahigher-orderconfirmatoryfactoranalysis(CFA).Itishigher-orderbecause,therearetwo-levelsoflatentfactors.I.e.,testsloadondomain-specificlatentfactors(e.g.,reasoning,spatialability),andthesedomainspecificlatentfactorsloadong. TheCFAestimationprocedureswillfindtheparameterestimatesthatbestmodelthedata(i.e.,thecovariance/correlationstructureofthetests). Sointhiscase,weseethatallthetestsloadfairlywellontheirdomains(i.e.,>.70)andallthedomainsloadong(>.65),althoughreasoningandspatialabilityloadalittlestronger. Ingeneral,multivariatestatisticstraininginpsychology(typicallypresentedatpostgraduatelevelandsometimeslatterundergraduate-level)willcoverthesestatisticaltechniques.Here'sBillRevelle'snotesthatcoversomepsyhometrictheory:http://www.personality-project.org/r/book/ Wouldn'tthisimplythatallofthefactorsaremulticollinearandmakeitdifficulttodistinguishwhichfactorsaremostsignificant? That'swhyresearchersoftenfocusmoreong(i.e.,thegeneralfactor).Butyes,youareinasensecorrect.Ofcourse,youcanstilldomultipleregressionandsuchwithcorrelatedpredictors;youcanthenlookatthingslikesemi-partialcorrelationstolookattheuniquepredictionofanyonedomain. Share Improvethisanswer Follow editedApr13,2018at0:41 answeredApr12,2018at7:47 JeromyAnglimJeromyAnglim 30.4k1111goldbadges8989silverbadges218218bronzebadges $\endgroup$ 1 $\begingroup$ @Jeromy_AnglimAwesome,itmakesalotmoresensenow.Thanksfortheanswerandthebookresource. $\endgroup$ – thevengefulco Apr12,2018at15:55 Addacomment  |  YourAnswer ThanksforcontributingananswertoPsychology&NeuroscienceStackExchange!Pleasebesuretoanswerthequestion.Providedetailsandshareyourresearch!Butavoid…Askingforhelp,clarification,orrespondingtootheranswers.Makingstatementsbasedonopinion;backthemupwithreferencesorpersonalexperience.UseMathJaxtoformatequations.MathJaxreference.Tolearnmore,seeourtipsonwritinggreatanswers. Draftsaved Draftdiscarded Signuporlogin SignupusingGoogle SignupusingFacebook SignupusingEmailandPassword Submit Postasaguest Name Email Required,butnevershown PostYourAnswer Discard Byclicking“PostYourAnswer”,youagreetoourtermsofservice,privacypolicyandcookiepolicy Nottheansweryou'relookingfor?Browseotherquestionstaggedneuroscienceintelligencecorrelationoraskyourownquestion. FeaturedonMeta PleasewelcomeValuedAssociate#1301-Emerson PlannedmaintenancescheduledforTuesday,August23,2022at00:00-03:00AM... Recentsiteinstability,majoroutages–July/August2022 Related 7 HowtointerpretaBBCnewsarticleontheeffectofraceonintelligence? 12 Correlationbetween"mechanicalaptitude"andIQ 5 DoesEmotionalIntelligence(EQ)demonstratetheFlynnEffect? 8 Linkbetweenvisual-spatial+verbalworkingmemoryandintelligence/academicachievement? 2 QuestionsonInterpretingFactorAnalysisResultsandScores 3 Correlationusedasexplanatorydevicein''TheneuroscienceofIntelligence' 3 Whatintelligencetheoryisbeingtaught? 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