Concepts, Theories, and Numbers: A Checklist for Constructing, Evaluating, and
Using Concepts or Quantitative Measures
OxfordHandbooksOnline
Concepts,Theories,andNumbers:AChecklistforConstructing,Evaluating,
andUsingConceptsorQuantitativeMeasures GaryGoertz
TheOxfordHandbookofPoliticalMethodology
EditedbyJanetM.Box-Steffensmeier,HenryE.Brady,andDavidCollier
PrintPublicationDate: Aug2008
OnlinePublicationDate: Sep
2009
Subject: PoliticalScience,PoliticalMethodology,Comparative
Politics
DOI: 10.1093/oxfordhb/9780199286546.003.0005
AbstractandKeywords
Thisarticlepresentsguidanceonhowtothinkabouttheconcepts.Itproposestoexploresomeissuesinthe
assessmentofconceptsandquantitativemeasures.Itpresentsthebasicprobleminitsgeneraloutlines.Itthen
offersaveryshortexample,typicallyusingpublishedresearch.Thestructuringandaggregatingconceptsand
measuresindicatesthatonemustfirstconsiderthetheoryembodiedintheconcept.Thenoneshouldsurvey
plausibleaggregationandstructuralrelationshipsthatcouldbeappliedinaquantitativemeasure.Itisnotedthat
oneneedstoaskabouttheexistenceornotofzeropoints.Thegrayzoneneedstobeexploredindependentlyof
thetwoextremes.Homogeneityisanotheraspectofcomparingwithinandbetweenvariousconceptsand
measuresofthesamephenomenon.Thisarticlegenerallyhighlightsthatitisthelackofintegrationoftheoryand
methodologywhichprovesproblematic.
Keywords:structuringconcepts,aggregatingconcepts,quantitativemeasures,aggregationprocedures,homogeneity,zeropoints,grayzone
1Introduction
IN thischapterIproposetoexaminesomeissuesintheevaluationofconceptsandquantitativemeasures.These
issuesconstituteachecklistofconsiderationswhenevaluatingorconstructingconceptsandquantitative
measures.Theyareimportant(p.98) questionsthattheuserofconceptsandmeasuresshouldaskwhensheis
planningtoconstruct,evaluate,orusethem.1
TheissuesIcovercanbegroupedintothreelargecategories.Thefirstisthatallcomplexconceptsandmeasures
useaggregationprocedures.Themathematicaloperationsusedinquantitativemeasuresneedtorepresent
theoreticalconsiderationsontheconceptside,whatIcallthestructureoftheconcept.Rarelydotextbooks
providealistofstructuraloraggregationalternatives.Yetconceptandmeasurevaliditydependsonwhyandhow
thedimensionsorindicatorsareaggregated.
Thesecondsetofthemesdealswithimportantpointsorzonesalongtheconceptormeasurescale.Frequently,
zeroandextremepointsplayacrucialroleinconceptandmeasureconstruction.Oftencertainscalepointsare
thefocusofthetheorytobetested.Similarly,thegrayzoneinthemiddleisasiteofcontentionbetweenmeasures
andaplaceofimportantchoiceswhendichotomizing.
Thethirdgroupofconsiderationsdealswiththequestionofequivalenceorhomogeneitywithinorbetween
concepts/measures.Tocodetwoobservationsasthe“same”reflectsdecisionsaboutaggregation,zero,and
extremepoints(amongothers).Yetrarelydoquestionsabouthomogeneityofmeasurementarise.Oftenoneasksif
twomeasuresagreeonagivenobservation,butrarelydoesoneaskifonemeasureisappropriatelycodingtwo
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observationsasthesame.
ForeachissueIintroducethebasicprobleminitsgeneraloutlines.Ithenprovideaveryshortexample,typically
usingpublishedresearch.Theendresult(seetheChecklistattheendforasummary)isalistofconsiderations
thatIthinkshouldbeautomaticandstandardwhenusing,constructing,andevaluatingconceptsandquantitative
measures.2
2StructureandAggregationinConceptsandMeasures
Oneofthemostfundamentaloperationswhenconstructingconceptsandmeasures(by“measures”Imean
henceforthquantitativemeasuresorvariables,includingdichotomousones)isthatofstructureoraggregation.I
preferthetermstructurebecausetheconceptormeasuremaynotreallybean“aggregation,”butIwilluseboth
termsmoreorlessinterchangeably,typicallyusingaggregationwhentheconceptor(p.99) measureinvolves
individualsasparts.Onthemeasuresideonetypicallyhastoaggregateindicators.Ontheconceptsideone
needstostructuredefiningcharacteristics.Henceacentralquestionwhenevaluatingorconstructinga
concept/measureiswhyandhowthisisdone.
Thequalitativeliteratureonconceptsandthequantitativeliteratureonmeasuresdifferradicallyonthedefault
approachtostructureandaggregation.Thesedifferencesreflecttheoriginoftheseliteraturesandwherepolitical
scientistshaveborrowedideas.Thequantitativeworkonmeasurement—whatIwouldcalltheLazarsfeld–Blalock
school—borrowedheavilyandexplicitlyfrompsychologyandeducationalstatistics(seeLazarsfeld1966fora
history).Forexample,currentworkonidealpointestimation(e.g.Bafumietal.2005)continuesthistraditionof
borrowingfromeducationaltesting.Thequalitativeliteraturegotitsideasfromphilosophicallogic.Forexample,
Sartori'sclassic1970articledrewitsbasicideaofconceptualstretchingdirectlyfromtheclassicCohenandNagel
book(1934)onphilosophicallogic.
Perhapsthemostfundamentaldifferencebetweenthesetwotraditionsisthestandardwaytostructureor
aggregateameasureorconcept.Drawingonphilosophicallogic(goingbacktoAristotle)thequalitativeliterature
hasstructuredconceptsintermsofnecessaryandsufficientconditions:Eachpartisnecessaryandalltheparts
togetherarejointlysufficient.Operationallythismeanstakingtheminimum(necessity)orthemaximum
(sufficiency)oftheparts.3 Quantitativeapproachestoaggregationmostcommonlyusesomeadditiveprocedure,
eitherthesumorthemean.Whenpresentedwithabunchofindicatorsofaconceptthenaturalfirstmoveistoadd
themuportaketheirmean.4 Thekeypointisthatthesequalitativeandquantitativetraditionsprovidedifferent
optionsonaggregation.Hencewhenconsideringaconceptormeasureoneneedstoaskabouttheaggregation
techniqueandwhetheritisbetterandmoreappropriatethanotheralternatives.
Onewaytostarttobridgethegulfbetweenthequalitativeandquantitativeschoolsistogoborrowingfrom
somewhereelse.Isuggestinthissectionthatagoodplacetogowhenthinkingaboutstructureandaggregationis
theliteratureonindividualorsocialwelfare,well‐being,orhappiness.Thisincludesawiderangeoftheoreticaland
empiricalstudiesfromeconomics,development,psychology,andphilosophy.Theconceptsofindividualwell‐
beingandsocialwelfarefundamentallydealwithaggregation.Socialwelfareinvolvesbydefinitionaggregating,
somehoworanother,thewelfareofindividuals.Individualwell‐beinginvolvesaggregatingthevariousdomainsof
lifesuchashealth,family,work,andlibertythatconstituteindividualwell‐being.
Oneofthefirstadvantagesofusingtheliteratureonwell‐being(individualorsocial)isthatonemovesawayfrom
thevariable–indicatorlanguagetypicalof(p.100) discussionsofmeasurement.Forexample,socialwelfareis
constitutedbythewell‐beingofindividualsinthesociety.Thewell‐beingofindividualsisnotanindicator,buta
constitutivepartofsocialwelfare.
Mostquantitativescholarsaredeeplysuspiciousoflanguageinvolvingwordslike“constitutive.”Thisisseenas
typicalofunclearsocialconstructivistthinking.However,thesocialwelfareexampleillustratesthatsuchlanguage
isquitenaturalandreasonable.Forexample,AmartyaSen,aprominentplayerintheeconomics,philosophy,and
developmentliteraturesonindividualwell‐beingandsocialwelfare,frequentlyusesthissortoflanguagetodiscuss
theconceptofwell‐being:
Thewell‐beingofapersoncanbeseenintermsofthequality(the“well‐ness,”asitwere)oftheperson's
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being.Livingmaybeseenasconsistingofasetofinterrelated“functionings,”consistingofbeingsand
doings.Aperson'sachievementinthisrespectcanbeseenasthevectorofhisorherfunctionings.The
relevantfunctioningscanvaryfromsuchelementarythingsasbeingadequatelynourished,beingingood
health,avoidingescapablemorbidityandprematuremortality,etc.,tomorecomplexachievementssuch
asbeinghappy,havingself‐respect,takingpartinthelifeofthecommunity,andsoon.Theclaimisthat
functioningsareconstitutiveofaperson'sbeing,andanevaluationofwell‐beinghastotaketheformof
theseconstitutiveelements.(Sen1992,39;emphasisintheoriginal).
Withsuchaconceptofindividualwell‐being,onemustaggregateinsomemannerorotherthevariousfunctionings
intoaglobalmeasure.
Theliteratureoninternationalconflictfacesthesameaggregationproblemasthesocialwelfareliterature,butona
muchreducedscale.Insteadoftheaggregationofmillionsofindividualsintoasociety,wehavetheaggregationof
twocountriesinadyad.Intheonecasewehave“social”welfare,intheotherwehave“dyadic”conceptsof
democracy,tradedependence,andthelike.Intheformercaseitis,forexample,theproblemofaggregating
individualutilitiesintosocialones;inthelatter,itisaggregatingindividuallevelsof,say,democracy,intoadyadic
concept.
Table5.1givesabriefsurveyofsomecommonvariablesintheliteratureoninternationalmilitarizedconflict.Many
ormostoftheseusualsuspectswillappearinalarge‐Nstudyofinternationalconflict.Thefirstquestionof
importancewhenlookingatdyadicconceptsinthistheoreticalandempiricalcontextiswhetherthereis
aggregationatall.InTable5.1,Ihavemarkedthosevariablesthatareinherentlydyadicas“relational.”Some
tangosrequiretwo,suchasmilitaryalliance.Thesearenotanaggregationofcountry‐levelvariables.Ifthelistin
thetableisrepresentative,thenabouthalfofcommonlyusedvariablesarenotaggregations.5
Thedemocracyvariableillustratessomeoftheimportantissueslinkingconcepttheorytoquantitativemeasures.
First,itisofnotethatnoneoftheaggregationmeasures—includingthedemocracyvariable—usesthesumorthe
average.Givenindividualdemocracylevels(onascalefrom−10to10),whynotdotheobviousthing(p.101)
andtaketheaverage?Someearlyworkdidinfactusesomevariationonthemean.6 However,Dixon(1993)made
astrongtheoreticalcasethatitwastheleastdemocraticofthedyadthatdeterminedtheimpactofdemocracyin
thedyadasawhole.The“weakest‐link”approachquicklybecamethestandardusedinthevastmajorityof
studiesontheliberalpeace.Others,notablyRussettandOneal(2001),haveextendedthislogictothetrade
dependencyvariable,andHegre(2000)hasuseditforthelevelofdevelopmentvariable.
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Table5.1.Dyadicconceptsandthestudyofinternationalconflict
Dyadicconcept
Samplecitation
Structuralrelationship
Dominantstructure
Democracy
Dixon(1993)
aggregation
weakestlink
Trade
Gleditsch(2002)
aggregation
weakestlink
Major/minorpower
Mousseau(2000)
aggregation
none
Levelofdevelopment
Hegre(2000)
aggregation
weakestlink
Armsrace
Sample(2002)
aggregation
none
Alliance
GiblerandVasquez(1998)
relational
n.a.
Contiguity
Bremer(1992)
relational
n.a.
Power
OrganskiandKugler(1980)
relational
n.a.
IGO
OnealandRussett(1999)
relational
n.a.
Issue,territory
SeneseandVasquez(2003)
relational
n.a.
n.a.—notapplicable.
Trade—leveloftradedependence.
Levelofdevelopment—e.g.GNP/capita.
Contiguity—geographicalcontiguity.
Power—militarycapabilities.
IGO—membershipsinintergovernmentalorganizations.
Territory—conflictisoverterritory.
Source:Goertz(2006,133).
Thedemocracyvariableillustratesthatingoodresearchthereisastrongtheoryofthedyadicconcept(e.g.
dyadicdemocracy)whichisusedtothestructureofthequantitativemeasure.Onecancontrastthestrongtheory
ofthedemocracyvariablewithanotherusualsuspect,majorpowerstatus.Thisvariableismycandidateformost
popularandleasttheorizedofthecommoninternationalconflictvariables.Itseemsthatabouthalfofthetimethis
iscodedas“atleastonemajorpower”(i.e.maximum)andabouthalfthetimeas“bothmajorpowers”(i.e.
minimum).Ifoneisconstantlyaskingthequestion“whatstructure”and“why”thenitislesslikelythatscholarswill
automaticallyincludesuchundertheorizedvariables.
Thetradedependencyvariableisagoodexamplewheredifferentstructuresareused,butthesearebasedon
goodtheoreticalpositions(whichmayormaynotbe(p.102) bornupinempiricalanalyses).Forexample,
Barbieri(2002)hasmadeastrongcaseforusingthegeometricmeanasameasureofthesalienceoftrade
relationships.Herewehaveacasewheredifferencesbetweenquantitativemeasuresreflectrealtheoretical
differences.
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Returningtotheliteratureonindividualandsocialwelfare,wecanseethatthestructurequestionisverymuch
abouttheweightingoftheindividualparts.Justastheweakest‐linkmeasureofdyadicdemocracygives
determiningweighttotheleastdemocraticcountry,sodovarioustheoriesofjusticegivedifferingweightsto
individualsinsociety.Forexample,theoriesof(social)justicehaveverylargeanddirectionimplicationsforthe
measurementofsocialwelfare.ARawlsiantheoryputstremendousweightontheindividualswhoareleastwelloff
inaggregatingtothesociallevel.Autilitariantheoryincontrastgiveseveryindividualequalweightindetermining
socialwelfare.Aswiththedyadicdemocracyvariable,itisatheory(inthiscaseanormativeone)thatdetermines
theweightingoftheindividualparts.Oftenwehaveweaktheoryandthatresultsintheequalweightingofthesum
oraverage.However,whenwehavestrongertheorythatcanoftenleadtounequalweighting.7 Itisthephilosophy
ofjusticeandwelfarethatdeterminestheweightingusedinanyeventualquantitativemeasure.Awidevarietyof
aggregationtechniqueshavebeenusedtoimplementatheoryofsocialwelfare,e.g.summaximization(Harsanyi
1955),lexicographicprioritiesandmaximin(Rawls1971;Sen1977),equality(Foley1967;Nozick1974;Dworkin
1981),oroneofvariousothercombiningrules(Varian1975;Suzumura1983;Wriglesworth1985;Baumol1986;
Riley1987).ItisbecauseofthevarietyofaggregationproceduresusedthatIhavesuggestedthewell‐beingand
socialwelfareliteratureasasourceofinspirationforthinkingabouthowthetheoryembodiedinconceptscanbe
implementedinvariousquantitativemeasures.
OneconceptandaggregationproblemPaulDiehlandIhavewrestledwithoverthelasttenyearsisthatofthe
severityofamilitarizedinterstaterivalry(DiehlandGoertz2000).Hereweseetheproblemofaggregationover
timesincearivalrybydefinitionischaracterizedbyaseriesofmilitarizedinteractions.Onequestionishowto
aggregatethoseinteractionsintoameasureofrivalryseverityatanygiventime.Oneobviousoptionwouldbea
weightedaverageofallthepreviousactions,witheachobservationexponentiallydiscountedbyitselapsedtimeto
thepresent(basicallythisistheCrescenziandEnterline2001proposal).Ihaverecentlybeenintriguedby
prominentfindingsinthepsychologicalliteratureonhappiness.Rivalrydealswithemotionsandfeelingsofhatred,
whilehappinessdealswiththeopposite,butbothfacethesameaggregationproblem.Aprominentfindingdueto
Kahnemanandhiscolleagues(e.g.Kahnemanetal.1993;Kahneman1999;Oliver2004)isthatcurrenthappiness
followsa“peak‐end”aggregationrule.Basically,currenthappinessistheaverageofthehappinessatt−1(i.e.
“end”)andthemaximumhappiness(i.e.“peak”)overtherelevanttimeperiod.
(p.103) Thisisaninterestinghybridstructureforaconcept/measure:Itusesboththeaverageandthemaximum.
Itmeansthatmostpastperiodsreceivenoweightatall,whichistheimpactofthemaximum.Itimpliesthat
exponentialmemorymodelsaredramaticallyoffsincethepeakexperienceremainsveryimportantandshowslittle
decay.Ihavenoideawhetherthiswouldmakesensefordyadicrelationshipsbetweenstates,butitisan
interestingaggregationoptionthatIhavepermanentlyaddedtomytoolkit.
Thisbriefsectiononstructuringandaggregatingconceptsandmeasuressuggeststhatonemustfirstconsiderthe
theoryembodiedintheconcept.Thenoneshouldsurveyplausibleaggregationandstructuralrelationshipsthat
couldbeappliedinaquantitativemeasure.Akeyissuethroughoutisthenatureoftheweightingschemeimplied
bythetheoryandimplementedbythemeasure.
3ZeroPoints
Thezeropointoftenplaysanimportantroleintheoreticalandmethodologicalresearchprograms.Asprospect
theoryandourcheckbooksshow,thereisamajordifferencebetweenpositiveandnegative.Methodologicallythe
existenceofzeropointshasmanyimportantimplications.Alongarticlecouldeasilybewrittenonzeropoints;I
wouldliketodiscussanexamplethatillustratessomekeyissuesthatusersofconceptsandmeasuresshouldbe
askingaboutwhenconstructingandevaluatingmeasures.
Letmestartwithapersonalanecdote.Thezeropointplaysalargeroleinsomeexpectedutilitytheoriesof
internationalconflict.Forexample,BuenodeMesquita's(1981)mainhypothesiswasthatanegativeexpected
utilitywasanecessaryconditionforwarinitiation.Asaresultheneededameasureofpreferencesandutilitiesthat
hadazeropoint.Hedevelopedwhatisknownastheτbmeasureofpreferences(becauseitisusestheτb
statisticalmeasureofassociation).WhenJoeHewittandIwerelookingforameasureof“willingness”toinitiatea
militarizedconflictweimmediatelythoughtoftheτbmeasure.Anegativeτbwouldbeasignalofhostile
relationshipsandhenceawillingnesstoinitiatemilitarizedconflict(otherfactorssuchasweaknessmightpreventa
8
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countryfromactingonthiswillingness).Operationally,willingnesswasthenanegativeτbscoreforadyad.8
WefirstpresentedthispaperataPeaceScienceConferenceandBuenodeMesquitawasintheaudience.Inthe
questionperiodheremarkedthatwemisusedhisτbmeasure.Thereasonwasthatthe“nominal”zerointhedata
(e.g.producedbytheEUgenesoftware)wasnotthe“true”zero.Thetruezeropointvarieswithsystemsizeand
correspondstoanegativenominalvalue.Assystemsizegoestoinfinitythe(p.104) nominalzeroapproaches
thetruezeroatzero.ThestoryendshappilywithBuenodeMesquitaworkingwithustodeveloptheappropriate
modifications(Goertz2006,ch.8).
Thisanecdotehasanumberofimportantlessons.
Thefirstlessonistoaskwhetherthetheoryinquestiondoesinfactneedazeropoint.Inmostusesofτb(orits
competitionS:SignorinoandRitter1999;seeSweeneyandKeshk2005forabibliographyofusesofSandτb)
thesemeasuresaretreatedasintervalones.9 Thezeropointplaysnorolesincethehypothesisisusuallyofthe
form,thelesssimilarthepreferencesthemorelikelywarormilitaryconflict.Thiscorrelationalhypothesisdoesnot
requireazerosinceitonlyproposesthatincreasingprobabilityofwarwithdecreasingpreferencesimilarity.Inthis
senseBuenodeMesquita's(e.g.1981)andourexplicituseofthezeropointisrelativelyrare.Themoralisthatone
needstoaskwhetherzeroplaysaroleinthetheoryandhencemattersinthemeasure.
Thesecondlessonisthatoneshouldaskwhetherthemeasureinfacthasazeropoint.Themainalternativetoτb
istheSmeasure(SignorinoandRitter1999):Doesithaveazeropoint?Ifyouexaminethedataasgeneratedby
EUgeneyouwouldsayyes,becausethedatarangefrom−1to1.However,ifyoulookathowthedataare
generated,theanswerisnotsoobviouslyyes.HereisasimplifiedversionoftheSmeasure(seeSignorinoand
Ritter1999andSweeneyandKeshk2005formoredetails):
Thelaststepinthemeasure‐generatingprocessconsistsof1–2(∙)whichstandardizesthemeasureintothe[−1,1]
interval.10 Thisisanarbitraryscaletransformationsotheresultingzeroisnotarealone.Asonecaneasilysee,
therangeofthesubstantivepartofthemeasureis[0,1].Insteadofzerobeingamiddlepointitisinfactan
extremepoint.Forexample,GiblerandRider(2004)use[0,1]Sdata,whichimpliesthattheydonotseeazero
pointinthemiddle.Thesecondlessonisthusthatjustbecausethescaleofthemeasurehaszerovaluesdoesnot
meanitisarealzero.11
Thisleadstothethirdlesson:Whatisthemeasurementtheorythatdeterminesthezeropoint?RecallthatBueno
deMesquitatoldusthatthenominalzerowasnotthetruezero.Hemustthereforehavehadameasurement
theoryaboutalliance(p.105) configurationsthatheusedtodeterminethetruezeropoint.Sooneneedsalways
toaskaboutthetheorythatdetermineshowtomeasurethezeropoint.12
Braumoeller(2004)andBrambor,Clark,andGolder(2006)havebroughttheattentionofthepoliticalsciencepublic
tothefactthattherearemanyeasy‐to‐fall‐intopitfallsintheuseofinteractionterms.Oneimportantimplicationof
thepresenceorabsenceofazeropointisexactlytheroleratiovariablesplayininteractionterms.
Oneissueininteractiontermanalysisliesintheinterpretationoftheindividualtermsoftheinteractionterm,e.g.β1
X1andβ2 X2 .Typically,theinterpretationisthatβ1istheimpactofX1whenX2 =0.Thisthenassumes
obviouslythatX2 =0reallymeanssomething.IfX2 isanintervalvariablethenX2 =0iscompletelyarbitrary
(seeFriedrich1982andAllison1977).Forexample,GiblerandRider(2004)useSininteractionwithlevelofthreat
tostudyalliancereliability.Sincelevelofthreatisalwaysgreaterthanzero,itcouldmakeasignificantdifferenceif
Sisseentohaveatruezero.
Inarelatedmanner,standardizationofvariableswithmeanzeroiscommon.Forexample,Beck,King,andZeng
(2004)dothisforallthevariablesintheirneuralnetanalysis.Thesestandardizedvariablesarethenusedina
largevarietyofinteractionterms.
Insummary,oneneedstoaskabouttheexistenceornotofzeropoints.Doesthetheoryneedthem?Doestheuse
ofthevariableininteractiontermsandthelikeimplythatthereisatruezeropoint?
4ExtremePointsandIdealTypes
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Theideal‐typewaytoconstructconceptshasalonganddistinguishedhistory.InthesocialsciencesitisMax
Weber(1949)whomadeaprominentcaseforthisprocedure(e.g.seeBurger1987foradiscussion).While
scholarsoftenuseidealtypestoconstructconcepts(e.g.GuntherandDiamond2003),treatmentofthe
methodologyofidealtypesisalmostcompletelyabsentfromtextbooks.Welackanalysesofhowtoconstructan
idealtype,orwhatconstitutesagoodidealtype.Inspiteofthis,onecandiscerntwodistinctivecharacteristicsof
idealtypesastheyappearinnature:(1)theidealtypeisanextremepointonthecontinuum,and(2)actualcases
ofthatextremearerareornonexistent.
Clicktoviewlarger
Fig.5.1. Distributionatextremepoints:politydemocracymeasure
Ihavearguedelsewhere(Goertz2006,ch.3)thatideal‐typeconceptsarenotreallyusefulonceonehasa
coherentsystemforconstructingconcepts.However,theideaofanidealtypedoesraiseanimportanttheoretical
andmethodologicalquestion(p.106) thatmustbeattendedtowhenevaluatingandconstructingconcepts:What
isthedistributionofcasesattheidealpointextreme?Ideal‐typeconceptsarecharacterizedbyzerocasesatthe
extreme:Isthatagood,bad,orindifferentcharacteristic?Onecanaskthecontrastingquestion:Isitgood,bad,or
indifferentiftherearealotofcasesattheextreme?
Figure5.1showsthedistributionofpolitydemocracyscores(JaggersandGurr1995)forallcountries1816–1999.
Youwillseeahighspikeatthedemocracyextreme.WhenIseeahistogramlikethismyfirstreactionistothink
thatthe“true”scalereallyextendsfurther.Becausethemeasurestopstoosoonwegetapilingupcasesatthe
barrier(Gould1996).13
LookingatthepolityscoresfortheUnitedStatesmightconfirmthefeelingthatthescalestopstoosoon.Beginning
in1870theUnitedStatesalwaysreceivesthemaximumscoreof10.However,thefactthatlargepartsofthe
population—e.g.blacks,hispanics,Indians—insomeregions,notablytheSouthandSouthwest,wereeitherdejure
ordefactopreventedfromvotingafter1870suggeststhatacountrycouldbemoredemocraticthantheUnited
States.
Themoralhereisthatoneneedstoexaminethedistributionofcasesattheextremes.“Idealtypish”conceptsand
measureswithfewcasesattheextrememightoftenbeagoodgoal.Ifourtemperaturescalemaxedoutat100
degreeswewouldbemismeasuringalotoftemperaturesas100.Whilenotnecessarilyconclusiveevidence
againstameasure,largeconcentrationsateitherextremeneedtobeconsciouslyjustified,notacceptedas“that
isjustwhathappenswhenyoucodethedata.”
(p.107)
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Table5.2.Disagreementinthegrayzone:levelofdemocracyinCostaRica,1901–10
Year
PolityIV
Vanhanen
Gasiorowski
BLM
1901
100
0
0
0
1902
100
0
0
50
1903
100
0
0
50
1904
100
0
0
50
1905
100
0
0
0
1906
100
1
0
0
1907
100
1
0
50
1908
100
1
0
50
1909
100
1
50
50
1910
100
1
50
50
Allmeasureshavebeenrescaledontothe[0,100]interval.
Source:Bowman,Lehoucq,andMahoney(2005).
5TheGrayZone
Whencomparingvariousconceptsandmeasuresoneusuallyfindsthatcorrelationcoefficientsareusedtoassess
similarity.Thisprocedureoftendramaticallyunderestimatesthedissimilarityofmeasures.Onereasonforthisis
thatobservationsattheendsofthespectrumusuallyhavemoreweight(instatisticalterms,moreleverage;
Belsley,Kuh,andWelsh1980)thanthoseinthemiddle.Itisoftenthecasethatconceptsandmeasuresagreeon
theextremecasessincetheyareclear‐cutandeasytocode,whileatthesametimedisagreeingfrequentlyon
casesinthemiddle.Pointsinthemiddleoftenhavea“halffish,halffowl”characterthatmakesthemhardto
categorizeandclassify.Icallthisareathegrayzone,becausevaluesinitareneitherblacknorwhite.
Democracyisaconceptwherethegrayzoneoftenplaysalargeroleinvarioustheoreticalcontextsrangingfrom
thewar‐pronenessoftransitionaldemocracies(e.g.MansfieldandSynder2002)tosuccessfuldemocratic
transitions(e.g.LinzandStepan1996).CostaRicahaslongbeenseenasoneofthemostdemocraticcountriesin
LatinAmerica.AsTable5.2illustrates,prominentmeasuresdiffersignificantlyonhowtheycodeCostaRicainthe
crucialfirstdecadeofthetwentiethcentury.
Whenthereisasignificantnumberofcasesinthegrayzoneusingacorrelationcoefficientasameasureof
similaritycanwildlyunderestimatediscrepanciesbetweenmeasures.Forexample,takethedemocracydatain
Figure5.1.Ifonetakesthecasesatextremevalues(i.e.−10and10)asgivenwhichconsistsof23percentofthe
data,andthenreplacesalltheobservationsinbetweenwithindependent,random,and(p.108) uniformdata
onestillgetsacorrelationcoefficientofalmost.5.Inshort,therecanexistextensivedisagreementbetween
measuresinthegrayzoneandonecanstillgetquiterespectablecorrelationcoefficients.
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Table5.3.Systematicdisagreementinthegrayzone
X1
X2
0
1
2
3
4
5
0
50
10
0
0
0
0
1
0
50
40
40
0
0
2
0
0
50
50
40
0
3
0
0
0
50
40
0
4
0
0
0
0
50
10
5
0
0
0
0
0
50
SupposethattherelationshipbetweenthetwomeasuresislikethatofTable5.3(seeGoertz2006,ch.3foran
examplewithrealdata).Thereisexcellentagreementontheextremesbutsubstantialdisagreementinthemiddle.
Yetahighcorrelationof.87masksdifferencesbetweenthetwo.NotablymeasureX1isalwayslessthanmeasure
X2 (thesekindsoftriangulardatapatternsarenotuncommonincomparativeresearch;seealsoBennett2005,
figure1foratriangularrelationshipbetweentwodyadicdemocracyvariables).Butbecausealargepercentageof
observationsdolieonthediagonalonewillgetsubstantialcorrelations.Thisexamplesuggeststhattheremaynot
onlybedisagreementonthemiddlezone,butthereisapatterntothatdisagreement.
PatternsofdisagreementlikethoseofTable5.3suggestthatthevariancebetweentwomeasureschanges
systematicallyasonemovesawayfromtheextremesandtowardthemiddle.Thechangeinvarianceisdriven
onceagainbyagreementattheendsanddisagreementinthemiddle.
Figure5.2chartsthechangesinvariancewhencomparingthepolityconceptandmeasureofdemocracy(Jaggers
andGurr1995)withFreedomHouse'sconceptandmeasure(Karantycky2000).TodothisIaddedthescoresof
theFreedomHousevariables“politicalrights”and“civilliberties”whicheachrangefrom1to7.Ithenconverted
themtoa‐10to10scalewhichthenmatchesthepolityscale.Figure5.2givesthevarianceofthepolityscoresfor
allcaseswheretheFreedomHousecodesanation‐yearatacertainlevel.
Clicktoviewlarger
Fig.5.2. Varianceanddisagreementinthegrayzone
Weseethenattheextremesofautocracyanddemocracy(i.e.‐10and10)thereisverylittlevarianceinpolity
codingswhentheFreedomHouseseesanextremeautocracyordemocracy.Forexample,ontheX‐axiswesee
thatthereisalmostnovarianceinthepolitymeasurecaseswhentheFreedomHousecodesamaximaldemocracy
(i.e.10).Aswemovetowardthegrayzoneinthemiddleweseethatthevariationinhowpolitycodesagiven
nation‐yearincreasessignificantly:Aswemovefrom10to0thevarianceincreases1,000‐foldfrom.025to22.6.
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Thesame(p.109) sortofthinghappensfromtheautocracyside,thoughtheincreaseis“only”byafactorof
10.14
Alessonhereisthatoneneedstousemultiplecriteriatoevaluateconceptsandmeasures.Inparticular,thegray
zoneneedstobeexaminedindependentlyofthetwoextremes.Table5.3andFigure5.2illustratetwopatternsthat
mightbequitecommon.Table5.3showsatriangularrelationshipbetweenmeasures,whileFigure5.2shows
increasingvarianceasonemovestowardthegrayzone.
Weneedagreatervarietyoftechniquesforevaluatingconceptsandmeasures.Inparticularoneneedstolook
closelyatparticularpartsoftheconceptcontinuum.Thiswilldependonthetheoryandhypothesesbeingtested,
butingeneraltheextremepointsandthemiddlealwaysdeservespecialattention.
6HomogeneitybetweenandwithinConceptsandMeasures
Akeyissueintheanalysisofindividualconceptsaswellasthecomparisonoftwoormoreconceptsormeasures,
iswhatPrzeworskiandTeune(1970)called“functionalequivalence”orwhatIprefertocall“concept
homogeneity”(GerringandThomas2005talkabout“comparability”).Withinaconceptormeasureoneassigns
thesamevaluetoapotentiallylargenumberofobservations.Theconcept(p.110) homogeneityquestionis
whetheralltheseobservationsarereallyinstancesofthesamething.Forexample,istheUnitedStatesreceivinga
polityscoreof10in1950homogeneousorequivalenttoitsreceivingavalueof10in2000?Thekeyquestionin
termsofconstructingandevaluatingconceptsandmeasuresthenisthedegreetowhichcodingswithinameasure
orbetweenmeasuresagreeoncodingobservationsasthesame.
Thehomogeneityissuearisesasadirectconsequenceofaggregation.Inshort,aggregationproceduresproduce
homogeneityclaims.Forexample,inthepolitydemocracymeasurethereareavarietyofwaystoget,say,5.The
homogeneityclaimisthatallthesewaysaresubstitutableorequivalentintermsofcausalanalyses.
Table5.3illustratestheproblemwithconceptsandmeasuresofdemocracyforCostaRica.Allmeasuresare
homogeneousfortheyears1909and1910.Theyseethelevelofdemocracybeingthesameforthosetwoyears.
Thisishomogeneitybetweenconcepts,or“relativehomogeneity.”Posner(2004,851)remarksthataproblemwith
theHerfindahlindex(usedtostudytheimpactofethnicfractionalization)isthatitgivesquitedifferent
fractionalizationsthesamevalue.Thisishomogeneitywithinameasure.Thesearebothimportantcriteriafor
evaluatingconceptsandmeasures.
Itisimportanttonotethatconcepthomogeneityisdifferentthanexaminingtheextenttowhichmeasuresor
conceptsagreeonagivenobservation.Fortheyears1909–10allthemeasuresarehomogeneousbutthey
disagreeradicallyonthelevelofdemocracy.Whilethedegreeofagreementonleveliscertainlycorrelatedwith
thedegreeofhomogeneity,theyareconceptuallyseparatecriteriaofevaluation.
Figure5.2directlyassessesthedegreeofrelativehomogeneityofthepolityandFreedomHousemeasuresof
democracy.ForeachlevelofFreedomHousedemocracywecandeterminehowhomogeneousthepolitymeasure
isrelativetoFreedomHouse.Ifthepolitymeasureanddatacodeddemocracyhomogeneouslywithregardto
FreedomHousethenthevarianceofthepolityscoreswouldbezero:Inotherwords,politywouldcodethesame
valueandthevariancewouldbezero.Noticeherewearelookingatthevariationofthescores,nottheirlevel.Itis
possible—ifveryunlikely—thatthelevelisnotthesame.InFigure5.2weseethatwhenFreedomHousecodes
observationsascompletelydemocraticthenitisalmostcertainthatpolitycodesthematthesamelevel.However,
oncewemoveintothegrayzonethedegreeofrelativehomogeneitydeclinesprecipitously.
Inshort,homogeneityisanotheraspectofcomparingwithinandbetweenvariousconceptsandmeasuresofthe
samephenomenon.AsthecomparisonofpolitywithFreedomHouseillustrates,thedegreeofrelativehomogeneity
betweenmeasurescanvarysignificantlyalongthecontinuumfromthenegativepoletothepositive.Lookingatthe
polityscoresfortheUnitedStatesovertimemightsuggestthattherearehomogeneityconcernswithinthepolity
measure.Homogeneitycomparisonsbetweenandwithinconceptsandmeasuresshouldbecomestandard
practicewhenevaluatingdifferentconceptsandmeasures.
(p.111) 7HomogeneityofNegativeorZeroCases
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Wehaveseenthatthezeropointcanplayakeyroleinconstructingandevaluatingconcepts.Thezerocategory
canbeproblematicfromahomogeneityperspective,especiallyfordichotomousvariables.Frequentlythezero
categoryisacatch‐allforallobservationsthatare“not1.”Forexample,MahoneyandI(2004)haveanalyzedthis
probleminthecontextofchoosingthepopulationof“negative”cases,whichtypicallyreceivezeroina
dichotomouscoding,e.g.nonsocialrevolutions.SweeneyandKeshk(2005)havediscussedthesameproblemin
thecontextoftheSmeasure.InoneapplicationofStheyusemilitarizeddisputedatacodeddichotomously.They
wonderabouttheverymanyzeros(i.e.nodispute)inthedatasince“thelargenumberofzerosintheMIDdata
maybeduetothefactthatcountriesdidnothaveanythingtofightaboutorbecausetheychosetosettleany
possibleconflictsinnonmilitarizedways(expressionsofforeignpolicypreferences),orthelargenumberofzeros
maybeduetothefactthatcountriescouldnotengageinMIDsbecausetheyweretoofarapartanddidnot
interactinanywaythatwouldgiverisetothepossibilityofaMID(mostassuredlynotaforeignpolicypreference
revelation)”(SweeneyandKeskh2005,174).Similarly,Goertz,Jones,andDiehl(2005)havearguedthatperiods
ofzeromilitarizedconflictaftertheendofarivalryarenothomogeneousastheyaretypicallyconsideredin
“repeatedconflict”studies(e.g.Werner1999).Thefirstfifteenyearsorsoafterthelastmilitarizedconflictare
differentbecausetherivalryisendingandthereisstillapossibilityoffurtherconflict.However,afterthosefifteen
yearstherivalryisoverandthedyaddropsoutofthedata‐set.Inrepeatedconflictstudiesthedyadremainsin
untiltheendoftheperiod,typically2001.Hence,Goertzetal.seeheterogeneityinthezerosofrepeatedconflict
studies.Thusinavarietyofsettings,thehomogeneityofthe“nodispute/war”observationscanbecalledinto
question.15
ThePrzeworskietal.(2000)analysisofthecausesandconsequencesofdemocracyillustratesthenatureofthe
problem.Theirdichotomousconceptofdemocracyusesthenecessaryconditionaggregationprocedureonfour
dichotomouscomponents.Theirconceptofdemocracystatesthatifacountryhasazerovalue(dichotomously)
onanyoneofthefourcomponents,thenthecountryiscodedasanondemocracy.Democracycanbeachieved
inonlyoneway(i.e.aoneonallfourcomponents),whereasnondemocracycanoccurinfifteendifferentways
(i.e.24 −1=15).
Thehomogeneityhypothesisthenbecomesthequestionwhetherthesefifteendifferentwaysofbeinga
nondemocracyhavethesameconsequencesforcausalinferencewhenintroducedintoanalysis.Forexample,
whenassessingtheconsequencesof(p.112) nondemocracyonfertilityrates,asPrzeworskietal.(2000)do,
canweassumethatacountrythathaszerovalueononlyoneofthecomponentsiscausallyequivalenttoa
countrythathasazerovalueonallfourcomponents?
Przeworskietal.'sfirstanalysisoftherelationship(2000,81)betweenthelevelofeconomicdevelopmentand
democracyisaprobitanalysiswithavarietyofindependentvariableswhichareprominentintheliterature.Asan
exercise,wecanexaminethehomogeneityofthenondemocracycodingsanditsimpactoncausalinference
usingPrzeworskietal.'sdataandmethods.
Giventhenecessaryconditionaggregationprocedureused,wecaneasilyrankinthezerosintermsofthe
number—1–4—ofcomponentsthatareequaltozero.Onecanthenempiricallyevaluatewhethertheassumptionof
theconceptualhomogeneityofzerosseemsconfirmedincausalanalysis.SinceIamalsointerestedincomparing
measures,itisusefultotakeademocracymeasurewithastructureanalogoustoPrzeworskietal.'sforthis
exercise.16
The“modifiedpolity”measureisonewiththreedimensions,“CompetitivenessofParticipation,”“Executive
Recruitment,”and“ConstraintsonExecutive”(seeGoertz2006,ch.4fordetails).Thefirsttwodimensions
correspondtothetwohigher‐leveldimensionsofthePrzeworskietal.viewofdemocracywhichare“Contestation”
and“Offices;”theformerreferstomultiplepartiesandexecutiveturnoverandthelatterreferstoexecutiveand
legislativeofficesbeingfilledbycontestedelections.17 AsIhavereformulatedthepolitymeasurewehavethree
dichotomousdimensionsandIrequirethatallthreebepresentforacountrytobecodedasademocracy.So
structurallywehavethesamebasiclogicforthePrzeworskietal.measureandthemodifiedpolity.Wealsohave
thesamepotentialproblemwiththehomogeneityofthenondemocracycases,whichcanbezeroon1,2,or3
dimensions.
Asiscommonlyreported,thecorrelationbetweenthemodifiedpolityandPrzeworskietal.measureofdemocracy
ishighat.87.Przeworskietal.(2000,56–7)saythatthestandardpolitymeasurepredicts91percentofPrzeworski
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etal.values.Ifitwerenotfortheabovesections,Imightclaimthatsincecorrelationsarehighthemeasuresare
basicallythesame.Table5.4showsthatinspiteofa.87correlationwhenusingthemodifiedpolitydatain
Przeworskietal.'sanalysisofthecausesofdemocracy,someimportantdifferencesappear.Thefirstcolumnof
Table5.4replicatestheprobitanalysisdiscussedinPrzeworskietal.(p.81).18 Somevariables,notablythekey
levelofdevelopmentvariable,areverysimilarwithbothmeasuresofdemocracy.However,abouthalfofthe
variablesdiffersignificantlyinsignorsignificancelevel,i.e.Stratification,Catholic,Moslem,andEthnic
Fraction(alization);consistentresultsshowupforDevelopment,New(p.113) Colony,BritishColony,and
Protestant.Hereisthenyetanotherexampleofhowhighcorrelationscanmasksignificantdifferences,thisinthe
estimationofcausalimpacts.
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Table5.4.Causalhomogeneityofnondemocracy:democracyanddevelopment
Variable
Przeworski
Polity
ModifiedPolityMeasure
Onezero
Twozeros
Threezeros
Intercept
−2.7976
−2.0734
.1729
−2.0839
−12.6123
(Pr>X2 )
.0001
.0001
.6817
.0001
.0001
Development
.0003
.0003
.0002
.0004
.0018
(Pr>X2 )
.0001
.0001
.0001
.0001
.0001
NewColony
−.8490
‐1.2740
‐3.7547
−1.1456
−11.4318
(Pr>X2 )
.0001
.0001
.0001
.0001
.9998
BritishColony
1.0167
1.2703
3.4428
1.4706
10.2029
(Pr>X2 )
.0001
.0001
.0001
.0001
.9998
Stratification
−.0000
−.1420
−.2386
−.1372
(Pr>X2 )
.9996
.0018
.0004
.0112
Catholic
.0038
−.0004
−.0058
.0000
−.0366
(Pr>X2 )
.0005
.7336
.0206
.9951
.0103
Protestant
.0025
.0043
−.0049
.0070
.4853
.0131
.0707
.0010
.0001
(Pr>X2 )
1028
∞a
—
Moslem
−.0038
−.0013
.0003
−.0005
.0225
(Pr>X2 )
.0030
.3448
.8879
.7571
.0001
EthnicFraction
.0163
.0709
−.7415
−.0517
8.4373
(Pr>X2 )
.3242
.0472
.0001
.2843
.0001
GlobalDemocracy
4.0812
1.9914
1.1357
1.8348
14.7266
(Pr>X2 )
.0001
.0003
.1587
.0031
.0001
Nofnondemocracy
2120
1738
346
1258
134
(a)ResultsarebasicallythesamewhenremovingtheStratificationvariableexceptfortheCatholicvariable,
whichchangessigns.
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TherestofthecolumnsofTable5.4examinetheimpactofhomogeneityassumptionsofthenegativecases.Each
ofthesecolumnsusesadifferentpopulationofnegativecases;forexample,“onezero”meansthatforthe
negativecasesoneofthemodifiedpolitydimensionsiszerobuttheothertwoareone.Hence,thesenegative
casesareclosertodemocracythanthenegativecasesusedin“threezeros”whichhavezeroonallthreepolity
dimensions.Thecasesofoneonthedependentvariableremainthesameinalloftheseanalysesbutthenumber
ofzerosvariesfromcolumntocolumn(theyaregivenatthebottomofeachcolumn).
Theprobitresultsinthe“onezero”columnrepresentwhatmightbecalledthe“mostsimilar”analysis.Theseare
thenegativecasesmostsimilartothepositiveonesbecausetheyaremissingonlyonedimensionofdemocracy.
Spaceconstraintsprohibitanextensivecomparison,butonecanlookatthreethingswhencomparingacross
columns:(1)signchanges,(2)significancelevelchanges,(3)trends,increasingordecreasing,inparameter
estimates.Comparingthe“polity”tothe“one(p.114) zero”columnsweseethatthecentraleconomic
developmentvariableisconsistent.However,theCatholicvariablewhichwasinsignificantinthepolitycolumnis
nowsignificantlynegative.Overall,fourvariablesvaryinimportantwaysbetweenthetwocolumns:Catholic,
Protestant,EthnicFractionalization,andGlobalDemocracy(ODWPinthePrzeworskietal.namingscheme).
Whenmovingfurtherawayfromdemocracybyexaminingthepopulationwithtwozerosconstitutingthenegative
population,wecanseeapatternformingthatsomevariablesarerobustwhileothersarenot.Onceagainthe
economicDevelopmentisveryimportantalongwiththeNewColony,BritishColony,andStratificationvariables.
Again,thereligionvariables—i.e.Catholic,Protestant,andMoslem,andethnicity—movealot.
Movingtotheleastsimilarcountries—i.e.thosewithzeroonallthreedimensions—weseeveryclear‐cutresults.All
thevariablesareveryimportant.InfactStratificationisaperfectpredictor.19 Allthereligionvariablesarenow
significant.Hencewhenwechoosethemostcontrastingsetofnegativecasesweclearlyseetheimpactof
variableswhicharesometimesambiguousinothercomparisons.
Ofcourse,thenumbersinTable5.4onlyprovideaquickfirstlookatthequestionofconcepthomogeneityina
causalsetting.Avarietyofotheranalyseswouldbeusefulinanextendedanalysis.Forexample,onemightwant
torunaPoissonornegativebinomialregressiononthenumberofzerosforthenondemocracycases.Thiswould
givesomeideaoftheextenttowhichtheindependentvariablescandistinguishbetweenvariouskindsof
nondemocracies.Onewouldwanttothinkabouthowdramaticandclearthefindingstendtobewhenonlyusing
completenondemocracies;thestratificationvariableinthe“threezeros”columninTable5.4perfectlypredictsthe
outcome,thoughherethesmallNofnondemocraciesmaybepartofthestory20
8Checklist
Whenstructuringandaggregatingconceptsandmeasurestherearethreerelatedsetsofitemsonachecklistfor
constructingorevaluatingconceptsandmeasures.
•Whatisthetheoryembodiedintheconcept?
•Howisthattheorytranslatedintoaquantitativemeasure?
•Whataretheplausibleoptionsforaggregation?Inparticular,whatistheweightingschemetobeused?
(p.115) Inadditiontooverallevaluationsofvariousconceptsandmeasures,oneneedstoinvestigateindividual
partsorpointsofthescaleorconceptcontinuum.
•Aretherebigspikesateitherextreme?Doesthatsuggestextendingthescale?
•Isthereazeropoint?Doesthetheoryunderexaminationneedazeropoint?
•Doesthezeropointorlackthereofplayaroleinthecreationorinterpretationofinteractionterms?
•Whatisthetheorythatdeterminesthezeropoint?
•Whatisgoingoninthegrayzone?Isthatzonecrucialfortheorytesting?
Allconceptsandquantitativemeasuresimplyhomogeneityclaims.Theseneedtobeinvestigated.
•Whencomparingmeasuresaretherezoneswherehomogeneityislow(e.g.grayzone)?
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•Doeshomogeneityvaryinasystematicmanneracrossthecontinuum?
•Ifthemeasureorconceptisdichotomousaretheresignificantconcernsaboutthehomogeneityofthe
negativeorzerocases?Shouldsomezerosberemovedfromthedata‐set?
•Doconcepthomogeneityconcernsappearincausalanalyses?Aresomevariablesmorerobustinthefaceof
heterogeneitythanothers?
Ofcoursethischecklistisnotexhaustive.Itisalistofconcernswhichrarelymakeitintomethodologyand
researchdesigntextbooksandcourses.Ihavetriedtoillustratebrieflyhowtheseissuescanariseincommon
data‐setsandconcepts.Ofcourse,alotwilldependonthespecifictheoryandhypothesisunderinvestigation.
Thischapterstressesthatitisthelackofintegrationoftheoryandmethodologywhichprovesproblematic.In
particularthisistrueofaggregationandstructureproblems.Typicallytheyarisebecausenumericmeasuresare
notcloselyenoughtiedtothetheoriestheyaresupposedtoembody.Thesameistrueofmanyoftheissues
surroundingzeropoints.Inshort,oneneedscontinuallytoaskwhetherthenumericmeasuresarereallydoing
whattheconceptsandtheoriesprescribe.
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Notes:
IwouldliketothankBearBraumoeller,BruceBuenodeMesquita,DavidCollier,BradJones,KevinSweeney,and
ChadWesterlandforcommentsonthischapter.IwouldliketoalsothankScottBennettandEricGartzkefor
respondingtoqueriesregardingtheSmeasure.
(1)ThechoiceoftopicsarisesfromworkonmybookSocialScienceConcepts:AUser'sGuide(2006).They
representissuesthatarealmostignoredinthatbook(e.g.theimportanceofzeropoints)orthosethatdeserve
muchmoreattentionthantheyweregiveninthebook.Thatbookfocusedonconceptconstructionandonly
secondarilyonquantitativemeasures.HereIreversethebalancebytiltingmoretowardissuesofconstructing
quantitativemeasures.Thedistinctionbetweenthetwoshouldnotbepushedtoofar,asweshallseemany
methodologicalproblemsreallyneedtoberesolvedfirstonthetheoreticalandconceptualside.
(2)Itshouldbeobviousthatthechecklistisnotexhaustive.Rather,itconsistsoffactorsrarelyconsideredbutthat
shouldbe.
(3)Davis(2005)criticizesthenecessaryandsufficientconditionviewofconceptsfromthequalitativeperspective,
buthisproposaltousefuzzylogicremainsinthedomainoflogic,albeitatwentieth‐centurykind.
(4)Thebigexceptiontothisruleseemstobeconceptsthatareusedtocollectpopulationsofdata.Herethe
dominantprocedureisanimplicit,necessary,andsufficientconditionstructure.Typically,apotentialobservation
mustsatisfyallthecodingrules(thesufficiencycondition)andifitfailsononecodingruleitisexcludedfromthe
population(i.e.necessity).SeeSambanis's(2004)surveyofcivilwarconceptsanddata‐setsforexamplesofthis.
(5)Aggregationissuescanariseevenintheserelationalvariables.Forexample,iftwocountrieshavemultiple
alliancecommitmentsthenonemustaggregatethemtoformasingledyadicalliancemeasure.Typicallythe
strongest(i.e.maximum)alliancecommitmentistheaggregationprocedureusedinthiscase.
(6)MaozandRussett(1993)usetheformulaDemij=((Demh+Deml)/(Demh‐Deml+1))whereDemhisthe
maximumdemocracyscoreandDemlistheminimum.Thisisinterestingbecauseitisbasicallyameasureofhow
spreadapartthetworegimetypesare.Thissuggestsonepotentialaggregationcategorybasedontheideaof
variance;measuresofinequalitywouldfallintothiscategory.SeeBennett(2005)foranothermeasureofspread
betweenregimetypes.
(7)Sometimesscholarsthinkthatbyusingnecessaryconditionaggregationthatnoweightingisused.Thisis
clearlyincorrect;foranexampleofthisconfusionseeKingandMurray's(2002)measureof“humansecurity.”
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Thismeasureiscloselyrelatedtoworkonsocialwelfare.
(8)MostoftenτborSisusedasacontrolvariableandhencetherearenorealtheoreticalclaimsregardingit,e.g.
Fortna(2003)orPevehouse(2004).
(9)AninterestingquestionistheextenttowhichthisisanissueforGartzke's(1998)measureof“affinity”which
usesSpearman'srankordercorrelation.Likeτbthisrangesfrom−1to1.
(10)Inequation(1)fppisthe“foreignpolicypreference,”kisastandardizationparameterwhichmakesthe
absolutedifferenceinforeignpoliciesrangefromzerotoone.TheNinthedenominatorthenmakesthisthe
averagedifferenceinforeignpolicies.
(11)Forexample,manypeoplerescalethepolitymeasureofdemocracy(JaggersandGurr1995)fromitsoriginal
[−10,10]to[0,20].Asanexerciseforthereader,Iaskwhetherthezeroineitheroftheserangescouldbe
consideredatruezero?Atruezerocanofcoursebethelowestorthehighestpointonascale.SeeBennett
(2005)foravarietyofexampleswherethescalingofthepolitymeasureisimportant.SeeBecketal.(2004,382)
whotreatthepolityscaleasratio.
(12)Forexample,SweeneyandKeshk(2005)notethatifthenumberofcategoriesusedinconstructingS
increases,themeasuremovestoward1.Thesameistrueasthesystemsizeincreases.Hence,theremaybe
othercomparabilityconcernsbeyondtheexistenceornotofazeropoint.
(13)SeethehistogramsinSweeneyandKeshk(2005,e.g.figures3and4)forotherexamplesoflargespikesat
oneextremefortheSmeasure.
(14)Ileaveitasanexercisetore‐evaluatePrzeworskietal.'s(2000,58–9)argumentthattheirdichotomous
codingofdemocracyproduceslesserrorthanacontinuousmeasureiferrorfollowsthevarianceasillustratedin
Figure5.2andthecutpointbetweendemocracyandautocracyiszero.
(15)ApotentiallyusefulstatisticaltechniquefordealingwiththeheterogeneityofzerosisZero‐InflatedPoisson
(ZIP)regression(e.g.,ChinandQuddus2003).Zerosaremodeledtoarrivethrougha“zero‐event”state,i.e.
wheretheeventbasicallycannothappen,orthroughastatewheren>0eventscanoccur.
(16)Thestandardpolitymeasureisaweightedaverageofthefiveindicators,henceIhavepreferredtousea
modifiedpolitymeasurewiththesamelogicalstructureasthePrzeworskietal.one.
(17)Thepolitymeasureisuniqueinitsincorporationofconstraintsontheexecutiveasacorepartofthe
democracyconcept.Infact,itisthemostheavilyweightedofthefiveindicatorsused;seeMunckandVerkuilen
(2002)foradiscussion.
(18)ThevariableRELDIF—religiousfractionalization—isnotinthedata‐setforthebooksoitdoesnotappear.
(19)Somesoftware,e.g.Stata,automaticallyremovestheseveryimportantvariablesbecauseoftechnical
problemsinstatisticalestimation.Iprefertoincludethemandindicatetheirimportancewithparameterestimatesof
“∞.”
(20)ItisstrikinghowthestratificationvariablewasnotsignificantwhenusingthePrzeworskietal.democracy
variablebutwasconsistentlyimportantusingthemodifiedpolitymeasure.
GaryGoertz
GaryGoertzisprofessorofpoliticalscienceattheUniversityofArizona.Heistheauthororeditorofninebooksandoverforty
articlesonissuesofmethodology,internationalinstitutions,andconflictstudies,includingNecessaryConditions:Theory,
Methodology,andApplications(Rowman&Littlefield,2003),SocialScienceConcepts:AUser’sGuide(PrincetonUniversityPress,
2006),ExplainingWarandPeace:CaseStudiesandNecessaryConditionCounterfactuals(Routledge,2007),Politics,Gender,
andConcepts:TheoryandMethodology(CambridgeUniversityPress,2008),andATaleofTwoCultures:ContrastingQualitative
andQuantitativeParadigms(PrincetonUniversityPress,2012).
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