Vol.27,No.1,January–February2008,pp.29–48issn0732-2399??eissn1526-548X??08??2701??0029

inf?

doi10.1287/mksc.1070.0331

?2008INFORMS

ALogitModelofBrandChoiceCalibratedonScannerData

BonanzaStreetBooks,WalnutCreek,California94596,guadagni@alum.mit.edu

SloanSchoolofManagement,MassachusettsInstituteofTechnology,Cambridge,Massachusetts02142,jlittle@mit.edu

PeterM.GuadagniJohnD.C.Little

A

multinomiallogitmodelofbrandchoice,calibratedon32weeksofpurchasesofregulargroundcoffeeby100households,showshighstatisticalsigni?cancefortheexplanatoryvariablesofbrandloyalty,sizeloyalty,presence/absenceofstorepromotion,regularshelfpriceandpromotionalpricecut.Themodelispar-simoniousinthatthecoef?cientsofthesevariablesaremodeledtobethesameforallcoffeebrand-sizes.Thecalibratedmodelpredictsremarkablywelltheshareofpurchasesbybrand-sizeinahold-outsampleof100householdsoverthe32-weekcalibrationperiodandasubsequent20-weekforecastperiod.Thesuccessofthemodelisattributedinparttothelevelofdetailandcompletenessofthehouseholdpaneldataemployed,whichhasbeencollectedthroughopticalscanningoftheUniversalProductCodeinsupermarkets.

Threeshort-termmarketresponsemeasuresarecalculatedfromthemodel:regular(depromoted)priceelas-ticityofshare,percentincreaseinshareforapromotionwithamedianpricecut,andpromotionalpricecutelasticityofshare.Responsevariesacrossbrand-sizesinasystematicwaywithlargesharebrand-sizesshowinglessresponseinpercentagetermsbutgreaterinabsoluteterms.Onthebasisofthemodelaquantitativepictureemergesofgroupsofloyalcustomerswhoarerelativelyinsensitivetomarketingactionsandapoolofswitcherswhoarequitesensitive.

ThisarticlewasoriginallypublishedinMarketingScience,Volume2,Issue3,pages203–238,in1983.

Keywords:choice;logit;marketing-mix;scanners

History:ThispaperwasreceivedMay1982andwaswiththeauthorsfor2revisions.

1.

Manufacturersandretailerswishtounderstandhowprice,promotionandothermarketingvariablesaffectthesalesandsharesoftheproductstheysell.Suchinformationistherawmaterialformarketingmixdecisions.Although?rstprioritygoestodetermin-inghowaproduct’svariablesaffectitsownsales,marketingmanagersincreasinglywouldliketolearnmoreaboutproductinteractionswithinacategory.Forexample,amanufacturerwouldliketoknowwhetherpromotingoneproducttakesawaysalesandsharefromothersinthesameline.Similarly,retail-ersareacutelyawarethatapricecutonanitemmayincreaseitssalesattheexpenseofarelateditemsomewhereelseinthestore.

Tounderstandsuchissuesweneedtomodelwholeproductcategories.Thistaskcanbepartitionedintodetermining,?rst,theeffectsofmarketingvariablesonshareand,then,effectsontotalcategorysales.Inthispaper,weaddressonlythequestionofshare,or,tobemoreprecise,weexaminetheeffectofmarketingvariablesoncustomerchoiceamongproductalterna-tives.Fromchoiceswededuceshare.

Manymodelsofchoicehavebeenproposed.Infact,theoreticaldevelopmentsseemtobeaheadofempir-29

Introduction

icaltesting,atleastinsofaraslivemarketingpracticeisconcerned.Fortunately,theautomaticrecordingofpurchasesatthepointofsaleopensupnewoppor-tunitiesformodelappraisal.Datanowbeingcol-lectedbyopticalscanningoftheUniversalProductCode(UPC)insupermarketsshouldpermitacare-fulexaminationofvariouscustomerchoicemodelsinthecaseofgroceryproducts.Weshallhereusescanner-collecteddataoncoffeepurchasestocalibrateamultinomiallogitchoicemodelandexaminebothitsscienti?cqualityasarepresentationofcustomerbehavioranditspotentialusefulnessformarketingdecisionmaking.

Scannerdatausuallycomeintwoforms:Storedataandpaneldata.Storedataprovideindividualitem(UPC)salesandpricebystorebyweek.Inaddition,thecompaniessupplyingdatamaycollectinforma-tiononotherstoreactivitiessuchasspecialdisplay,couponredemption,retailadvertising,andshelf-spaceallocation.Paneldatapresenthistoriesofpur-chasesforasampleofhouseholds.Acooperatinghouseholddisplaysanidenti?cationcardatcheckout.Thestoreclerkkeysthehouseholdnumberintothecashregister,therebycausingthepurchaserecordto

GuadagniandLittle:ALogitModelofBrandChoiceCalibratedonScannerData

30

begitudinalsegregatedcustomerandstored.Overtimethiscreatesalon-recordScanneritemthedatasaleshavehistory.

actofspecialtheadvantages.Theydirectlyinlevel,therebyavoidingindividualthepipelinecustomereffectsfoundatthetialfactorythecostisshipmentslowsinceandthewarehousedataarewithdrawals.Ini-quentstore’snerspeed,dataprocessingbasictransactionaspinofffromarepotentiallyandstorageprocess.However,subse-deliverablecanbetoexpensive.userswithScan-greatereding.willalthoughdependhowontheirfasttheywillactuallybedeliv-areThedatatendtobeverytime-valueaccurateindecisionmak-becausetheyingregisterprocess.partoftheAtpresentstore’ssomecashcollectionandaccount-duresmoredeterminearoundthescanner,purchasesbut,sinceenterstoretheproce-cashotherstoresusethethepercentagedataforinventoryofgoodsscanned,asincrease.informationalmentComparedtopurposes,diarypanels,accuracycontrolscannerwillfurtherandacrossisstepproducts.relativelyItunobtrusive,thereforerepresentsbias-freeandmeasure-completesoldforwardingatheringinformationaboutasigni?cantproductsisThethroughgreatestsupermarkets.

thethattheyprovideadvantagethecompetitiveofscannerenvironmentdata,however,ofwhatcustomeridentifythecustomerdecision.boughtConventionalanditspricediarybutdatatellactivitiesthepurchase.impingingotherproducts,donotontheprices,andmarketingordescribestoreauditSimilarly,customeratthetimeofdatastandardforageographicwarehouseregionwithdrawaldonotstoresthecompetitivesituationwithinindividualrich,levelsdisaggregatedinthewayscannerdetailthatstoredatado.Itisthisnewofcustomerandmarketunderstanding.offershopeforJustnewasthroughoutmeasurementsprogressthehistoryhaveofdrivenscience,advanceswecaninhopetheorycategories:Currenthere.

forscanner(2)ketsnationalsamples(1)groupsdataservicesfallinthreebroadofstoresof,storesand(3)ininstrumentedsinglemarkets,tunities.Agroupofstoresinasinglemarketoffersoppor-mar-scanner-collectedforconvenientin-storeexperimentsusingloyalstoredata.Whenpanelsofstore-bilitiesshopperstestedincrease.areCoupons,added,fortheexample,experimentationcanbevalidlypossi-tomerforbecomebehaviorthe?rstwithtime,respectandmodelsofindividualcus-generalizationsNationalpossible.

topriceandpromotionstoresamplespermitmanufacturerstomakea?cultsinglemarket.thatGoodmightrandombedistrustedsamplesifmadefromdistributiontoobtaincalstudiesofofstorescannersbecauseoftheirregulararegeographicstilldif-databutcanthisdeterminewillchange.salesresponse

Empiri-MarketingScience27(1),pp.29–48,?2008INFORMS

tolookingpromotionandpriceatonofferings.

retailer’sacrossresponsestores,toinformationthestoremanufacturers’canlevelbepromotionalgatheredand,byners,Themostdramaticnewservicestimulatedbyscan-smallhowever,grocerytomediumissizedtheinstrumentedmarket.Thisisaforstores.Inaddition,citywiththescannerscityisinallmajorhardwarehighcablebeisintroducedtelevisionsothatcoverageandpre-selectedsplitcablements.setupandIn-storetoreceivehouseholdpanelscanobservationsdifferenttelevisionadvertise-per’ssoaremarkablycompletecanpicturealsobeofconducted,theshop-promotions,marketingenvironmentispossible:sales,prices,sion),advertising(bothnewspaperandtelevi-istising,idealcoupons,foravarietydisplayofandtesting:shelf-facings.newThesettingusingMuchstoremeasurementpromotions,andetc.

products,adver-modelbuildingliesaheadstep.householdItthesewillvariousfocusonservices.achoiceThemodelpresentapplicablepaperisonetoindividualdatacollectedinpanelsassociatedwithmentedTobystoresstoredataorinstrumentedontheshoppingmarkets,environment.supple-exampleindicateofholdsamajorofbrandscannerthetaskatofcollectedhand,coffeeindata.FigureapanelThe1displaysanofmarket100house-shareoverallshowsstandandtrendgreatpredictandinvariationoverayear’stimebothinsuchspeci?cbehavior.

peaks.Wewishtounder-2.TheMultinomialLogitChoice

TheityattributesofmultinomialModel

choosinglogitmodelcomputestheprobabil-hasofalltheanalternativesalternativeasavailable.afunctionofthedecisiontheappealinwhatmarketing.variables.ofbeingstochasticandyetTheadmittingmodelHlavacVariousandauthorsLittle(1966)haveuseemployedasome-itandealership.automobilesimilarmodelbuyertopurchasesrepresentathecarprobabilitythattheiructs.pre-test-marketSilkandUrbanevaluation(1978)imbedatatheparticularlogitindescribePunjandStaelin(1978)employprocessforthenewmodelprod-toandcompareReckerstudents’(1979)choiceprovideofabusinessgeneralschools.expositionGenschsionthe?ttingabilityofthelogittothatofregres-andhastheanforevenshoppers’moreextensivechoosinggroceryhistoryofstores.Thelogitpredicting?eldofe.g.,carorantransportationapplicationinbusindividual’splanning,(DomencichchoiceparticularlyforandMcFaddenofmode1975).oftravel,2.1.AsAxiomaticaxiomaticachoicesideranindividualderivationmodel,View

the,i,whichmultinomialconfrontedwebrie?ylogitpermitsanwithaoutline.choiceCon-from

GuadagniandLittle:ALogitModelofBrandChoiceCalibratedonScannerData

MarketingScience27(1),pp.29–48,?2008INFORMS

31

Figure1

TheShareofPurchasesofaMajorCoffeeBrand-SizeasRecordedinaPanelof100KansasCityHouseholdsShowsGreatVariability(DatesShownAretheStartingDaysofFour-WeekPeriods)

60

50

Purchase share

40

30

20

10

MAR 08.79

MAY 03.79JUN 28.79AUG 23.79OCT 18.79DEC 13.79FEB 07.80

4 week periods

aset,Si,ofalternatives.Inoursettingthealternativeswillbedifferentproductsinacategory.Wesupposethat:

(1)Alternativek∈Siholdsfortheindividualapreferenceorutility,

uk=vk+??k??

(1)

where

vk=adeterministiccomponentofi’sutility,tobecal-culatedfromobservedvariables,and

??k=arandomcomponentofi’sutility,varyingfrom

choiceoccasiontochoiceoccasion,possiblyasaresultofunobservedvariables.

(2)Confrontedbythesetofalternatives,individ-ualichoosestheonewiththehighestutilityontheoccasion.I.e.,theprobabilityofchoosingkis

pk=P??uk≥uj??j∈Si????

(2)

Notice,however,thatthisprocedureproduceslargerutilityvaluesinamodelthatexplainsmorevariancethaninonethatexplainsless.Weshallobservethisphenomenoninourempiricalwork.

Givenassumptions(1)–(3),itcanbeshown(Theil1969,McFadden1974)thatindividuali’schoiceprob-abilitieshavetheremarkablysimpleform

????vk

evj??(4)pk=e

j∈Si

Thisexpressionisknownasthemultinomiallogit.

Wenotetwopropertiesthatwillbeusedlater.First,since(4)canbewritten

????

e??vj?vk????pk=1

j

(3)The??k,k∈Si,areindependentlydistributedran-domvariableswithadoubleexponential(Gumbel

typeIIextremevalue)distribution

P????k≤????=e?e??

???

???<??<????(3)

Thisformofthedistributionappearsto?xthemeanandvarianceof??quitearbitrarily,since(3)hasamean0.575andavariance1.622,bothdimension-less.Amoregeneralformwouldincludeafurtherloca-tionparameterandascaleparameter.However,anylocationparameter,evenonedependentonk,canbeabsorbedintovkwithoutlossofgeneralityand,sincethescalingofutilityisarbitrary,wecansetitsothatthevarianceofthe??kisthe1.622valueimpliedby(3).

itfollowsthatutilityisundeterminedtotheextentofanadditiveconstant.Thus,forexample,ifapricevariablehasanin?ationarytrendthataddsaconstanttoallalternatives,pkwillnotbeaffected.

Second,pkisS-shapedinvkwhenothervjareheldconstant.Therefore,asshowninFigure2,verylargeorverysmallvaluesofvkmakepk?atandinsensitivetochangesinvk.

Wealsonotethat,asthevarianceoftherandomcomponentofutilitygoestozero,thescalingof(3)pushesindividualvj(andanydifferencesbetweenpairsofvj)towardin?nity.Asaresult,thelargestvkproducesapkthatgoesto1,whileothersgoto0,aswewouldwish.

Inourcasetheindividualchoice-makersarehouse-holds.Wedonotknowwhethertheirbehaviorsatis-?estheassumptionsusedtoderive(4).However,the

GuadagniandLittle:ALogitModelofBrandChoiceCalibratedonScannerData

32

Figure2

ChoiceProbabilityIsS-ShapedinUtilityvk

Choice probability (pk)

Utility (vk)

conceptanormalizedlatentvariableofutility(orpreferenceorattractiveness)asandfunctionandofachoiceprobabilitythatissome1981).

alonghistory(Lucethat1959,variableYellotthas1977,muchMcFaddenappealalternativesAchiefcomplaintabout(4)isexistingmightalternative,anewonesayessentiallythat,ifweaddtothethekth,theidenticalnewtosomeityreasonablybeexpectedtosplitk’salternativeprobabil-insteadandleavetheothersuntouched,but,by(4),willTheofissuereduceiswhethertheprobabilitieschoicessatisfyofallthealternatives.assumptionAppendix“independencefromirrelevantalternatives.”(SeeingVarious1schemesforfurtherhavediscussion.)

beenproposedforthemthechyinvolvepotentialdif?culty(McFadden1981).overcom-ManyofThusorinstantatreetreestructurearrangingrepresentationthatthegroupsalternativesintoahierar-ofcoffeessimilarmightalternatives.haveinbrandsinonebranchandallregularbrandsall(4)another.bratedadoptingWeshallstaywiththesimplemultinomialtheknownapplication,modelthewillpragmaticviewthattestsofthecali-pitfalls.

however,determineweitsendeavorquality.Intosettingavoidupits2.2.TheLinearUtility

forofalternativedeterministickwillcomponentbeofacustomer’sutilityofobservedandthesewillvariables,beattributescalledexpressedofthetheattributesasalinearoffunctionk.Someenvironmentothersmaybeattributesoftheproduct(e.g.,price)favor(e.g.,incomeorstore)thatcustomerdifferentiallyorthegeneralonealternativeoveranotherforsomereason.Invi??k=bjkxi

T

jk(5)

j∈wherexijk=observedvalueofattributejofalternativekfor

bcustomerutilityi,

jk=Werequiredshallweightofattributejofalternativek.

fordropclarity.

thesuperscriptiwhenitisnotMarketingScience27(1),pp.29–48,?2008INFORMS

breaktheFromamodelingpointofviewuct(1)Tattributesintotwoclasses.

itisconvenientto

k={attributesbutmayhavefeaturesuniquethatothertoalternativeproductsk}.Aprod-jables∈Twhichcontributetoitsutility.Forsuchdoattributesnothavek,theicoef?cients.maybedenotedbjkandvari-Although(2)byTx=jk

C{attributescommontoallalternatives}.uniquelyannioustoattributeeachproduct,suchasapricemodelmightbeassignedaswouldasingleinthenumberofparameterswouldmoreuseparsimo-priceFordenotedsuchhaveattributeattributesthesameacrossj∈coef?cientallproducts.Tforallalternatives.ThenpriceCi,Inspecializedbjandvariablesformxjk

.thecoef?cientsmaybe

vi??(5)becomes

??k=bjkxij∈Tjk+bjxi

j∈Tjk??(6)

k

C

toAlthoughstillstartmodelalinearbuilding,formwefornoteutilitythatisanaturalplace

thecanobservationalleavesthechoiceprobabilityquitelinearitynonlinearforvinkbewrittenvariables,xjk.Thenumeratorofpkevk=??

ebjkxjk

j∈T

sotiplicativethatthethanmodeladditive.

is,inanimportantsense,moremul-2.3.EquationsCalibration

tice(4)directly.wecannotandobserve(6)eitherpresentutilitiesthemodel.orInprac-ues.eachTheRather,individual:

dataconsistweobserveofachoicessetofchoiceandattributeprobabilitiesrecordsval-for??yk

??n??=?1if??

oncustomerthenthchoiceichoosesoccasionalternative??ki0otherwise??alongtivesonwitheachthechoicevaluesoccasion:

oftheattributesofthealterna-xi

jk

??n??=valuepurchaseofattributeoccasionjforforcustomerproductki??

onnthofInwithinaproductourcasebyachoiceaorobservationisthepurchaseconstantstheproductcustomerclass.Theonbtheoccasionofbuyingjkandtioncompletepurposes,tobedeterminedbycalibration.bjareForunknowncalibra-vation,setofeachdataattributeacrossalternativesisthoughtofashavingaalternativeevenfordoesthoughanattributeuniquefortoeachaspeci?cobser-anotheralternatives.notappearTohandleinthethisutilitysituation,expressionssuchtowhichattributeitisisnotassignedrelevant.

azerovalueforalternatives