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Figure4PredictedShareofPurchasesTracksActualShareCloselyfortheCalibrationSampleovertheCalibrationPeriod

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Perhapsamodestrelationshipexists,althoughonlySmallCandSmallEattheextremeshavesigni?cantt-values(2.5and?4.7).Onewouldconjecturethatanexplanatoryvariablemaybemissing.Atopcandi-datewouldbequalityofdisplayduringapromotion.SmallEstandsoutevenfurtherthanthiswouldbeexpectedtoexplainand,infact,isaslightlydifferentproductwithcertainuniquequalities.

Lookingatthecontrolvariablesfurther,weseethatregularandpromotionalpricecoef?cientshaveaboutthesamemagnitude.Wedonotexpectthisaprioribecausethepromotionalpriceislikelytobeadver-tisedinthenewspapersandbysignswithinthestore.Similarityofcoef?cientsdoesnotnecessarilyimplysimilarityofpriceresponse,however,becauseoftheothertermsintheutilityfunction.

Promotionisthemostinterestingcontrolvariable.Notonlyisitseffectlargebutusuallyitisaccom-paniedbyapricecutthatenhancestotalimpact.Somemarketersbelievetheeffectofpromotionstobeentirelyduetopricebutthatviewisnotsupportedbyourresults.Evenwithapricecutofzero,alarge

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probabilitymuchorexperiencegainisthatcalculated.specialThisisconsistentwithtomerfreestandingpositions)playdisplaysamajor(e.g.,roleend-aisleincus-importantTheresponse.

pastaquestionpromotioninpackagevariableisdirectedatanlikelycustomerbuystowhobuysaproductgoodsonpromotionmarketing:lessIsisitrepurchaseunderordinarythatproductcircumstances?thanacustomerThewhotionalneeded(1977),activity.forassessingTheworkofthetruevalueofpromo-answer(1981)Dodsonetal.(1978),andShoemakJonesanderandZufrydenShoafnegativeindicatesthatthepromotionalpurchasehasaTheeffectonsubsequentpurchaseprobability.thebuyingeffect.presentAmodelpromotionalpermitspurchaseanexplicitaffectsassessmentofpriorcustomerpromotionalthroughbrandpurchaseloyalty,variables.sizeloyaltysubsequentSupposeandtheThenperiod’sthebuys(usingutilitycontributionaparticularthataasaresultofthatbrand-sizeonpromotion.ofthepurchaseloyaltytovariablesthenexture3,andcoef?cientsthede?nitionsfromS6ofofxTable1,the??sofFig-is6andx7):

??3??92????0??125????1??+??2??97????0??188????1??=1??05??

However,promotionalthispurchasecontributionvariable:

isdiminishedbytheprior???0??22????1??=?0??22??

Thisofleavesaingnothavingnetpurchasedplusofthe0.83relativetoasituationoftheprocesstothenextpurchase,brand-sizetheatcontributionall.Carry-variablestheoriginalis:

purchasetoutilitythroughtheloyalty??3??92????0??875????0??125????1??+??2??97????0??812????0??188????1??=0??88butpurchaseisdiminishedvariable

bythesecondpriorpromotional???0??46????1??=?0??46

forpromotionalanetofpreviouspurchase0.42.Thevariablesnegativeeffectofthepriorperiodsauthors,butnetcontributionisinagreementoverthewithtwotionthesaysremainsthatthepositive.customerInisothermorewordsthecalcula-chasedpromotedbrand-sizethanifithadlikelynottobeenpurchasepur-beenanonpromotionalinthe?rstplace,purchase.

butlesslikelythanifithad6.

TheTesting

chases)holdoutbratedmodel.providessampleTrackinganopportunityof100households(1609pur-shareofpurchasestochallengebythe4-week

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periodonlyvariesdoeswillsharebeourloomprimaryimportantmethodinpracticeofevaluation.butitNotalsoaskseveraldramaticallyovertimeandoverbrand-size.share(1)Howquestions:

Wewelldoesperiodinthehold-outsamplethemodelduringpredictthebrand-sizesametimetime(2)Howusedwellinthedoescalibration?

themodelpredictshareduringdata(3)periodsCanthesubsequentmodel,usingtotheconstantscalibration?

derivedfromwithinthatsusindividualmixestogetherstores?Inallcomparingstores,predictpredictedsharesver-especiallyactual,purchasesforwelowneedshareameasurebrand-sizes,ofrandomvariation,Accordingly,maybeveryfewinaparticularwhosefournumberweeks.ofdictedsize,share.Forweobservationcalculateastandardiandanyerrorofpre-Giventhemodelpredictsaprobabilityofgivenpurchasebrand-pi.correct,theLettingthenullactualhypothesispurchasethatisbinomiallythecalibratedmodelisofobservations,

sdenotethepredictedshareandndistributed.thenumbers=??

np??in??

??

i=1SE??s??=

??n??1/2p??

i??1?pi??

n??

i=1

whereSE??s??isthestandarderrorofshare.

theFigurethecasearemodelof5displaysprediction,SmallA.anTheexampleofhold-outtracking,thedottedupperandlinelowerinthemiddleisdence±1.64SEandsoformapproximatelya90%solidcon?-linespre-periodband.TrackingSeptemberTheloyalty14,variables1978throughareinitializedMarchinaMarchusedforecastby8,thenthe1979takescalibrationthroughplaceOctoberduringtheperiod7,1979.fromsampleand17,1979onintopreviouslyanew,1980.

periodOctober18,1979throughMarch5,AAsmaybeseen,agreementmotionalgeneralupwardtrendiscaptured.isremarkablySoisagood.pro-interruptedpeakandthenadownwardtrendthatismodeltemporarilybyanotherpromotion.TheWeenvironmentcreditisimpressivethistodetailedintrackinginformationtheseupsanddowns.promotion,tors)andatpromotionalthetimeofpurchaseabout(namely,theprice,storehistorypluspricecutforallcompeti-variables.

summarizedinformationinaboutthethebrandcustomer’sandsizepurchaseloyaltytheOfonlyperiodspecialOctoberinterest18isthetoMarchgoodquality5,sinceofheretrackingwenotiningsample.outsideareusingInthetheahold-outforecasttimeperiodsamplebutalsoareforecast-periodusedwecontinuebythecalibrationtoemploy

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Figure5

TrackingofSmallAPurchaseShareinaHoldoutSampleof100CustomersShowsActualShareFallingAlmostEntirelyWithintheCon?denceBand

Share of purchases

60

Actual purchase sharePredicted purchase share90% confidence band

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20

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Notes.Theverticallineseparatesthecalibrationtimeperiodfromtheforecastperiod.Duringtheforecastperiodloyaltyvariablesareconstructedfromsimulatedpurchases.

theactualpricesandpromotionsofallthebrandsizes(i.e.,themodelisnotattemptingtopredictwhatmar-ketingdecisionswillbemade).Adilemmaarises,however,overtheloyaltyvariables.Loyaltyusespur-chasesinitsconstructionandyetthepurposeoftheholdoutsampleistopredictpurchases.Wecan,ofcourse,simplyusethepurchasesjustforthecon-structionoftheloyaltyvariables.Thisseemsjusti-?edsincewearealwayspredictingaheadintimerelativetothepurchasesenteringthecalculation.WeusethisprocedureforMarch8toOctober17,1979.However,forOctober18,1979toMarch5,1980,weadoptanew,MonteCarlomethodsoastobeabovereproachontheissue.Weconstructasyntheticpur-chasehistoryforeachcustomerasfollows:Whenanactualpurchaseisneededtoupdatetheloyaltyvariables,wedrawarandomnumberanduseittoselectabrand-sizetobepurchased,thisbeingdonesothattheprobabilityofpickingabrand-sizeconformstoitsmodel-calculatedpurchaseprobability.Astheforecastperiodproceeds,thesyntheticpurchasehis-toryunfoldsforeachcustomerandenterstheloyaltyvariables.

WeseeinFigure5that,evenwiththeseveretestofanewsetofcustomersandaconservativeloyaltycalculation,trackingisgoodinthepost-calibrationperiods.Figure6displayscorrespondingplotsforallbrand-sizes.Themodelfollowstheturnsandtrendsofsharequitewell.Enoughpointslieoutsidethe90%con?denceband,however,tosuggestthemodelhasnotcapturedallphenomenaand,indeed,weknowsomevariablesaremissing.

Inmostcasesthesharechangesarefollowedwithinastandarderrororsobutsometimestheabsolutelevelismissed.ThedeviationofSmallBinthefore-castperiodisanexample.Itwouldappearfromthequalityof?tingeneralthatthemodelcapturesquitewelltheaverageeffectof,say,promotion,butanindi-vidualpromotionmaybemoreorlesssuccessfulthanaverage.TheoneforSmallBinthemiddleoftheforecastperiodappearstohavebeenlesssuccessful.Thedeviationpersistsafterthepromotionbecausethemodelincreasesthecustomers’loyaltiesonthebasisoftheirassumedpromotionalpurchases,whereastheactualcustomersexperiencenosucheffect.Despitetheleveldifference,however,thedirectionalchangescontinuetobecorrect.

SmallDshowsaleveldifferencethatputstheactualshareentirelyabovethecon?denceband.Presumably,thisisduetoamiscalibrationofthebrand-sizecon-stant.Oncheckingback,itturnsoutthatthecalibra-tionsamplecontainsonly31purchasesofSmallDoutofatotalof1021duringthecalibrationperiod(3.0%share).Despiterandomselectionofcustomersforthetwosamples,theholdoutgrouphasmanymorepurchasesofSmallD,about93outof916(10.2%share)inthesameperiod.Alargerbrand-sizecon-stantwouldproduceabetterrepresentationoftheunderlyingpopulationthatbothsamplesaredrawnfromandwouldcertainlyimprovetheappearanceoftheSmallDplot.Bethatasitmay,thesharechangesaretrackedwellsothat,withrespecttothenormativequestionsofwhathappenswhenthedecisionvari-ablesarechanged,theSmallDplotisreassuring.Anotheropportunitytotestthemodelarisesfromthepresenceofdifferentstoresinthesample.Thepanelpopulationconsistsofstore-loyalcustomersfromfourstores,eachofwhichhasitsownindivid-ualpersonality.Oneofthemisalargeconventional

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Figure6

GuadagniandLittle:ALogitModelofBrandChoiceCalibratedonScannerData

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TrackingofPurchaseShareintheHoldoutSampleIsQuiteGoodforAlmostAllBrand-Sizes

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supermarket;anotherasmaller,moreneighborhoodmarket;stillanotherisawarehousestore;andthelastisaconventionalstorewithunconventionalmer-chandisingpractices.Thecalibrationprocesstakesnoaccountofthedifferencesamongstoresbeyondwhat-evermanifestationsthesemaygeneratethroughval-uesoftheattributevariables,nordoesthecalibrationconsiderthatdifferenttypesofhouseholdsmayshopatdifferentstores.

Breakingthecustomersdownbystorereducessam-plesizes.TocompensateweaggregateoversizestobrandlevelandalsofocusontwohighsharebrandsAandC.Figure7presentstrackingforthesebrandsinthefourstores.TheformatisasinFigure5:holdoutsample,predictedandactualshareswithcon-?denceband.Theresultsareverysatisfactory,withthemodelpredictingbehaviorwellacrossthefourstores.NoticeinparticularthetrackingofthedeclineofBrandCinStore3.Theimplicationisthatifweknowwhatishappeningtothecontrolvariablesinthestore,wecanpredictsharequitewell.

Theparsimonyofthemodeldeservesemphasis.Omittingthebrand-sizeconstantswhich,aswehavediscussed,determineonlyaverageshare,thecoef?-