The inter-store mobility of supermarket shoppers

The inter-store mobility of supermarket shoppers

Hongjai Rheea, David R. Bellb,1,*aKorea Information Society Development Institute, 1–1 Juam-dong, Kwa-Chun, Korea 427–070

bWharton School, University of Pennsylvania, 1400 SH-DH, Philadelphia, PA 19104, USA

Abstract

The allegiance of a particular customer, and the distribution across customers of strength of affiliation to a store are important indicatorsof store health. It is therefore important to understand the extent and determinants of shopper mobility among competing retailers. Whileshoppers often patronize many stores, they typically have a primary affiliation to a “main store” that captures the majority of their purchases.We examine, in detail, the tendencies of shoppers to transition away from the current main store and adopt another in its place. That is, ratherthan study all types of store switching behavior, we focus on the decision to change primary allegiance. The model is established in a discretetime hazard framework and estimated as random-effects probit. Data from 548 households taking 88,945 shopping trips among five storesare used to calibrate the model.

We find that state dependence is prevalent with nearly three quarters of the shoppers showing progressive attachment to their currentmain store. Interestingly, this finding is not simply driven by location (i.e., because shoppers are captive to a single store based ongeographical distance). More likely, shoppers are unwilling to give up the benefits of store-specific knowledge of assortment, layout andprices. Second, the decision to transition from a current main store is not influenced by temporary price promotions on a common basketof items: Shoppers will cherry-pick, but this alone does not cause them to change primary allegiance. The majority of transitions occur acrosscompeting stores of the same price format, which suggests “format loyalty” is an important aspect of shopper behavior. After controllingfor unobserved heterogeneity, we find little relationship between observable demographics and the transition probability. We do, however,find that shoppers who spend more per trip are less likely to change main stores, as are less frequent shoppers. Implications for retailmanagement strategy are discussed. © 2002 by New York University. All rights reserved.

Keywords: Shopping behavior; Retail competition; Store loyalty

Introduction

Retailers need to strike a balance between acquiring newcustomers (newcomers to the market), stealing competitors’customers and retaining existing customers. Simply put,success hinges on the ability to protect existing customersfrom turnover, and at the same time to attract more “out-side” customers. In this article we study the extent anddeterminants of shopper mobility among stores: We are notconcerned with temporary switches of small dollar value,but rather, transitions which involve a major change ofallegiance. “Mobility” is defined as the willingness of shop-pers to undertake these transitions and move the majority oftheir purchases from one store to another.

Our research adds to the findings of recent studies on

store switching and choice dynamics (e.g., PopkowskiLeszczyc et al., 1996; 1997, 2000) and shares some con-ceptual similarities with work in labor economics (e.g.,Blumen et al., 1955; Farber, 1994). In the latter literature,choice decisions are analyzed as if they collectively repre-sent a process of movement or potential movement betweentypes of employment. At any given point in time there issome probability that an individual will abandon the currentline of employment and transition out to another employeror career. Of interest in this study is the likelihood that ashopper will transition from the current main store to acompetitor as their preferred destination.

This notion of transition—as a major change in alle-giance—is conceptually and practically useful for customermanagement. Trips to stores involve time and financialoutlay and place constraints on the product and price as-sortment the consumer will encounter. Shoppers adapt tostore environments over time and indeed derive benefitsfrom the accumulation of store-specific knowledge such thatthey and are in effect willing to pay higher prices to shop in

* Corresponding author. Tel.: �1-617-452-2088.E-mail address: [email protected] (D.R. Bell).Present address: Sloan School of Management, MIT, Room E56–329,

38 Memorial Drive, Cambridge, MA 02142, USA.

Pergamon

Journal of Retailing 78 (2002) 225–237

0022-4359/02/$ – see front matter © 2002 by New York University. All rights reserved.PII: S0022-4359(02)00099-4

stores that they know well (Bell et al., 1998). One mighttherefore expect shoppers to deliberate carefully before de-veloping allegiances and having done so, remain somewhatfaithful, or at least think carefully before making majorchanges. This type of positive state dependence has been thefocus of previous work on brand switching and brand choice(e.g., Gonul and Srinivasan, 1993; Trivedi et al., 1994;Keane, 1997; Chintagunta, 1998; Seethuraman et al., 1999)but has yet to be fully explored within the context of storeselection decisions.

A reevaluation of the current preferred store may occurwhen the shopper perceives a substantial relative change inthe marketing environment. This could be the result of newinnovations in pricing and assortment by competitor stores,or perhaps by a relative deficit on the part of the currentstore. Alternatively, some shoppers may be cherry pickersor variety seekers by nature (e.g., Trivedi et al., 1994; Laland Rao, 1997) and simply change stores from time to timefor intrinsic reasons. In sum, we believe it is worthwhile toconsider the time series of customer selection decisions asindicative of relationships with stores, rather than as simplya collection of independent choices or transactions. The taskof the retail manager is to retain the existing customerswhile trying to capture new customers. To help the retailmanager discern the nature of this task, we provide answersto the following questions:

1. What is the extent of mobility? Do shoppers showpositive state dependence? If so, do they exhibit loy-alty to particular formats?

2. What are the key determinants of store mobility?How much variation is explained by the observablecharacteristics such as household income and familysize?

3. How do marketing activities such as aggregate pricedifferences between stores influence shopper mobil-ity?

4. Does the innate level of mobility change with theduration a shopper stays with the current main store?

The answers to these questions are valuable to retailmanagement. If most shoppers are immobile, this has im-portant implications for strategy—in particular the develop-ment of loyalty programs. If observable characteristics ofshoppers account for a large portion of the variation inmobility, retailers could tailor strategies accordingly. If mo-bility is influenced by temporary marketing initiatives suchas price cuts, coupons, and so forth, this has implications forhow to optimize resource allocation across the various com-ponents of the marketing mix. Increased emphasis on cer-tain types of expenditures, for example, may not be accom-panied by any long-term improvements in the size andstability of the shopper franchise.

Our key findings are as follows. There is a substantiallack of mobility—almost three quarters of the customers areunlikely to change their main stores. This is quite remark-able given the presence of several competing stores within

a small geographically contiguous area (i.e., shoppers arenot constrained by distance or the lack of options). Second,for shoppers who do transition, their behavior is not gov-erned by observable demographics: These effects are notsignificant after unobserved consumer heterogeneity is con-trolled for. This result is perhaps surprising given that Bellet al. (1998) show that demographic variables have a strongeffect on store choice. We do, however, find strong effectsfor the “shopping behavior profile” as average expenditureper trip and the frequency of shopping explain considerablecross-sectional variation.1 This is consistent with recentwork which links shopping behavior variables to overallconsumer price sensitivity (e.g., Ainslie and Rossi, 1998;Bell and Lattin, 1998; Manchanda et al., 1999).

Third, relative product prices on particular shopping tripsdo not have a significant effect on transition probabilities.This does not imply that price-related variables per se areunimportant, but rather, that long-term store selection ismore likely made on the basis of aggregate price images(e.g., Alba et al., 1994) instead of actual price differentialsat specific instances in time. This highlights an advantage ofour focus on transitions from main stores—as opposed totrip-to-trip store choices—as the dependent measure in thestudy: While temporary price cuts induce store switching,they need not generate long term gains in the number ofcustomers or levels of expenditure per customer. Fourth, thelikelihood of main-store turnover decreases significantly thelonger the current store remains the main store. This findingis consistent with the idea that it is more cost-effective toprotect existing customers than to try to acquire outsidecustomers.2 The paper is organized as follows. We providesome background and introduce the model and estimationapproach in the next section. Section 3 describes the dataand a descriptive analysis of the transition process. Section4 reports the findings and section 5 concludes the paper.

Background and model

Related work

A variety of related studies of shopper behavior investi-gate trip timing, store choice and store switching. Earlywork on store choice processes utilized the negative bino-mial model (NBD) and the Dirichelet (e.g., Wrigley andDunn, 1984). These relatively parsimonious models do asurprisingly good job of capturing aggregate patterns in thedata. Nevertheless, such approaches typically involve re-strictive assumptions regarding the homogeneity of the storevisit timing decisions and the way in which covariates canenter the model. In an effort to improve on these earlierapproaches, Popkowski Leszczyc et al. (1996) develop acompeting risk hazard model to analyze the store visittiming decisions of households, while also recognizing thattime to the next visit may depend upon the store currentlyselected. They find that the Gamma distribution provides

226 H. Rhee, D.R. Bell / Journal of Retailing 78 (2002) 225–237

the best characterization of the intervisit timing process andaccount for sources of observed heterogeneity. In a furtherextension of this work, Popkowski Leszczyc et al. (2000)incorporate a third shopper decision—the amount tospend—and also account for unobserved heterogeneity us-ing a finite mixture approach.

A second stream of research looks more explicitly at thestore choice decision (rather than the visit timing decision)of individual shoppers. Work in this area dates back toclassic studies on location (e.g., Huff, 1964), retail centerattractiveness (e.g., Fotheringham, 1988) through to moreconventional panel data studies (e.g., Bell et al., 1998).These approaches focus on store and shopper level charac-teristics and typically treat choice decisions as independentthrough time. A third important stream investigates thebehavior of store switching consumers. A number of authorshave examined store sales data and tried to relate switchingpatterns to the temporary marketing activities of stores(price and promotion in particular). Studies include those byKumar and Leone (1988) and Hoch et al. (1994). While theformer study found that consumers switch stores in responseto price promotions in a single category (in this case, dia-pers), the latter reports that most consumers appear rela-tively insensitive to increases or decreases in price. More-over, Bucklin and Lattin (1992) find no evidence for directeffects of marketing activity on store choice (i.e., consumersto do not switch stores in response to price specials on asingle category).

In this paper we build upon these various methods andfindings, yet establish a relatively new methodology, focus,and approach. Like Popkowski Leszczyc et al. (1996, 2000)we are concerned with the transition process from one storeto another, however we are more concerned with the prob-ability of transitioning within a specific period, than the timeto transition per se. Our objective is quite different: Wewant to understand the factors that influence the stability ofthe customer base at a particular outlet. Moreover, we areable to consider a class of store covariates that we notavailable to those authors.3

While much of the store switching literature (e.g., Buck-lin and Lattin, 1992; Kumar and Leone, 1998; PopkowskiLeszczyc, 1997) deals with store switching at a particularpoint in time, we are interested in factors (i.e., shopper orstore characteristics) that determine whether or not a par-ticular shopper is inherently switchable over a longer term.It is one thing to conclude that price promotions lead con-sumers to move among stores for particular trips and quiteanother to conclude that such activities are capable of in-ducing long term shifts in customer affiliation. This concep-tual difference also motivates our methodological approachin which we link a traditional random utility choice frame-work to a discrete time hazard model for the transitionprocess.

In sum, the distinguishing features of our work are afocus on: (1) individual shopper (versus aggregate) behav-ior, (2) a rich set of covariates including both store and

shopper characteristics, and (3) a unique modeling approachin which the decision to switch main store affiliation, ratherthan simply switch stores, is the dependent variable ofinterest.4

Model

A shopper’s relationship with a store can be understoodthrough an analysis of transitions across a series of consec-utive discrete time intervals of equal length. Central to ouranalysis is the idea that at each time interval, the shopperhas a main store: The main store is defined as the store thatreceives the greatest allocation of consumer expenditures inthe associated interval.5 Each discrete time period providesan opportunity for the shopper to continue with the storeselected previously as the main store, or to switch to analternative. We model the shopper’s decision to transition(or not) from the previous main store in the current timeperiod.

While our approach is different to that taken in a per-tripstore choice framework in which one models store selectionfrom a fixed competitive set, there are some importantsimilarities. The decision to transition away from a pre-ferred store is akin to the concept of “disadoption” of thestore and disadoption occurs when the shopper reaches acertain threshold level of relative dissatisfaction with thecurrent main store.6 As shown by Allison (1982), there is adirect mathematical relationship between a random utilitymodel of choice and a discrete time hazard model in whichthe decision maker decides to adopt a particular innovation.Our discrete time hazard formulation can also be viewed asa model of “rejection” as we uncover the factors that en-courage shoppers to abandon their historically preferredenvironments.

For shoppers, there are real benefits to maintaining af-finity with primarily one store, or at least a small set,including economic benefits from loyalty programs andcognitive effort benefits related to knowledge of the storelayout, and so forth (e.g., Tang et al., 2001). Despite this,the shopper may be motivated to seek out a new main store.The shopper could be inherently variety-prone, or a sub-stantial change in store features or policies could precipitatea switch. From a management point of view, it is importantto know whether such tendencies are related to observablecharacteristics of the shopper, or explicit actions taken bythe store. Moreover, the implicit cost of disadoption andswitching away from a main store could increase with timespent at that store.

Specification

We now describe the model specification. In the nextsection we discuss specific covariates and the importantconstructs of main store and time interval. The dependentvariable in the model is an indicator function that capturesthe transition behavior of the shopper, defined with respect

227H. Rhee, D.R. Bell / Journal of Retailing 78 (2002) 225–237

to the main store and time interval. Consider the storetransitions of a sample of shoppers i � 1, . . . , I visiting aset of competing stores s � 1, . . . , S. These shoppers areassumed to have access to all stores and the potential tomake active choices at each occasion. Let si,t be the mainstore of shopper i at time t. The dependent variable ortransition index yi,t is defined as

yi,t � 1�si,t � si,t�1�, (2.1)

that takes the value 1 if the current main store is differentfrom the previous main store. This occurs when the shop-per’s relative dissatisfaction with the current main storereaches a critical threshold. Using this interpretation of thetransition index we can invoke the notion of random utilityand define the probability of transitioning away from themain store. Specifically, we define pi,t � Pr(yi,t � 1), andthen using the standard normal link function, �, relate theprobability of turnover to observable and unobservablecharacteristics of the store-household pair at each time oftransition

pi,t � ��i � q�i,t� � m�i,t�i�. (2.2)

In equation (2.2) �i represents the unobserved innate mo-bility of household i, and qi,t is a vector of time-invarianthousehold demographic and shopping behavior variables aswell as k-1 time-varying dummy variables for the identity ofthe current main store (where store k is the base).7 mi,t

includes a measure of the distance between the shopper andthe store, the relative price for a common basket of goods,and duration dummy variables. � and �i are the responseparameters that are either assumed common or shopper-specific, depending on the model formulation to be esti-mated. To see the link between the discrete time hazardinterpretation and the random utility approach let zi,t repre-sent the relative utility of switching main stores. In this casewe have

zi,t � �i � q�i,t� � m�i,t�i � �i,t, (2.3)

where �i,tiid Normal (0,1). The relationship with the transi-

tion index is clearly seen when we write the probit model inequation (2.2) as

yi,t � 1� zi,t � 0�. (2.4)

Our model formulation has a very parsimonious structure.In addition, it links the discrete time hazard notion of tran-sitions to an underlying utility model where the latent utilityis the “utility of switching main stores” rather than theutility of a particular alternative per se. Thus, our model iswell suited to understanding the long-term evolution of acustomer base.

Observed and unobserved heterogeneityIt is well known that one must account for both observed

and unobserved heterogeneity in models of this type (seeAllenby and Rossi, 1999 for a review). This is especially

true in the store selection context given wide variationacross households in frequency of shopping and expenditurelevels. In order to fully explore the role of heterogeneity, weestimate four versions of the model. Model [1] representsthe base case and we restrict the response parameters to becommon across all shoppers in the sample. Model [2] al-lows for heterogeneity in intercept term �i N(�, ��

2) while�i � � and all i. Because the shoppers differ only in theirinnate mobility, this formulation approximates the so-called“mover-stayer” model in the job mobility literature (e.g.,Farber, 1994).8 Model [3] introduces heterogeneity into theslope parameters. Letting i � (�i, ��i)�, and xi,t � (1, m�i,t),the latent variable can be reformulated as

zi,t � q�i,t� � x�i,ti � �i,t, (2.5)

with i N(, ). Model [4] is motivated by recent work onthe role of shopping behavior variables in choice behavior(e.g., Ainslie and Rossi, 1998; Manchanda et al., 1999). Foreach shopper we compute the average expenditure per tripand the average shopping frequency. We are then able tobreak down the differences in household-level responseparameters i using the finite segmentation based on thesetwo variables. Using the sample medians as cut off points,we assign shoppers into four nonoverlapping segments (seeTable 1).

With wi as a vector of dummy variables representing thesegment, we allow the mean of the random effect parame-ters to interact with the segmentation variables. That is, i �N(w�i� , ). This approach allows us to tie our analysis ofunobserved heterogeneity in transition propensity to twovariables that are readily observable by retail managers. Italso opens up a way of linking our discrete time analysis oftransitions to existing findings from the literature on storechoice.

Caveats and estimationWe assume that the probability of turnover, that is,

switching main stores, is independent of the destinationstores. More generally, one could work with a durationmodel in which each pair of origin and destination storeshas its own hazard function (for a brand switching applica-tion see Vilcassim and Jain, 1991). In order to conserve datafor estimation we include only two duration variables (seenext section for details) and as a consequence it is notpossible to see the entire profile of the duration dependence.

Table 1Segmentation of Shoppers

Segment Weekly expenditure Weekly trips % of households

Large-Frequent Large Frequent 23%Large-Infrequent Large Infrequent 27%Small-Frequent Small Frequent 26%Small-Infrequent Small Infrequent 24%Cut-off (median) 32.45 dollars 1.259 trips H � 548


In theory, while an explicit hazard model with a flexiblebaseline hazard function could alleviate this problem ourdata argue in favor of our simple probit as an approximatediscrete time hazard model with two states (main store andother stores). This is because 30% of the shoppers neverchange their main stores during the entire sample period.

We assume the heterogeneity distribution is normal. Thisis a popular assumption in the marketing literature (e.g.,Allenby and Lenk, 1994; Allenby and Rossi, 1999), but cansometimes be restrictive. One alternative is to extend themodel with a nonparametric approach to heterogeneity us-ing a Dirichlet prior (see Escobar and West, 1995; Hirano,2001). We estimated this model and the results are verysimilar to those based on the normal distribution. This is alikely due to having many observations per household.9

To minimize the impact of the prior, we use either flat orweakly informative priors.10 Estimating the hierarchicalrandom effect probit model is straightforward using theGibbs sampling method (Gelfand and Smith, 1990) and thedetailed computational algorithm is well documented inprevious literature (e.g., Allenby and Rossi, 1999, Rossi etal., 1996). To assess convergence, we run 10 parallel Gibbschains with different starting values (Gelman and Rubin,1992). We found that the Gelman-Rubin statistics for mostparameters were very close to 1 after the first 5,000 itera-tions of each chain.

Data and preliminary analysis

We analyze interstore transitions of 548 shoppers shop-ping over a two-year period (June 1991–June 1993), takinga total of 88,945 shopping trips at five local supermarkets.We observe shopper demographics, location relative to eachstore, and the merchandizing activity of the stores. Table 2highlights differences in the number of trips received bystores and in their price formats.11

Main stores and time indices

To define transitions it is first necessary to establish atime interval over which main stores are defined, and thendefine the main store itself. In principle, we could define

every change of shopping place (e.g., consecutive trips totwo stores in a day) as a single transition, however, such asmall window will blur the distinction between “major”shopping trips and some temporary “fill-in” trips (Kahn andSchmittlein, 1989, 1992) in instances where customerscross-shop. Alternatively, if we set the time window toowide (e.g., one month), we would observe too few transi-tions per shopper (there are only two years of data, so wewould have a maximum of 24 time intervals per shopper).The length of window is therefore at the discretion of theanalyst, but must be established keeping in mind the objec-tive to create an appropriate definition of a “main” store.The empirical distribution of trips across shoppers andwithin shoppers over time suggests that one week is anappropriate time window for our data.12 We do the follow-ing: for each of the 104 weeks we define the “main” grocerystore of a shopper based on the total weekly expenditure (indollars) at each of the five stores.13 In a given week, themain store of a shopper is the store where the shopper spentthe most. From a customer management point of view,dollars spent is a meaningful measure for the retailer and itis striking that the main stores defined in this way accountfor approximately 94% of the total expenditure for all pe-riods. The weekly average grocery expenditure per shopperis $40.25, so that a typical household spends $37.71 perweek in their main grocery store and $2.54 in secondarystores.

Table 3 summarizes the transition sample. If each of the548 households has a shopping record in each of the 104weeks, we would have 56,992 (548 � 104) main stores,however, some households have missing weeks so we in-stead have 43,612 transitions. The transition index, which isthe dependent variable in our study, is constructed by com-paring the main stores of a household for two consecutiveweeks. It is set equal to 1 if the two stores are the same and0 otherwise. In other words, the transition indices are de-fined over 43,064 (43,612 � 548) pairs of consecutive mainstores. We use two duration covariates, which requires us toset aside more data. “Dur1 � 1” if the current main store hassurvived for more than a week and “Dur2 � 1” if the mainstore has survived for more than two consecutive weeks. As

Table 2Frequency of Trips (N � 88,945) and Pricing Format by Store

StoreI.D.

TripFrequency (%)

Mean BasketPrice (S.D.)

AdvertisingPricing Format

1 15933 (17.9) 22.22 (1.05) EDLP2 19346 (21.8) 22.61 (1.26) EDLP3 31706 (35.6) 25.78 (1.57) HILO4 12318 (13.8) 27.94 (2.34) HILO5 9642 (10.8) 27.72 (2.35) HILO

Note: For consistency with prior literature, we replicate the basket pricescomputed by Bell et al. (1998, p. 357), who also used these data.

Table 3Sample Selection Procedure

Sample Description Observation

Total weekly main store 104 week � 548 households 56,992Main store not defined Incidence of no weekly

purchase� 13,380

� 43,612Transition Pairs of 2-consecutive-week

main stores� 43,064

Initialization First 2 weeks per householdfor duration dummies

� 1,096

Hold-out Last 2 weeks per householdfor out-of-sample prediction

� 1,096

Calibration � 40,872


such, we have to exclude the first two transition observa-tions for each household (“Initialization” in the table). Wefurther divided the remaining sample of 41,968 transitionsinto a calibration sample of 40,872 transitions and a holdoutsample of 1,096 transitions consisting of the last two obser-vations for each household.14

In the calibration sample, the number of observations pershopper ranges between 34 and 101 (76.58 on average). Themean of the transition indicator in the calibration and hold-out samples is 0.183. This says that on average, customersdo not change their main stores very frequently. However,there is wide variation in transition rates across the house-holds (Fig. 1 displays the histogram of transition rates byhousehold). 162 households never change their main storesat all during the entire sample period, yet 17.1% householdsswitch their main stores in more than 40% of the weeks.

We examined whether the nonswitching behavior of the162 households is “forced” by geographical distance. Non-switchers have an average distance of 2.17 miles betweentheir current main stores and other stores and this is notdifferent from the average of 2.10 faced by the rest of thehouseholds. This implies nonswitching arises from con-scious choice and is not dictated by distance to other stores.

Table 4 contains the sample transition matrix by originand destination store and shows a clear stratification of thestores in terms of mobility. Shoppers are much more likelyto turn over to stores of the same price format (e.g., 88.9%of turnovers from store 1 (EDLP) were to store 2 (EDLP),and 87.3% turnovers from store 4 (HILO) were to store 3

(HILO)). They not only appear to be loyal to particularstores, but also when they do transition they remain loyal toparticular formats.

Selection of model covariates

While we do not develop specific hypotheses per se, theselection of model covariates is motivated by previous re-search. The covariates fall into two broad classes: (1) vari-ables that are household-dependent, and (2) those that aretransition-dependent. The first category includes demo-graphic and shopping behavior profiles, while the secondcaptures store characteristics (tailored to individual shop-pers). The covariates serve a substantive purpose and alsoallow us to control for observed heterogeneity.15 Shopper-dependent covariates capture the fact that the willingness toabandon a main store may be a consumer trait, whereas the

Fig. 1. Distribution of transition rates across households.

Table 4Store Transition Observations

Origin store Destination store

1 2 3 4 5 Total

1 (EDLP) 6,821 1,318 82 7 75 8,3032 (EDLP) 1,313 9,652 405 95 195 11,6603 (HILO) 78 405 11,109 1,171 434 13,1974 (HILO) 8 84 1,176 3,199 78 4,5455 (HILO) 84 188 418 87 3,486 4,263Total 8,304 11,647 13,190 4,559 4,268 41,968


transition-dependent covariates provide a role for store-specific characteristics to influence the consumer’s pre-ferred state (i.e., to shop in one store or another). The pricevariable represents the aggregate price advantage of onestore over the others in a particular week, independent of thedifferent shopping baskets of the households. Though some-what restrictive in nature, this specification is in line withthe previous research (e.g., Dickson and Sawyer, 1990) thatfinds that customers rarely recall the price of a specific itemwhen shopping, but can form impressions with respect tooverall price image (e.g., Alba et al., 1994).

Table 5 lists each variable along with a full description ofhow it is operationalized and the reports the mean andstandard deviation.16 The entries in the table indicate sig-nificant variation in each of the covariates utilized in thestudy.

Empirical analysis

We begin with model calibration and validation thenproceed to interpret the marginal posterior parameter distri-butions. Because the models are nested in an increasingorder of heterogeneity allowed for, it is straightforward todetermine the marginal impact of each additional compo-nent on the model fit by comparing the posterior estimates.All reported results (means and standard deviations) arebased on the last 5,000 posterior draws from the Gibbssampler whose convergence is verified by the first 5,000“burn in” iterations using the Gelman-Rubin statistic. Thesignificance of a parameter in a Bayesian analysis should bebased on the entire shape of the marginal posterior distri-

bution, however, an illustrative significance measure is con-venient for ease of exposition. Following Rossi et al. (1996),we say that a parameter is significant if the posterior prob-ability that the parameter has the same sign as the posteriormean exceeds 0.90.

Model calibration and validation

We computed the log marginal density17 for each modelusing an approximated bootstrap method (Newton andRaftery, 1994). It is clear from Table 6 that the fit of themodel increases with the corresponding increase in level ofheterogeneity. The magnitude of the improvement is sub-stantial when one compares models [1] and [4], howeverthere is a clear tapering off in the improvement of model [4]over model [3].

For “out-of-sample” fit, we predict the transitions of1,096 holdout observations (2 per household) using theavailable posterior draws from the corresponding Gibbssampler. Table 6 contains two different predictive measures.One is the average log predictive density, and the other theaverage percentage of correct predictions (i.e., the hit rate).Using either criterion, however, we see that the predictiveperformance significantly improves as we introduce heter-ogeneity in the intercept (model [2]) and also in responsesensitivity (model [3]). Model [3] is able to predict 80% ofthe holdout transitions correctly. In contrast, the differencein predictive performance between models [3] and [4] is notparticularly large. Though model [4] produced a superiorlog predictive density (�361.4 versus �365.1), there wasless than a 1% gap in hit rate in favor of model [4], which

Table 5Model Covariates

Covariate Description Means (S.D.)

Household-dependentFamSize The number of family members in a household 2.32 (1.38)Income Log of annual household income. The variable was imputed as the mid-point of the bracket that

each household belongs to.10.20 (0.92)

White 1 if the main household head is white 0.73News 1 if the household subscribes to at least one newspaper 0.36Old 1 if at least one household head is older than 55. the age variable is originally grouped by 6

categories.0.55

College 1 if at least one household head has a college equivalent degree. 0.44Single 1 if male or female household head is absent. 0.49Unemp 1 if no household head is working. 0.38Retire 1 if the main household head has retired. 0.32Expend Log of average weekly shopping expenditure ($) at all stores during the entire sample period. 3.57 (0.45)Trip Log of average weekly shopping trips at all stores during the entire sample period 0.27 (0.57)

Transition-dependentDistance The relative distance to the current main store differenced by the average distance to the other

stores�1.37 (1.55)

Price The relative price of a fixed shopping basket at the current main store differenced by theaverage price at all other stores for the week of transition

�0.75 (3.11)

Dur1 1 if the current store has retained the main store status for more than 1 previous week. 0.82Dur2 1 if the current store has retained the main store status for more than 2 previous weeks in a row 0.73


employs the two-way segmentation of the households byexpenditures and frequency.

One possibility here is that the disparity in predictiveperformance could be an artifact stemming from the smallsize of the holdout samples. To check this we re-estimatedthe two models using almost equal sized calibration (N �21,109) and holdout (N � 20,859) samples. In this case,model [4] maintains an edge in calibration sample fit(�5,922.0 versus �5,933.7). The difference amounts to aBayes factor (see Kass and Raftery, 1995) of 1.2 � 105 infavor of model [4], if we assume the prior odds to be one.For holdout, model [4] had a slightly higher log predictivedensity than model [4] (�8,052.2 versus �8,054.8), andmodel [4] had a superior hit rate (0.798 versus 0.794). Thus,we conclude that overall model [4] is marginally preferredover model [3].

Substantive findings

Table 7 lists the parameter estimates and shows in bold-

face those that are significant based on the 90% posterior-band criteria. The model is specified such that the turnoverprobability increases with the covariate effect, so the tableshould be read as follows: “the main-store turnover proba-bility is higher (lower) on average if the posterior mean ofthe associated parameter is positive (negative).” Differencesin the level of heterogeneity accounted for by each of thefour model specifications can be seen by looking across thefour columns of Table 7 (we elaborate on this shortly).

The effect of demographicsDemographic variables are an important source of ob-

served heterogeneity. In Model [1] the store turnover prob-ability is significantly higher for households subscribing toa newspaper (�4 � 0.08), and having unemployed (�8 �0.10) or retired heads (�9 � 0.07). This suggests that mainstore substitutions may be initiated by some new informa-tion (via promotion or advertising) on the relative merits ofthe alternative stores, and newspaper subscribers are morelikely to be exposed to such information. Furthermore, the

Table 6Comparison of Model Performance

Performance Criteria Model

[1] [2] [3] [4]

For calibration sample (N � 40,872) �14,999 �13,067 �11,950 �11,937Log Marginal Density

For hold-out sample (N � 1,096) �420.0 �386.4 �365.1 �361.4Log Predictive DensityHit Rate 0.769 0.784 0.800 0.809

Table 7Gibbs Sampling Results with Different Levels of Shopper Heterogeneity

Parameter Model 1 Model 2 Model 3 Model 4

DemographicsIntercept (�) 0.603 (0.46) Random effect r.e. r.e. with segmentsFamSize (�1) 0.038 (.006) 0.110 (.041) 0.010 (0.46) 0.029 (.038)Income (�2) 0.044 (0.12) 0.161 (0.35) 0.039 (0.38) 0.068 (0.53)White (�3) 0.010 (.021) 0.061 (.076) 0.121 (.092) 0.148 (.104)News (�4) 0.082 (.018) 0.062 (.083) 0.039 (.105) 0.024 (.093)Old (�5) �0.050 (.023) �0.033 (.102) �0.032 (.098) �0.032 (.111)College (�6) 0.034 (.019) 0.050 (.098) 0.113 (.100) 0.128 (.082)Single (�7) �0.019 (.022) �0.048 (.103) �0.073 (.106) �0.015 (.108)Unemp (�8) 0.105 (0.28) 0.280 (.126) 0.147 (.129) 0.155 (.119)Retire (�9) 0.072 (.027) 0.035 (.126) 0.034 (.150) 0.019 (.120)Shopping behaviorExpend (�10) �0.330 (.023) �0.727 (.095) �0.490 (.094) �0.518 (.125)Trip (�11) 0.248 (.016) 0.542 (.070) 0.305 (.080) 0.135 (.138)Store dummiesStore 2 (�12) �0.086 (.005) �0.144 (.033) �0.094 (0.84) �0.090 (.080)Store 3 (�13) �0.166 (.035) �0.187 (.056) �0.362 (.133) �0.347 (.132)Store 4 (�14) 0.141 (.048) 0.299 (.069) 0.274 (.138) 0.305 (.133)Store 5 (�15) �0.088 (.050) �0.030 (.071) �0.060 (.118) �0.088 (.134)Other variablesDistance (�1) 0.068 (.005) 0.075 (.008) r.e. r.e. with segmentsPrice (�2) �0.002 (.005) 0.001 (.005) r.e. r.e. with segmentsDur1 (�3) �0.411 (.026) �0.393 (.026) r.e. r.e. with segmentsDur2 (�4) �0.998 (.024) �0.405 (.026) r.e. r.e. with segments


opportunity cost of gathering such information will be lowerfor retired, or nonworking households.

Note, however that all effects of the demographic covari-ates disappear once unobserved heterogeneity is accountedfor (see columns 3 and 4 in Table 7). This implies that retailmanagers are unlikely to be successful in preventing detec-tions purely by using demographic targeting. It is of somecomfort, however, to see that the main effects of shoppingbehavior variables generally remain strong even in the moreflexible models.

The effect of shopping styleInterstore mobility decreases with average expenditure

per trip (�10 � 0) and increases with the average shoppingfrequency (�11 0). Frequent shoppers are price-sensitivein brand choice (e.g., Ainslie and Rossi, 1998) possibly dueto better knowledge of price distribution acquired throughexperience. This same phenomenon could also drive themto transition main stores more often. Large-basket shoppersare less sensitive to category level price promotions inselecting stores (Bell and Lattin, 1998) and their largerexpenditures per trip may lead them to expend more effortto initially determine the “right” store and stay with it.

In all four models, the duration variables are highlysignificant. The longer a shopper stays with a main store, themore likely the shopper is to continue with that store. Thiseffect is present even after accounting for both observed andunobserved heterogeneity. Further insight into the effect ofstate dependence can be gained by looking at how theexpenditure and frequency variables stratify the sample.The interactions for the random effects are shown underModel [4] in Table 8 (recall that the segments are identifiedby expenditure level (average dollars spent per week), andthen by shopping frequency (average number of trips perweek)). For both duration variables the turnover probabilityis lower for the large basket shoppers (for the same fre-

quency type). That is, the values of �3i and �4i are morenegative for (Large-Frequent) in comparison to (Small-Fre-quent) and (Large-Infrequent) in comparison to (Small-Infrequent).

It is also interesting to see that the main effect of thefrequency variable is no longer significant once the differ-ence in state dependence by the relative size of this variableis controlled for (see the estimate for �11 for Model [4]given in Table 7). In contrast, the cross-sectional differenceby average expenditure remains significant in Model [4](�10 � �0.52 in Table 7). In sum, large basket shoppers areless likely to transition away from their current main stores.

The effect of distance and store characteristicsThe chance of customer turnover increases when a main

store is more remote (�1 0 for models [1] to [3]). This isconsistent with prior work that shows a more convenientlocation has a positive influence on store selection (Huff,1964). The inconvenient store could therefore be subject to“double jeopardy”—the remote location works against ini-tial choice and also makes the store more vulnerable todefection. The interaction with the segmentation schemecan be seen from the estimates of �1i given in Table 8.Large basket shoppers, regardless of the shopping fre-quency, are less sensitive to the distance when deciding totransition from one main store to another (�� 1 � 0.18 versus�� 1 � 0.27 for small basket shoppers). This result is intuitivefor the following reason. The relative importance of a “fixedcost” such as distance traveled to the store decreases as thetotal expected cost of a shopping trip (travel time plusproduct expenditures) increases.

The absence of a basket price effect is worth noting. Forboth Model [1] and Model [2] �2 is insignificant. In Model[3] the mean of the random effects, �2i, remains insignifi-cant as do the interactions with the four shopping stylesshown in the segmented analysis of Model [4] (see Table 8).

Table 8Distribution of Random Effect Heterogeneity

Parameter Mean (�� , �� ) Variance (diag())

Model [2]Intercept (�i) �0.276 (.15) 0.73 (.07)

Model [3]Intercept (�i) 1.042 (.08) 0.47 (.08)Distance (�1i) 0.229 (.03) 0.46 (.03)Price (�2i) 0.014 (.01) 0.04 (.01)Dur1 (�3i) �0.509 (.05) 0.23 (.03)Dur2 (�4i) �0.374 (.05) 0.27 (.04)

Segment Model [4]

(Lge-Freq) (Lge-Infreq) (Sml-Freq) (Sml-Infreq)

Intercept (�i) 0.98 (.34) 0.70 (.38) 0.83 (.35) 0.76 (.38) 0.44 (.07)Distance (�1i) 0.18 (.06) 0.18 (.07) 0.27 (.06) 0.26 (.07) 0.25 (.03)Price (�2i) �0.02 (.02) 0.03 (.03) 0.02 (.02) 0.02 (.03) 0.05 (.01)Dur1 (�3i) �0.49 (.08) �0.74 (.12) �0.38 (.07) �0.58 (.10) 0.24 (.03)Dur2 (�4i) �0.30 (.08) �0.68 (.11) �0.24 (.07) �0.46 (.10) 0.28 (.03)


These results are consistent with the notion that shoppersselect main stores based on the relative price image rein-forced by past experiences, rather than by a more frequentanalysis of actual current price levels. That the null resultfor basket price persists in Model [4] suggests a modifica-tion of our previous claims regarding the effect of shoppingbehavior variables—average expenditure and shopping fre-quency—on shopper mobility. Earlier, we attributed someof the effect of these variables on mobility to the fact thatthey are strongly related to consumer price sensitivity (e.g.,Kim and Rossi, 1994; Manchanda et al., 1999). That is, wesimply rationalized that because less frequent shoppers areless price sensitive in brand choice, this means that onecould expect them to also be less mobile in changing mainstores. In other words “these consumers are insensitive toprice, so why would they change?” The fact that there is stillno variation in the price effect across shopper types seg-mented by basket size and shopping frequency as shown bythe mean values for �2i, suggests that some nonprice ele-ments could be contributing to the significance of the ex-pend and trip variables, shown by �10 and �11, respectively.While we cannot verify this directly, one could reasonablyconjecture that a large basket shopper, almost by definition,also has a more favorable impression of store layout, ser-vice, assortment and so forth, all other things equal, and itis this “lock in” that reduces the incentive to change themain store.

One key substantively interesting pattern emerges fromthis collection of empirical findings. While traditional de-scriptive and purely exogenous characteristics like demo-graphics do little to explain mobility, variables that explainthe shopper’s “state” are much more important. That is, theway in which shoppers are accustomed to shopping and thelength of time they have been affiliated with a particularenvironment. The good news is that while these character-istics may become fairly stable for many consumers, there isroom for the retailer to influence them. We explore thistheme in more detail in the next section.

Discussion and conclusion

Our research is motivated by the relative absence ofwork on customer mobility in retail settings. Most studiesfocus on transaction-specific choice behavior, rather thanthe long-term transition process that is the focus of thisresearch. As argued here, the notion of mobility is central tounderstanding customer allegiance and to the practice ofcustomer management. It is just as important for retailers tounderstand the drivers of long-term or stable shopper be-haviors, as it is to analyze the determinants of temporaryswitching behavior. In fact, it may be misleading to con-clude that a particular marketing tactic is useful when theonly real effect involves short-term switches and low dollarexpenditures. We offer the following general findings andimplications for retail managers (particularly, but not exclu-

sively, to those in grocery retailing or similar environ-ments).

Shopper behavior

1. Mobility. Supermarket shoppers are relatively immo-bile—in the sense that they are unlikely to makemajor changes in where they spend most of theirdollars—even in the presence of several competingalternatives. It is important to realize that this findingis not directly comparable to or in conflict with pre-vious findings that retail promotion has a positiveeffect on store substitution (e.g., Kumar and Leone,1988). While that effect is partly due to temporarycross shopping, our result pertains to the transition ofshoppers’ main association-–which is a much morestringent condition.

2. Observed Characteristics and Mobility. Once unob-served heterogeneity is controlled for, demographiccharacteristics play no role in explaining main-storeturnover. On the other hand, the observed “shoppingstyle” is highly predictive. Large basket shoppers andinfrequent shoppers are considerably less likely tochange their main-store allegiance. This finding com-plements and goes beyond existing work. While pre-vious papers have tied these variables to price sensi-tivity and store selection (e.g., Ainslie and Rossi,1998; Bell and Lattin, 1998) we show that they alsocontribute to stickiness with the preferred store over alonger time horizon.

3. Distance, Price Levels and Mobility. Shoppers aremore likely to change a main store if the store is lessconveniently located. Change is less likely for shop-pers who already spend large amounts per trip. Theseshoppers can amortize the relative inconvenience oflarger distances against the accumulation of otherbenefits across a wide range of product categories(e.g., lower product prices, preferred assortments,etc.). Temporary changes in price levels do not appearto have any real effect on mobility. While shoppersundoubtedly switch for some trips on the basis ofprice changes, these changes to do not induce anylasting transition from the favored or main store. Thissuggests that customers consider the aggregate priceimages of the stores (e.g., Alba et al., 1994)—perhapsin the initial selection of a main store—rather thansearch over prices at each trip and then select the mainstore on that basis.

4. Status Quo Bias. We find strong evidence for statedependence in store mobility: The longer a shoppercontinues with the current main store, the less likely atransition away becomes. This result complementsearlier work on brand choice (e.g., Keane, 1997) andcross-category purchasing behavior (e.g., Seethura-man et al., 1999). In total, nearly three-quarters of oursample shows state dependence.18 Most shoppers pre-


fer the status quo and this effect only increases withtime at the current alternative. This effect is no doubtreinforced by the benefits associated with consumerslearning about a particular store over time (e.g., storelayout, product assortment, etc.).

Implications for retail management

1. Prioritizing and Targeting of Shoppers. The relativelack of mobility in the sample and the tendency forshoppers to increasingly prefer the status quo overtime suggests that retail management should prioritizecustomers in the following order: (1) existing loyalcustomers, (2) new entrants to the market, and (3)shoppers who are potentially switchable from com-petitors. Existing customers are by nature less mobileand the longer they are immobilized the more likely itis they will remain in this state. New entrants to themarket may shop around initially, but will most likelysettle into a “steady state” of immobility. The thirdgroup will be the most difficult to attract and may bethe most expensive from a marketing resource pointof view. It is striking that many retail managementpractices appear to implicitly focus on (3), given thatour research highlights the inherent difficulty ofachieving any long-lasting gains with this group.

2. Shopper Identification and Metrics. Efforts to identifysegments of customers based on shopping style willbe more valuable than targeting on the basis of ob-served demographics. While such variables can ap-pear to be important in explaining mobility, all effectsdisappear once unobserved heterogeneity is ac-counted for. Given the strong effect of average basketsize in limiting mobility, retailers should measure itand try to increase it. This may be a more worthwhilegoal than simply increasing store traffic. The lattergoal could be accomplished by short-term price pro-motions that have no long-term positive effect on thecustomer franchise. An increase in the average basketsize should engender long-term benefits: cross-sec-tionally, there is a negative correlation between aver-age weekly expenditure and the probability of transi-tioning away from the main store (r � �0.21, p �0.01). It is interesting to speculate that basket size andstate dependence together create a “virtuous circle”for retailers: Large basket shoppers are the most sta-ble and attractive customers, and once shoppers startbuying larger baskets per trip, they increasingly favorthe status quo.19

3. Marketing Activity. Marketing activities center onlonger-term strategic issues (e.g., price format, posi-tioning, location, assortment, etc.) and more variableshort-term tactics (price promotions, features, cou-pons, etc.). We find some evidence that of the two,longer-term strategic choices by stores have moreimpact on shopper mobility. Table 4 shows that shop-

pers who transition do so to stores of similar formats(even though stores of different formats may be moreconveniently located). This suggests that the overallpositioning of the store is critical to the ability toimprove the customer franchise. A retailer wanting toactively target customers of a competitor should focuson a competitor of the same basic price format. Storelocation has some role to play as more convenientstores see less mobility overall. While we have notstudied it directly, the composition of the assortmentis vital in solidifying long term affiliation and is nodoubt linked to time spent in the store and averagebasket size—variables that have a significant impacton mobility. Retail programs that build store loyaltythrough the development of category-specific loyaltymay also be successful in this regard (see Dreze andHoch, 1998). Conversely, short-term price and pro-motion changes appear to have no significant influ-ence on the long-term composition of the customerbase.20

We began by noting that stores with less mobile cus-tomer bases are likely to be more successful over the longrun. The less mobile the customer base, the more the retaileracts as a “local monopoly” with respect to the shopperfranchise. A store with a more transient population of cus-tomers faces two disadvantages: (1) greater variability in therevenue stream, and (2) continual pressure to replenish thecustomer base. By linking the concepts of “random utilityfor switching” with a discrete time duration framework, wearrived at a relatively simple random-effects probit modelwith which to investigate this main store transition process.While parsimonious, the model also accounts for a consid-erable degree of observed and unobserved heterogeneity.

We document the relative lack of mobility and the pres-ence of strong state dependence, while also identifyingsome of the key drivers and moderating variables. The mostimportant drivers relate to shopping style rather than strictlyexogenous characteristics such as demographics. The goodnews for retail managers is that these “traits” can be subjectto influence by marketing activity and can easily be moni-tored through simple metrics such as average basket size.We hope this effort stimulates further work on what retailerscan do to limit mobility and improve the quality of theircustomer base.

Notes

1. In some instances demographics could correlate withshopping behavior profiles. We thank an anonymousreviewer for making this point.

2. Rosenberg and Czepiel (1983) contend that attractinga new customer to a brand costs more than six timeswhat is needed to keep an existing customer. This islikely to be a conservative estimate of the differentialin a store selection context.


3. There are also some methodological differences.Both studies account for observed heterogeneitythrough shopper covariates, however we account forunobserved heterogeneity in a Bayesian random ef-fects model.

4. As we discuss shortly, we link the discrete timehazard approach to mobility to a random utility for-mulation of the “utility of switching.” This offers theadvantage that the model can be estimated in a sim-ple binary choice framework, given the appropriatedefinition of the dependent variable.

5. We provide precise definitions of “main store” and“time interval” in Section 3. For the moment it suf-fices to consider these terms conceptually.

6. Relative dissatisfaction with the current main store isclearly mathematically equivalent to the case inwhich other stores become relatively more attractive.Furthermore, it is only the change in the relativedifference that is required to identify the model.

7. The store dummies change over time as customersmove across stores. This is the reason that qi,t has atime index. More justification for the covariates willbe given in the next section.

8. Technically, a pure stayer is a shopper with �i � ��.9. Details of these results are available from the au-

thors.10. Our results are not sensitive changes in priors. Again,

this is due to the large sample size per shopper. Theexact prior specification is given in a Technical Ap-pendix available from the authors.

11. These data come from the Stanford IRI Market Bas-ket Database. The first two stores advertise an EDLPformat, while the other three are HILO operators.Stores 1–3 are from different chains and stores 4–5are from the same chain.

12. A practical benefit of the one-week window is thatmany grocery retailers alter marketing variables suchas prices, store flyers and coupons on a weekly basis.

13. The average number of shopping trips per shopperper week is 1.42 and the standard deviation is 0.87.

14. To ensure our findings were robust, we also usedvarious other splits of the data and report the resultsin the next section. The qualitative findings wereunchanged and full results are available from theauthors.

15. We also control for unobserved heterogeneity viarandom effects. To our knowledge this is the firststudy of individual shopper transition behavior thathas such a rich array of covariates and fully accountsfor unobserved heterogeneity.

16. The distance variable is calculated from the shop-per’s home so we are not able to explicitly capturetrips initiated from work. We have no reason tobelieve that trip initiation varies systematicallyacross customers, so this should not introduce bias.Because only the difference will affect store selec-

tion, we subtract the average values of price anddistance for all other stores from the variables for thecurrent main stores (Fotheringham, 1988). We alsodefined the variables relative to the best of those forthe other stores, which is consistent with the notionof opportunity cost, however the results were similarto those reported here and we do not explore themfurther. Details are available from the authors.

17. The marginal density is the average likelihood inte-grated with respect to the prior density of the param-eters. See Kass and Raftery (1995) for details.

18. Table 8 shows that the variances of the heterogeneitydistribution for the duration parameters are large, soit is not immediately clear how many households arestate dependent in their selection of main stores. Toanswer this question, we computed at every iterationof the Gibbs sampler, the percentage of householdswhose duration parameters are both negative. From5000 iterations, the mean was 72.3%.

19. The overriding objective of increasing the averageorder size per customer and per visit also suggestsother important metrics. Retailers have long recog-nized that keeping a shopper in the store for longerperiods of time increases the incidence of unplannedpurchases (e.g., Park, Iyer and Smith). Store manag-ers should actively try to increase the time spent byshoppers as they walk through the store and manageto this metric accordingly.

20. While these activities do not lead to main store tran-sitions, we cannot rule out the hypothesis that suchactivities are important in keeping existing custom-ers. We thank an anonymous reviewer for this in-sight.

Acknowledgments

The authors are very grateful to Doug Honnold, IRI Inc.,for providing the data used in this study and to KeisukeHirano and Christophe Van den Bulte for comments. Wegreatly appreciate the suggestions and advice of the Co-Editors and three anonymous reviewers of this journal.

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The inter-store mobility of supermarket shoppers