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Live shopping promotions: which categories should a retailer discount to shoppers already in the store?


Digitalization allows retailers to target customers with personalized promotions when they enter the store. Although traditional promotional retailer objectives, such as store visit, become obsolete once the shopper is already in the store, retailers still tend to target customers based on indicators that drive store visit, such as recency, frequency, and monetary value (RFM). In order to improve promotional efficiency, the authors propose targeting shoppers based on information derived from regularity patterns in individual interpurchase times at the point of sale. When compared to RFM-based targeting, the proposed live targeting approach translates into higher redemption rates (+ 10.5 percentage points), revenues (+ 42.3 percentage points), and purchase frequencies (+ 44.2 percentage points). The findings emphasize the importance of promotional timing and of considering customers’ outside potential for dynamic in-store targeting.


Digitalization is one of the key drivers of personalization in retailing. In particular, online marketers have the opportunity to deliver the right promotion (or content) to the right customer at the right point in time (Johnson et al. 2013; Wamsler 2021; Zhang and Krishnamurthi 2004) due to customer-specific data collection. In-store coupon systems that provide customers with personalized price promotions for their current shopping trip—such as the CVS coupon centerFootnote 1—enable marketers to do the same offline (e.g., (Breugelmans et al. 2015; Gabel and Guhl 2021; Gabel and Timoshenko 2021; Gedenk et al. 2010)). Specific to both, online and instant redemption in-store coupons, is that the time since the last purchase in a category is a valuable source of information for regularly purchased categories, since it can be used to provide customers with well-timed promotions.

For traditional out-of-store promotions such as flyers or leaflets, retailers often focus on redemption rates as a promotional metric. High redemption rates reflect that attractive products have been on offer. However, they are also indicative of store visits, which makes redemption rates a relevant metric for retailers. Conditional on store visit, however (i.e., when the shopper is already in the store), high redemption rates more likely reflect shoppers who would have bought these products anyway (i.e., even without the promotion). In this case, high redemption rates indicate promotional expenditures that are most likely avoidable. Therefore, the question for dynamic in-store or live targeting is how to identify the product categories which a customer is not likely to purchase during the focal shopping trip but rather purchases at the competition. We argue that this question cannot be addressed well by cosine similarity (CS)-based (Levy and Goldberg 2014) or RFM-based targeting metrics—that retailers and providers of targeting solutions typically use—since these metrics are uninformative about both, what and when customers purchase at the competition, and therefore about customers’ outside potential.

Due to their simplicity, RFM-based models are among the most popular approaches for segmentation and predictive modeling (Verhoef et al. 2002). To detect customers with outside potential, who remain unobserved under existing targeting methods, such as CS- or RFM-based targeting (Verhoef et al. 2002; Kumar and Reinartz 2012), we suggest analyzing regularities in customers’ category purchase patterns (i.e., interpurchase times). Instead of analyzing customer behavior on the overall basket level, we focus on the category level. This seems practically feasible and promising for two reasons: (1) Customers’ store loyalty is category driven (Bell et al. 1998; Zhang et al. 2017) and (2) Personalized price promotions are often run on the category level (Osuna et al. 2016; Reutterer et al. 2017; Venkatesan and Farris 2012).

Our approach to detect regularities in purchase patterns provides the focal retailer with insights into an individual’s true category-level interpurchase times (involving unobserved purchases at the competition), category-level share-of-transactions, and reaction to price promotions, only using observed purchase data as model input. We validate our model estimates using two years of data from a European consumer panel in five product categories and two years of transaction data from a European grocery retail chain in seven product categories.

The aim of our study is to provide retailers with a category-level approach to improve the dynamic targeting of personalized live promotions and thereby increase a retailer’s share-of-transactions in a product category. Using the data from a focal retailer who offers loyalty cardholders seven CS-based personalized price promotions when they enter the store, we show how to improve the selection of promotions compared to CS- and RFM- based targeting.

Our research is related to three different streams of research: customers’ share-of-wallet, personalized price promotions with a focus on timing, and machine learning-based targeting approaches. We estimate customers’ category-level share-of-transactions—a construct related to customers’ share-of-wallet (e.g., Chen and Steckel 2012; Jang et al. 2016). Share-of-transactions (similar to share-of-wallet) can be used to select customers for targeting based on their growth potential. Moreover, personalization plays an increasingly important role online and offline (Grewal et al. 2011), as customers expect offers and promotions to be personalized (Capgemini 2017). Selecting categories for personalized price promotions based on customers’ true category-level interpurchase times is an important step in the personalization process as it ensures promotional relevance and allows retailers to increase customers’ category-level share-of-transactions. Furthermore, we relate our research to recent targeting approaches from the realm of machine learning.

We suggest live targeting of customers based on their category-level share-of-transactions and the overall time since their last category purchase. This new targeting approach is our main contribution. Based on an ex post application of our approach with the information available at the respective time and a matching analysis, we show that live targeting substantially improves the efficiency of personalized in-store price promotions relative to CS- and RFM-based targeting. We find that the redemption rate in the target group based on our model is significantly higher than the redemption rate in the CS- and the RFM-based target groups. Moreover, we find that our proposed targeting approach has a stronger impact on revenues and purchase frequencies than the RFM-based approach. Our results illustrate that our targeting approach is successful in proposing promotional products to customers that they would likely have purchased at a competing retailer otherwise.

The remainder of this article is organized as follows. We classify our contribution within related areas of research. We then introduce and evaluate our proposed model before illustrating its implications for customer targeting. Finally, we conclude with a general discussion of the findings and limitations of our study and provide an outlook on prospective research avenues.

Literature review

Related literature on share-of-wallet and related concepts

While previous research has mostly focused on share-of-wallet—using a variety of similar but distinct definitions (e.g., Chen and Steckel 2012; Du et al. 2007; Glady and Croux 2009)—our study involves the related construct share-of-transactions. In the following section, we briefly define both terms and provide an overview of existing research, which we summarize in Table 1.

Table 1 Overview of related research

Most commonly, the total expenditures of a customer in a particular product category define his/her size-of-wallet, while the proportion of category-level expenditures at a focal company defines his/her share-of-wallet (e.g., Kumar and Reinartz 2012; Jang et al. 2016). We, however, focus on the proportion of a customer’s category-level transactions at a retailer. This is equivalent to share-of-visits (cf. Mägi 2003) but at the category instead of basket level. We do so, as we are particularly interested in purchase incidences and their timing. Moreover, our share-of-transactions metric could be extended to share-of-wallet when it is multiplied by a customer’s category-level spending. We model share-of-transactions as the long-term probability that a customer purchases at a focal retailer in a particular category. In addition, we focus on customers’ outside potential (cf. potential-of-wallet, Glady and Croux 2009) involving their transactions at competing retailers. These are precisely the purchases that a focal retailer would like to turn into his/her own. To the best of our knowledge, we are the first study to analyze category-level share-of-transactions in grocery retailing based on the transaction data of a single retailer. So far, studies in grocery retailing have relied on customers’ self-reports (Mägi 2003) or panel data (Meyer-Waarden 2007) and have analyzed share-of-wallet measures on store level (Mägi 2003).

Existing studies that have focused on multiple product categories in financial services have directly incorporated cross-category effects (symmetric effects for ten categories: Du et al. (2007); asymmetric effects for two categories: Jang et al. (2016)). However, the variety of product categories in grocery retailing complicates the inclusion of cross-category effects. For this reason, we have decided not to include separate cross-category effects but to include the impact of basket-level purchasing behavior on category-level share-of-transactions via semi-informed priors in the Bayesian estimation process. This approach incorporates cross-category purchase behavior through basket information while decreasing complexity.

Our approach to derive category-level share-of-transaction estimates requires only transaction data and does not rely on data augmentation strategies through customer surveys. In line with Glady and Croux (2009), who were the first to use customer survey data only for model validation (not for model estimation), we use panel data to validate our models, which we ultimately run on the data from a single grocery retail chain.

The key objective of share-of-wallet research is to identify and target customers with outside potential (i.e., high potential-of-wallet) (Chen and Steckel 2012; Jang et al. 2016; Du et al. 2007; Glady and Croux 2009). We follow this line of research as we select categories in which customers still have outside potential (i.e., low share-of-transactions, high potential-of-transactions) and we extend this research by incorporating information on true category-level interpurchase times in the category selection process.

As in grocery retailing, personalized price promotions occur frequently, we control for their impact on customers’ share-of-transactions. To do so, we estimate a measure of customers’ reaction to purchases on personalized price promotions; i.e., an increase in share-of-transactions.

Related literature on (personalized) price promotions and the importance of timing

Our research contributes to the existing research on (personalized) price promotions—such as coupons—and the crucial role of timing. Coupons are still widely used by customers, as a recent survey by Inmar (2018) highlights: 88% of customers use coupons, and 83% of the customers using coupons indicate that the coupons influence their shopping behavior. At the same time, demand for personalization has increased; according to a study by Capgemini (2017), 65% of customers become frustrated when promotions are not personalized.

In our empirical application, we focus on categories in which customers have made purchases but are still able to expand their share-of-transactions because they frequently purchase at competing retail chains (cf. Gedenk et al. 2010; Osuna et al. 2016; Venkatesan and Farris 2012). This enables us to leverage the category-level share-of-transactions information that we infer based on customers’ transaction data at a retailer. Our research follows Osuna et al. (2016), who derive brand-level and category-level guidance on drivers of redemption rates and incremental sales (cf. p. 248, Table 5). We extend their perspective by incorporating (coupon) timing when selecting the categories for which to offer personalized price promotions at a particular point in time.

There has also been research on the timing of in-store coupons, illustrating that the average observed category-level interpurchase time does not coincide with the point in time where coupon redemption is most likely (Vuckovac et al. 2016). In contrast with our study, however, Vuckovac et al. (2016) do not relate coupon redemptions to the true category-level interpurchase times (i.e., involving observed and unobserved purchases) nor do they model potential effects of promotions on share-of-transactions (i.e., endogeneity).

Regarding the optimal timing of personalized promotions, Zhang and Krishnamurthi (2004) are among the first to acknowledge its importance, along with discount depth, by investigating what discount to offer and to whom on a given shopping trip. They optimize discounts conditional on store visit while accounting for the importance of timing through inertia and variety-seeking as time-varying behavioral traits. Johnson et al. (2013) take the analysis of customized promotions one step further by allowing customized promotions to influence customers’ purchase timing. They analyze what discount to offer to whom and at what point in time from the perspective of a manufacturer. For their analyses, they use panel data and the data of a single retail chain which they treat similar to panel data (i.e., no store switching). We provide a summary of the relevant literature on the timing of personalized price promotions in Table 1.

Related literature on machine learning-based targeting approaches

Loyalty program datasets may contain hundreds of thousands or millions of customers with dozens of shopping trips. Therefore, considering cross-category or even cross-product effects in models for personalized targeting is typically not feasible when traditional modeling approaches are used. However, important recent contributions (see Table 1) in the field of machine learning (ML) even allow for considering cross-product effects in a sparse form. ML approaches for product choice modeling show an exceptional performance and good scaling properties for targeted price promotions (Gabel and Timoshenko 2021; Jacobs et al. 2016; Ruiz et al. 2020).

Ruiz et al. (2020), for instance, model how customers select products and consider interactions between products and price changes. They test their efficient posterior inference algorithm on a large dataset containing shopping baskets from a grocery chain and identify complementary and substitutable product relationships.

Recently, Gabel and Timoshenko (2021) developed a deep-learning model at the product level to optimize the assignment of personalized in-store coupons. They find that their model performs particularly well when cross-category promotional effects are pronounced. Their highly flexible nonparametric product-level model allows for the detection of a broad variety of interesting relationships in an exploratory way. One of their key findings (Gabel and Timoshenko 2021, p. 18) is that the last purchase of a product in a category is extremely important in improving their forecasts compared to other benchmarks. More specifically, the more recent the last purchase, the lower the likelihood of a purchase in that category in the near future. Their finding is well aligned with our more restrictive parametric assumptions and (like our model) in full contrast with RFM-based targeting approaches that many large retailers use (assuming that the response probability is higher when a customer’s last purchase is more recent). Thus, our paper complements the more explorative nonparametric work of Gabel and Timoshenko (2021) with a parametric model. Differences between their product-level approach and our category-level model can also be found in terms of customization effort and generalizability of the findings. While Gabel and Timoshenko’s (2021) model is very convenient (no customization effort) in the sense that no categories or cross-product effects have to be laboriously defined, an advantage of our proposed methodology is that our parametric model yields insights that (due to the parametric nature) can easily be generalized for use in heuristic approaches.

In contrast with the work by Johnson et al. (2013) or Gabel and Timoshenko (2021), our study focuses on the category level instead of the brand or product level, taking on the perspective of a grocery retail chain instead of a single manufacturer (e.g., Ailawadi et al. 2006). Both, product-level models and category-level models have their merits. If promotions are offered at the category level, they provide more freedom of choice to customers than promotions that are limited to specific brands (e.g., discounting all shampoo brands vs. discounting a specific brand). Thus, if customer satisfaction is a retailer’s key objective, category-level promotions seem more attractive as they preserve customers’ freedom of brand choice. In this context, the private label share in the assortment may also influence whether a category- or product-level approach to promotions should be pursued. Retailers, like Aldi or Migros that have a large private label share may prefer a category-level approach in order to let the consumer make the final brand or product choice within the category. In contrast, retailers with many brands in their assortment like EDEKA or LIDL may leverage the competition between manufacturers and let manufacturers pay for “their” promotions. In such a case the product-level approach of Gabel and Timoshenko (2021), which provides information about substitutes (e.g., the likelihood of buying a Coke decreases with a recent purchase of a Pepsi), is more closely linked to manufacturer’s objectives. However, retailers do not only focus on the costs of promotions. As mentioned above, an important objective for retailers is to increase their customers’ category-level share-of-wallet. In this case, the category-level perspective seems particularly attractive since it is directly linked to this important objective. An advantage of our approach is that we model purchases at the competition, which is necessary to estimate a focal retailer’s share-of-transactions.

With the retailer perspective in mind, we propose to target customers who are about to cover their category-specific needs at competitors of the focal retailer, as they have a comparatively low share-of-transactions. Our targeting approach is based on information about true category-level interpurchase times, customers’ category share-of-transactions, and customers’ sensitivity to promotions.

In particular, we suggest the following two-step in-store targeting approach to grocery retailers. At the beginning of every shopping trip, a customer scans his/her loyalty card and receives a set of (in our case seven) personalized price promotions on a printout. (1) The system used to determine the set of personalized price promotions per customer should use the true category-level interpurchase time to decide for which categories a promotion would be well timed at that particular point in time. (2) Among these categories, the system should select the ones where the particular customer has a relatively low share-of-transactions (i.e., highest potential-of-transactions). This ensures that customers get personalized price promotions that are relevant while the retailer uses the opportunity to turn competitors’ sales into own sales. Note, that this is in strong contrast to RFM-based approaches which prioritize recent and frequent buyers.

Model and methodology

Our model follows Chen and Steckel’s (2012) approach to solve the incomplete information problem, which describes the general issue that retailers lack information about customers’ transactions with competitors.Footnote 2 We adapt and extend the assumptions to our particular application of improving the targeting of (personalized) price promotions at a grocery retail chain. In the following, we give an overview of the model assumptions; we provide more detailed information on the respective assumptions in Appendix 1 and Appendix 2.

Model assumptions

1. Individual true category-level interpurchase times \(T_{ir}^{\prime }\) (involving observed and unobserved purchases) are Erlang (2, βi), βi ≥ 0, distributed with \(t_{ir}^{\prime }\) describing the rth true interpurchase time of customer i.

$$T_{ir}^{\prime } \sim {\text{ Erlang}}(2, \beta_{i} ), \;f(T_{ir}^{\prime } ) = f(t_{ir}^{\prime } ;2, \beta_{i} ) = \beta_{i}^2t_{ir}^{\prime } \exp ( - \beta_{i} t_{ir}^{\prime } ), \;t_{ir}^{\prime } , \beta_{i} \ge 0$$

The expected mean of the Erlang (2, βi) distribution is 2/βi and describes a customer’s average true category-level interpurchase time. The Erlang assumption identifies our model as it determines which purchases the focal retailer does and does not observe (Chen and Steckel 2012).Footnote 3

2. A customer’s individual probability of purchasing in a given product category at the focal retailer (conditional on his/her category-level purchase) is determined by a Bernoulli process. The focal retailer observes a category-level purchase of customer i with probability pi. We call this share-of-transactions (i.e., ShoTi) and assume that the customer’s purchase probabilities across categories are in general independent and only related due to the basket prior of the ShoTi.

3. When a customer purchases on promotion in a particular category at the focal retailer, this increases his/her category-level probability of purchasing at the focal retailer. As this positive effect decreases over time, a customer i’s share-of-transactions at point n in time is given by:

$${\text{ShoT}}_{in} = \left\{ {\begin{array}{*{20}c} {p_{i} + \delta_{i} \exp ( - a_{i} \frac{{ {\text{tslpp}}_{in} }}{{\frac{2}{{\beta_{i} }}}})^{ } , {\text{ if}}\;{\text{tslpp}}_{in} \ge 0} \\ {p_{i} , {\text{otherwise}}} \\ \end{array} } \right.$$

With δi increase in his/her category-level share-of-transactions (i.e., δi ≥ 0), tslppin time since last purchase on promotion at point n in time, ai decay parameter (i.e., ai ≥ 0).

4. We do not specify a dropout process but assume that the data are right-censored. Thus, customers remain active customers of the focal retailer during the complete observation period in the respective categories.

5. To account for the impact of basket-level share-of-transactions (i.e., store-level purchase behavior) on category-level share-of-transactions at the focal retailer, we use a semi-informed prior.

It follows from our assumptions that the expected observed interpurchase time Tir of an individual i in a category at point n in time is:

$$E(T_{ir} ) = \frac{2}{{\beta_{i} }} \frac{1}{{{\text{ShoT}}_{in} }}$$

Derivation of a probability density function for observed interpurchase times

While the estimation of true category-level interpurchase times and of the share-of-transactions both require information that is unknown to a single retailer, we can jointly estimate them using the transaction data of a single retailer (Chen and Steckel 2012).

Given customer i’s vector of parameter estimates at point n in time θ, we can derive the probability density function for observed category-level interpurchase times Tir. For customer i, the distribution of observed interpurchase time Tir in a category at point n in time is described by the following equation:

$$g(T_{ir} |\theta_{in} ) = \mathop \sum \limits_{m = 0}^{\infty } (1 - {\text{ShoT}}_{in} )^{m} {\text{ShoT}}_{in} {\text{Erlang}}[t_{ir} | 2(m + 1), \beta_{i} ]$$

The term Erlang[tir|2(m + 1), βi] describes the application of the additivity property of the Erlang-k distribution, i.e., the sum of m independent random variables following an Erlang (kβi) distribution is Erlang (km, βi) distributed. As Eq. (4) provides the probability density function for the time between observed purchases in a product category, we have to allow for m unobserved purchases (at competitors) to lie between two observed purchases (at the focal retailer). The geometric distribution described by the first term gives the probability that m unobserved purchases lie between two observed purchases of customer i in a particular category at point n in time.

Bayesian estimation

For every customer in every category, the analysis begins with his/her first observed purchase. When estimating the model, we set up the following likelihood function for observed interpurchase times Tir, where i (to I) denotes the index for the customer and r (to Ri) denotes the rth observed interpurchase time indexing the point n in time as follows:

$$L = \mathop \prod \limits_{i = 1}^{I} \left\{ {[\mathop \prod \limits_{{r_{i} = 1}}^{{R_{i} }} g(T_{ir} |\theta_{{in_{ } }} )] [1 - \mathop \smallint \limits_{0}^{{t_{h} }} g(T_{ir} |\theta_{in} ){\text{d}}t]} \right\}$$

The second part of the likelihood function accounts for right censoring and describes the probability of observing no purchase between the last observed purchase and the end of the observation period (th) (Chen and Steckel 2012).

To derive model estimates, we follow a Bayesian sampling approach. To obtain individual priors, we run the model (in a reduced form without the impact of personalized price promotions) on customers’ basket-level purchases deriving an overall basket-level share-of-transactions for each customer, which is then used as the prior distribution for our category-level analysis. As sparse data and increasing complexity prevent us from including cross-category effects, the use of a semi-informed prior allows us to link store choice (i.e., basket-level information) to category-level purchases. We provide detailed information on the Bayesian estimation procedure in Appendix 2.

How price promotions increase category-level share-of-transactions (assumption 3)

Purchasing on promotion is likely to interfere with a customer’s purchase routine and therefore needs to be incorporated in the model to avoid biased model estimates. Per se, our model structure offers two potential avenues for modeling the influence of purchases on promotion on customers’ purchase behavior: through customers’ probability of purchasing at the focal retailer in a particular category (conditional on category purchase, i.e., the share-of-transactions) and through the true category-level interpurchase times (i.e., via the rate parameter of the Erlang distribution). We pursue the former approach, as it implies that a purchase on promotion affects observed interpurchase times through its impact on share-of-transactions but does not affect the true category-level interpurchase time (cf. Equation (2)). This is in line with our proposition that promotions can be used to turn competitors’ sales into one’s own (i.e., an increase in customers’ share-of-transactions).

Figure 1 exemplifies how a customer’s share-of-transactions is influenced by purchases on promotion. Every purchase on promotion triggers an increase in a customer’s category-level share-of-transactions of the same magnitude (i.e., δi ≥ 0). This increase levels off over time (i.e., tslppin increases and starts again at zero with the next purchase on promotion) (Pauwels et al. 2002). To allow for heterogeneity in the impact of time on the increase in share-of-transactions, we include a customer- and category-specific decay parameter (i.e., ai ≥ 0).Footnote 4 Moreover, we normalize the decreasing impact of time since the last purchase on promotion, with a customer’s average interpurchase time in the respective product category (i.e., 2/βi) to facilitate cross-category comparisons.

Fig. 1
figure 1

Illustration of the influence of redemptions on share-of-transactions

The increase in share-of-transactions in reaction to a purchase on promotion is conditional on a customer’s purchase on promotion. Thus, the expected effect of such a promotion on share-of-transactions is given by the category-specific probability to purchase on promotion times the average share-of-transactions increase effect.

Model validation using panel data

Before validating our model, we conduct initial exploratory analyses that serve as model-free evidence. To do so, we use a panel data set that was provided by a European consumer panel and that contains information about consumers’ regular and promotional grocery purchases. We analyze a sample of 85 panelists and their transactions in five product categories (i.e., 117 unique panelist-category combinations) from 05/2015 until the end of 04/2017. We provide more detailed information on our panel data set and the model-free evidence in Appendix 3.

We analyze the panel data set from the perspective of a single grocery retail chain, namely, the one that provided us with a data set on their customers that will be analyzed in the following section. Even though the number of panelists is relatively small (compared to the overall panel size), our analyses enable us to make two important observations: (1) We do not find strong evidence that purchase quantities at the focal retailer are affected by promotions. This finding justifies our focus on purchase incidence instead of quantities and is in line with our focal retailer’s store format (i.e., small-to-midsize neighborhood stores). (2) We do not find evidence for an impact of promotions on true interpurchase times. This indicates that purchases at the focal retailer would have happened even in the absence of a promotion or would have happened at the competition instead. On closer examination, we see that promotions immediately shift purchases from the competition to the focal retailer and have a longer-lasting (albeit small) positive impact on customers’ share-of-transactions. This supports our model, as we expect promotions to have an immediate effect that gradually levels off. Next, we validate our model using the panel data set.

As the panel data contain true interpurchase times and observed interpurchase times from the perspective of a single/focal retailer, we validate our model on both. The advantage of using panel data for model evaluation is that they include not only purchases at our focal retailer but also purchases at competing retailers and therefore provide a ground truth such that we can evaluate the predictions of our model.

Estimation procedure To estimate our proposed model, we apply a holdout-estimation approach and split the data into an estimation (i.e., 14 months) and a holdout set (i.e., 10 months) to assess the predictive accuracy of the model. We use a semi-informed prior to estimate category-level share-of-transactions. To determine the prior, we run a Metropolis–Hastings algorithm (with 2,000 iterations of which 1,000 are discarded as burn-in) on the basket-level purchase data of the selected panelists. We estimate all parameters through a Metropolis–Hastings sampling algorithm with 10,000 iterations and a 20% burn-in (i.e., we keep 8000 iterations; mmax = 10Footnote 5). We fix the decay parameter at ai = 0.1 (cf. Appendix 2).

Benchmark model To test our model, we benchmark its performance against the performance of a naïve Erlang-2 model. The naïve benchmark assumes that interpurchase times are Erlang-2 distributed, does not allow for unobserved purchases (i.e., each customer’s share-of-transactions at the focal retailer is 100%), and ignores the endogeneity arising from purchases on promotion.

Panel data results and discussion Table 2 contains the results of our model applications to the final panel data set. We validate the true and observed (see Eq. (3)) category-level interpurchase times against our model estimates using the mean absolute error (MAE) as an evaluation metric (cf. Jang et al. 2016). To reduce complexity, we focus on the weighted average of all product categories. The results of the estimation-holdout validation on observed interpurchase times are in a similar range to the results presented by Chen and Steckel (Chen and Steckel 2012). Our results show that our proposed model provides significantly lower MAE regarding true interpurchase times than the naïve benchmark model (p < 0.001). When comparing the MAE of the observed interpurchase time, the naïve benchmark performs on par with our proposed model.

Table 2 Model validation using panel data based on true and observed interpurchase time (holdout period: 07/2016 until end of 04/2017)

As the number of panelists for our focal retailer is rather small (i.e., 85 panelists and 117 unique panelist-category combinations), we have repeated our panel analyses focusing on the same product categories at the largest HILO retailer in the country of analysis (i.e., 2744 panelists and 4350 unique panelist-category combinations). Even though an initial exploratory analysis provided evidence that purchase quantities—and to a lesser extent interpurchase times—at the larger HILO retailer are affected by price promotions, we still find that our model estimates and model fit are robust (although we do not incorporate purchase quantities). The parameter estimates are in the same range as our parameter estimates regarding the focal retailer and so are our MAEs regarding true and observed interpurchase times (due to space constraints, detailed results are available upon request).

Model application using retailer data

Data description

For our model application, we use the transaction data from the loyalty program of a European grocery retail chain. Our data cover almost two years (i.e., 05/2015 until the end of 03/2017) and involve transactions of loyalty cardholders in 149 stores of the grocery retail chain in a major European country. For our analysis, we focus on a subset of loyalty cardholders with a sufficient number of transactions for fitting and evaluating the model (i.e., six purchases and at least one redemption of a personalized price promotion in the fourteen-month estimation set, and four purchases in the nine-month holdout data set). We select a subset of 3,335 loyalty cardholders and their transactions in seven product categories. The product categories are comparable to those analyzed in the panel data set but have been complemented by two fresh product categories (i.e., bananas and tomatoes, for which the grocery retail chain issues many personalized price promotions).

At the focal grocery retail chain, loyalty cardholders remain anonymous, as no personal information except for their transaction data is stored. The transaction data also contain information on personalized price promotions received and redeemed, starting at the point in time when the focal retailer initiated this loyalty program. Thus, our data include information on the first redemptions of all loyalty cardholders. To distribute the personalized price promotions among loyalty cardholders, the retailer uses an in-store coupon system, i.e., customers scan their loyalty card at the store entrance and receive a list of seven personalized price promotions that can be redeemed during their current shopping trip.

Such in-store coupons mitigate one potential drawback of customized checkout coupons: the temporal distance between receipt and redemption (Zhang and Wedel 2009). As coupon receipt coincides with coupon usage, such in-store coupons are expected to result in higher redemption rates than traditional checkout coupons as they work through pull (from the customer) instead of push (from the retailer). While customers cannot be lured to the store through personalized price promotions because they are received on-site, an in-store system can be useful to trigger unplanned category purchases (Briesch et al. 2009; Heilman et al. 2002; Inman et al. 2009).

Both the retailer and manufacturers can use the in-store coupon system to distribute coupons among the retailer’s loyalty cardholders. To choose the seven most promising personalized price promotions for loyalty cardholders, the proprietary system calculates the similarity between the loyalty cardholder’s transaction history and the active promotional campaigns, taking into account heterogeneity in price sensitivity when assigning the individual discount. Our analysis focuses on promotional timing, the customer’s share-of-transactions in the respective product category, and his/her increase in category-level share-of-transactions when redeeming a personalized price promotion. We neglect the discount height because it is already covered in the current assignment procedure. As we do not have information on regular one-size-fits all price promotions (for instance, via store flyers), we only capture the impact of redeemed personalized price promotions (i.e., increase in share-of-transactions). We provide summary statistics of the grocery retail data in Table 3.

Table 3 Descriptive statistics including mean and standard deviation of the retailer data set (estimation period: 05/2015 until the end of 06/2016)

The descriptive statistics show that there is considerable variation in the number of purchases, purchase spending, quantities, and observed interpurchase times across categories. Similarly, the promotion intensity (i.e., the number of received price promotions in the observation period ranges from 5.8 to 21.0) and redemption rates (ranging from 0.18 to 0.41) vary strongly across categories.

In addition to our model validation using panel data, we also validate our model on the data set provided by the grocery retail chain. As the data set only contains information on observed interpurchase times, we use those for model validation following an estimation-holdout approach. The results of this estimation-holdout validation are comparable to the results using panel data, for which we provide more detailed information in Appendix 3.

How to select categories per customer for targeting based on our model insights

The focal retailer can leverage the insights from our modeling approach when assigning personalized price promotions via the in-store coupon system. In particular, every time a customer scans his/her loyalty card, the system should use the true category-level interpurchase times to determine for which categories a promotion would be well timed at that particular point in time. These should be the categories to be considered when distributing personalized price promotions to a customer. Then, the system should look at the customer’s share-of-transactions in the categories to be considered and select the categories with the lowest share-of-transactions. This is because at the focal retailer, customers with a low share-of-transactions tend to have a higher share-of-transactions increase in reaction to a purchase on promotion. We illustrate this relationship with a third-degree fitted polynomial in Fig. 2.

Fig. 2
figure 2

Relationship between share-of-transactions and increase in share-of-transactions at the focal retailer (fitted third-degree polynomial curve)

As the personalized price promotions a customer gets are limited to seven, the focal retailer should focus on categories that combine the best timing and highest transaction potential according to our proposed approach.

Comparing our proposed targeting approach to an RFM-based targeting approach

To evaluate ex post whether our proposed model indeed helps target customers with personalized price promotions that are most likely to satisfy their demands at competing retailers, we compare our approach with an alternative RFM-based targeting approach.

In practice, heuristics such as RFM are often used to determine which customers to address with targeted marketing campaigns (e.g., personalized price promotions) (Verhoef et al. 2002). Such heuristics often achieve similar results, as do more advanced modeling techniques, as Wübben and von Wangenheim (2008) note. The popularity of the RFM model and its variants among practitioners arises from their simplicity. Information on RFM is observable, easy to obtain (also based on an anonymous loyalty card), easy to understand, and easy to analyze. RFM methods can even be applied on the product and category level (Heldt et al. 2021) which is particularly useful when assigning personalized price promotions. Even though companies (such as retailers and providers of targeting solutions) often keep their targeting rules confidential, customers who receive targeted price promotions have been shown to have higher recency, frequency, and monetary value scores than those who do not receive targeted promotions (Park et al. 2018). This is because recency and frequency provide information on whether a category is relevant for a customer while monetary value provides insights on customer’s price sensitivity. Therefore, we use the RFM approach as a relevant industry benchmark. Besides RFM-based targeting, another frequently implemented method to generate personalized price promotions is based on a customer-product matrix and the respective cosine similarity between a decomposed customer- and a product-vector (cf. Levy and Goldberg 2014). Since all the personalized price promotions in our dataset were generated by a CS-based recommendation engine, this approach serves as a basic benchmark for the RFM-based targeting approach and for our proposed targeting method.

We apply the RFM-based approach and our live targeting method to the data of the focal grocery retail chain. To do so, we take the data period that we used to estimate our model (i.e., 05/2015 until the end of 06/2016) to determine two groups of target customers for personalized price promotions. Then, we evaluate the target groups based on redemption rates, the parameters of our proposed model, and RFM-scores.

For the RFM-based target group, we assign scores for recency, frequency, and monetary value (i.e., total category-level revenues) to all customers in the respective product category. In particular, we assign values ranging from 1 to 5 to the recency, frequency, and monetary value quintiles and sum these values to receive a final score per customer and product category, which ranges from 3 to 15. This corresponds to assigning equal weights to all elements of the RFM model. We then select the customers with the highest RFM scores.

To determine the target group based on our proposed model, we follow a two-step process. First, we consider all customers who receive personalized price promotions at a point in time that is in line with our proposed model. Second, we rank order these customers according to their share-of-transactions estimate and select the customers per product category with the lowest share-of-transactions. This is in contrast with the RFM approach, which prioritizes customers with high frequency and high monetary value (i.e., proxy for a high share-of-wallet) as well as recent category-level purchases.

The number of customers per category who received promotions whose timing is in line with our proposed model is 980. We consider the promotional timing of a personalized price promotion to be in line with our proposed model when the deviation from the point in time for which we expect the highest likelihood of redemption was lower than or equal to 20%.Footnote 6 The categories in which the most customers received well-timed promotions are the fresh categories, namely, bananas, tomatoes, and bread (in total 870 of the 980 customers).

Since only 980 customers received well-timed promotions according to our proposed model, this serves as an upper limit for customer selection (i.e., share-of-transactions is not taken into account). To consider share-of-transactions, we then select the top 10% or the top 50% of customers with the lowest share-of-transactions (i.e., 98 or 490 customers). Importantly, we select customers who have received at least one promotion at the point in time suggested by our model during the application period; however, those customers could also have received and redeemed personalized price promotions whose timing was not in line with our proposed model.

When we apply the ex post selection strategies using the RFM-based approach, we select the customers with the highest RFM score to match the respective number of customers under our proposed approach (i.e., 98 or 490). The customers selected under the RFM-based approach have received at least one personalized promotion during the application period. Table 4 provides an overview of our ex post selection strategies.

Table 4 Summary of customer selection strategies

We compare the three targeting approaches. The basic cosine similarity-based recommendations, the RFM-based approach and the one using the insights from our proposed model—and present the aggregated results in Table 5.

Table 5 Comparison of different targeting approaches: CS, RFM, and live targeting

The results for the standard method of the retailer of generating targeted recommendations (i.e., CS) show a redemption rate of 27.7%. The results show that the redemption rate for RFM-based targeting (25.5% for top 10%, 29.7% for top 50%), is not significantly different from CS-based recommendations. The redemption rate in the target group based on live targeting (42.4% for top 10% and 33.8% for top 50%), in contrast, is significantly higher than the redemption rates in the CS- and RFM-based target groups. As expected, the increase in redemption rates for our proposed targeting method as compared to the other two approaches is higher when only 10% of the customers are targeted as compared to the situation when less stringent selection criteria (i.e., 50%) are applied. On average (over targeting 10% and 50% of all customers), the proposed targeting method leads to an increased redemption rate of 10.5 percentage points versus RFM-based targeting.

In addition to the redemption rates, Table 5 also indicates that the three targeting methods differ in terms of several characteristics. Since live targeting and CS-based targeting approaches do not select based on RFM scores, these scores are clearly below those of the RFM-based approach (14.03 for top 10% and 12.71 for top 50%). Naturally, the share-of-transactions parameter is lowest while the increase parameter is highest for the target groups based on our proposed live targeting model.

Our analyses reveal that most of the personalized price promotions are not well timed under CS- and RFM-based targeting approaches (as indicated by the lower redemption rates) which supports our focus on promotional timing. Next, we conduct further analyses on revenues and purchase frequency.

Revenue and purchase frequency analysis using propensity score matching

As a second illustration of the power of live targeting vs. RFM-basedFootnote 7 targeting, we use a matching analysis and measure effects on revenues and purchase frequencies. Using propensity-score matching, we estimate and compare the impact of targeting as opposed to not targeting customers under both approaches (e.g., Gensler et al. 2012; Ma 2016).

Following the RFM-based approach, a customer’s propensity to receive a promotion during the application period as opposed to no promotion is a function of his/her respective recency, frequency, and monetary value scores. Following our suggested targeting approach, a customer’s propensity to receive a (well-timed) promotion (as opposed to no promotion) is a function of his/her estimated true category-level interpurchase time, his/her share-of-transactions, and his/her response to purchases on promotion (i.e., share-of-transactions increase). We match customer pairs (one receiving a promotion under the respective targeting approach, the other one not) within a product category applying one-to-one nearest neighbor matching. As a distance measure, we use the Mahalanobis distance (cf. Gensler et al. 2012).

Propensity-score matching occurs based on customers’ transactions during the selection period and either takes the customers’ recency, frequency, and monetary value scores into account (RFM-based targeting approach) or the customers’ estimated true category-level interpurchase time, share-of-transactions, and share-of-transactions increase (our proposed targeting approach). We evaluate purchase frequency and revenues based on customers’ transactions during the application period. Table 6 contains the results of the revenue and purchase frequency analysis aggregated across product categories. Although fresh product categories (i.e., bananas, tomatoes, bread) drive our results as they contain the majority of observations (i.e., 74% under the RFM approach and 87% under our proposed approach), our results are stable across all categories. We find that both targeting approaches have a positive impact on customers’ purchase frequency and revenues. However, live targeting triggers greater absolute and relative increases in purchase frequency and revenues when compared to RFM-based targeting. For average purchase frequencies per customer and category, we find a significantly higher increase (p < 0.001) under our proposed targeting approach of 1.548 units (i.e., 113.74 percent) as opposed to 0.945 units (i.e., 69.54 percent) under the RFM-based targeting approach; i.e., an increase of 44.2 percentage points in terms of purchase frequency. The same holds for average revenues per customer and category as we find a significantly higher increase (p < 0.001) of 2.20€ (i.e., 99.28 percent) as opposed to 1.27€ (i.e., 56.96 percent) under our proposed targeting approach; i.e., an increase of 42.32 percentage points in terms of revenues. There are no significant differences between the control groups of both targeting approaches.

Table 6 Results of the revenue and purchase frequency analysis using propensity score matching

Thus, when selecting customers based on our model insights as opposed to selecting customers based on an RFM-based approach, the focal retailer can achieve higher purchase frequencies and revenues in addition to higher redemption rates. This also holds when we only select customers with particularly high RFM scores (i.e., ≥ 10) under the RFM approach and customers with rather low share-of-transactions parameters (i.e., ≤ 0.5) under our proposed approach.

Guidelines when implementing live targeting

When implementing live targeting, we recommend companies to first focus on customers for which there are enough category-level transactions to estimate our model. However, a retailer typically wants to use such a targeting approach for all customers in the loyalty program. This includes customers for which the retailer does not have enough observations to run our model. However, what a retailer can do for the customers with too few observations is to try to predict the parameters from our proposed model using customer, category, and store characteristics including the competitive situation around the focal store. We did this using a reduced form of our proposed model (that does not account for endogeneity and neglects the share-of-transactions increase parameter) and predicted the category-level share-of-transactions parameter for customers with too few observations.

We present the predictors and their relative importance in a boosted tree model in Table 7. The boosted tree modelFootnote 8 (Friedman 2002) yielded substantially better out-of-sample forecasting accuracy (r2out-of-sample = 0.54) in terms of root mean squared error (i.e., RMSE = 0.089) as compared to the results of an ordinary least squares (OLS) regression (RMSE = 0.168). Our results show that customer-level descriptors, derived from transaction data are of the highest relative importance followed by category-level descriptors. The spatial descriptors regarding the store and its catchment area hardly possessed any predictive power in explaining the share-of-transaction parameter. Table 7Footnote 9 shows that a customer's total purchase value with the retailer, the extent to which the customer seeks variety, her/his shopping frequency at the focal store, and the extent to which a customer can be considered habitual (Liu-Thompkins and Tam 2013) are the most important predictors of the share-of-transaction parameter. Total purchase value and more habitual customers relate to a higher share-of-transactions while the effect of variety seeking relates to lower share-of-transactions (i.e., customers with generally bigger overall interpurchase times and customers that purchase a wide variety of different products tend to have lower share-of-transactions).

Table 7 Relative importance of predictors used in boosted tree model

Thus, based on the results of this boosted tree model, parameters for customers with too few observations can be predicted. Based on these predictions, the same targeting logic can be applied as demonstrated for the customers with sufficient data for direct model estimation.

General discussion

Summary and contribution

Digitalization is one of the key drivers of personalization in retailing. It allows retailers to provide personalized promotions to their customers for those products that they are likely to shop elsewhere just when they enter the store. However, established targeting methods based on observed information such as RFM or recommender systems based on CS fail to incorporate the timing of promotions and neglect customers’ outside potential. In addition, a single retailer observes neither information on a customer’s true purchase timing across retailers nor information on the customer’s purchases at competitors (Gedenk et al. 2010). Knowing about such unobservable purchase patterns would enable the retailer to improve his/her targeting strategy by addressing customers with personalized price promotions in the right product category at the right point in time.

To do so, we suggest a live targeting approach that leverages customers’ purchasing patterns (i.e., interpurchase times) on the category level. Our approach uses observed purchase data of the focal retailer and provides the retailer with information on an individual’s true category-level interpurchase times, share-of-transactions, and reaction to price promotions—accounting for endogeneity arising through purchases on promotion. Retailers can use the category-level insights gained from our model to improve the targeting of personalized price promotions during a store visit.

To validate our model, we ran it on transaction data from a panel provider who tracks purchases on promotion and on transaction data of a grocery retailer who provides in-store personalized price promotions to his/her loyalty cardholders (Appendix 3 and Appendix 4).

We then provided a targeting strategy for retailers to choose the right category-level promotions for their customers when they enter their store: (1) Retailers should use the customer’s true category-level interpurchase time to determine for which categories a promotion would be well timed when the customer enters the store. (2) To select a subset among these well-timed categories, retailers should look at the customer’s share-of-transactions and the expected increase in response to purchases on promotion. At the focal retailer, the results showed that the promotional effect for well-timed categories is highest when the category-level share-of-transactions is lowest. Therefore, among those categories that are well timed when a customer enters the store, we recommend retailers to choose those where the customer’s share-of-transactions is lowest.

For a comparison of live targeting with CS- and RFM-based targeting, we then (ex post) simulated the application of different methods on data from a grocery retailer who actually provides targeted promotions when customers enter the store. Furthermore, we estimated the effect size of RFM-based vs. live targeting-based promotions using propensity score matching. These results show that the reaction of customers to personalized price promotions was significantly stronger when they faced live-targeted promotions as opposed to RFM-based promotions. Matching analysis shows that live targeting has a stronger impact on purchase frequency and revenues than RFM-based targeting (purchase frequency: + 113.74 percent vs. + 69.54 percent; revenue: + 99.28 percent vs. + 56.96 percent). The results illustrate that live targeting can assist retailers in a digital environment in identifying and targeting customers right before a purchase that might have otherwise taken place at the competition.

Limitations and avenues for future research

There are several limitations of our research that might be addressed in future research. First, our model is subject to parametric assumptions. However, the fact that even flexible models with less restrictive assumptions such as the recent nonparametric model of Gabel and Timoshenko (2021) come to similar conclusions, namely the negative impact of a recent purchase in a category on all products within the category, provides support for our parametric assumptions.

The inclusion of more categories, however, increases complexity, and the question arises whether large category-level models should directly incorporate cross-category effects (instead of indirectly via a semi-informed prior) (cf. Jang et al. 2016). Previous research has found that cross-category effects are often small or nonexistent (Gelper et al. 2016; Russell and Petersen 2000). However, recent research (Gabel and Timoshenko 2021; Ruiz et al. 2020) has found promising ways to model the impact of assortment interactions even at the product level. It would be interesting to see future work compare state-of-the-art product-level models like SHOPPER (Ruiz et al. 2020) or the deep learning method of Gabel and Timoshenko (2021) with our proposed live targeting approach.

Availability of data and material

We received the panel data from GfK for the purpose of this project and the transaction and promotion data of a grocery retail chain from our research partner (who wants to remain anonymous). Both data sets are proprietary. The results of all additional analyses are available upon request.

Code availability

To prepare our data and conduct the analyses, we used custom code in Python and R.


  1. Source:

  2. The incomplete information problem is similar to the problem of underreporting in underreported count models (e.g., Fader and Hardie (2000); i.e., panel participants not reporting all their purchases). A potential problem of underreporting could, for instance, arise when customers are not using their loyalty card. However, at our focal retailer customers do not receive price discounts without showing the loyalty card. Therefore, throughout this paper, we assume that underreporting is not an issue and that the focal retailer observes all purchases made at his/her own stores. The frequency of “missing information,” in contrast, should be much higher in the incomplete information setting like ours; i.e., when a retailer only observes purchases at his/her own stores and not at the competition.

  3. For reasons of simplicity, we assume that there is no time-varying unobserved heterogeneity that affects customers’ true category-level interpurchase times.

  4. To reduce complexity, we set the decay parameter ai to .1 when estimating our model. We benchmarked this value against ai ∊ {0.2, 0.25, 0.5} on data from a single grocery retailer and found that a value of .1 resulted in the lowest holdout error. Therefore, we chose this value for all of our analyses.

  5. We analyzed how many unobserved purchases lie between two observed purchases in the panel data set from the perspective of our focal retailer. In approximately 99% of all cases, the number of unobserved purchases between two observed purchases is smaller than or equal to ten (i.e., mmax ≤ 10).

  6. We took 20% deviation as a limit in order to still receive a high enough amount of promotions for evaluating the different targeting approaches. Of course, when applying the proposed methodology to the whole customer and category base of a retailer, the percentage can be further reduced to further improve the timing.

  7. Since we did not find any significant differences between CS and RFM (Table 5), in the second analysis, we focus on the comparison between RFM-based targeting and our proposed method.

  8. We used a boosted tree model with an interaction depth of 2, a shrinkage parameter of 0.01 and 10,000 trees in total.

  9. For the sake of readability, Table 7 only shows relative importance factors > 0.5. See Vuckovac (2018) for the full list of variables derived from purchase data, category data, and store characteristics.

  10. As we later split the data set into an estimation (i.e., 14 months) and holdout set (i.e., 10 months), we use the estimation set for our exploratory analyses.

  11. We also control for the quantity purchased on promotion. Our results stay robust when we do not take the quantity purchased on promotion into account.

  12. As for the retailer data we do not know mmax, we set it to 50. Thus, we allow 50 unobserved purchases (at competitors) to lie between two observed purchases at the focal retailer. Chen and Steckel (2012) allow for 100.


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We thank our research partner who wants to remain anonymous for providing us with transaction and promotion data of a grocery retail chain and GfK for providing us with panel data to evaluate our models. We are also grateful for the helpful feedback provided on earlier versions of this paper by Yuxin Chen, Thomas Reutterer, Florian von Wangenheim, Agnes Bäker, Christiane Barz, Harald van Heerde, Jochen Reiner, and Debora Costa. We highly appreciate Friederike Paetz’s clear guidance through the review process and the many useful recommendations of the review team. This research was supported by the University Research Priority Program “Social Networks” at the University of Zurich.


Open access funding provided by University of Zurich. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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All authors contributed to the study conception and design. The first draft of the manuscript was written by Julia Wamsler, and all authors complemented, adapted, and commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Martin Natter.

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Appendix 1: Model assumptions 1 and 2

Assumption 1: distribution of true category-level interpurchase times

We assume that individual true category-level interpurchase times are Erlang (2, βi) distributed (Johnson et al. 2013; Chen and Steckel 2012). The Erlang-k distribution is a special case of the gamma distribution that has an integer shape parameter k and contains the exponential distribution as a special case (k = 1). Whereas the exponential distribution is memoryless and is used to model random interpurchase times (e.g., Fader et al. 2005; Schmittlein et al. 1987), the Erlang-k distribution with k > 1 is used to model regular interpurchase times (i.e., purchase regularity increases with k) (e.g., Chen and Steckel 2012; Platzer and Reutterer 2016) and has been widely used on the category level (e.g., coffee, crackers, margarine, laundry detergent) (e.g., Johnson et al. 2013; Gupta 1988; Herniter 1971). However, the regularity (or randomness) of interpurchase times depends not only on the type of product category but also on the type of shopping trip (i.e., quick vs. regular trip to the store) and the type of shopper (Kahn and Morrison 1989; Kahn and Schmittlein 1989). One way to allow for both random and regular interpurchase times on the individual level would be to use a more flexible gamma distribution (Platzer and Reutterer 2016). However, to avoid the estimation of an additional shape parameter, we deliberately decided on the Erlang-2 distribution instead. Our decision is further backed by Wheat and Morrison’s (1990) summary statistic, which we used to explore reasonable values for k on the category-level data from our grocery retail chain. As our k-values exceed 1.5 (in six out of seven categories), the results support our use of the Erlang-2 distribution (Platzer and Reutterer 2016).

Assumption 2: probability of purchasing in a product category at the focal retailer

To determine which category-level purchases a retailer observes, we propose a simple (zero-order) Bernoulli process (e.g., Morrison and Schmittlein 1988). Thus, conditional on category purchase, the decision at which retailer to purchase is made anew each time with probability p.

We follow research proposing that customers’ store loyalty is also category-driven (Bell et al. 1998; Zhang et al. 2017). Thus, customers hold stronger or weaker preferences for a particular retailer depending on the product category (Zhang et al. 2017; Briesch et al. 2013; Drèze and Hoch 1998). These preferences are reflected in the probabilities of the Bernoulli process. In light of a customer’s planning of a shopping trip, one might argue that his/her category-level purchase probabilities should be allowed to correlate. We assume independence though, as our model is based on (observed) purchases and as the observed purchase pattern of one product does not provide additional information about the observed purchases of another product.

Appendix 2: Metropolis–Hastings algorithm

To derive parameter estimates \(\tilde{\theta }\), we apply a Metropolis–Hastings algorithm. All parameters are initialized randomly within the accepted parameter range. New parameter candidates are proposed based on a random walk, where \(\tilde{\theta }^{*}_{h + 1} = \, \tilde{\theta }_{h} + \, \Delta_{h}\), the jump to a new parameter point Δh is a draw from Normal(0, 0.16I) and I is the identity matrix of relevant size. The acceptance ratio α is derived based on the posterior probability of the initial parameter estimate and the proposed next iteration and can be formalized as follows:

$$\alpha_{h } = \frac{{ \pi (\tilde{\theta }_{h + 1}^{*} | Z) }}{{\pi (\tilde{\theta }_{h} | Z)}}$$

This suggested new point is always accepted if the posterior probability is higher relative to the previous point; if the posterior probability is lower, the proposed jump is accepted with certain probability, depending on αh and u, a random draw from uniform (0, 1), namely, as follows:

$$\tilde{\theta }_{h + 1} = \left\{ \begin{array}{ll} \tilde{\theta }_{h + 1}^{*} , &\quad {\text{if}}\; u < \alpha_{h} \\ \tilde{\theta }_{h} ,&\quad {\text{if}}\; u \ge \alpha_{h} \\ \end{array} \right.$$

where min{αh, 1} can be interpreted as the acceptance probability of a new point on the trajectory. Thus, the Metropolis–Hastings algorithm proceeds by randomly moving around the sample space, sometimes accepting moves and sometimes remaining in place. Because all individual parameters of each customer i are independent, the draws can be generated sequentially or in parallel for each customer. Based on the generated sample distribution of all parameters, individual point estimates can be derived using the mean of the generated individual posterior distribution.

In the Metropolis–Hastings algorithm, p and δ are restricted to individually and jointly (i.e., when summed up) lie between 0 and 1 and β between 0 and 2 for all customers. We set the maximum number of consecutive unobserved purchases to mmax and thus expect that customers purchase at most mmax consecutive times at competitors without any purchase at the focal retailer. We initialize all starting parameters randomly within the accepted parameter range and conduct 10,000 iterations in the Metropolis–Hasting estimation (we discard the first 2000 as burn-in).

We always use an uninformed flat prior for the parameters β and δ (Beta distribution with both shape parameters equal to 1). For parameter p, we use a semi-informed prior based on customers’ basket-level share-of-transactions. To derive the semi-informed prior, we first apply a reduced form of our proposed model—neglecting the impact of promotions by not estimating δ (i.e., ShoTi = pi)—to customers’ total basket-level transactions from the single retailer during the estimation period. For this basket-level estimation, we use a Beta-distributed prior for p with shape parameters 1 and 3 to account for the average share-of-transaction of the focal retailer within the metropolitan region. We then use the results from this basket-level estimation as a prior for the parameter p in the actual category-level share-of-transactions estimation. To do so, a Beta distribution is fitted to each individual trajectory of p based on Maximum Likelihood Estimation, with the two shape parameters of the Beta distribution constrained to be between 0 and 5 (thereby avoiding a too strongly informed prior, as this would prevent customers from having a category-level share-of-transactions that is substantially different from their true basket-level share-of-transactions). This prior distribution is then used in the Metropolis Hastings algorithm to derive the actual category-level share-of-transactions estimates.

Appendix 3: Panel data

Model-free evidence

Data The data we received from a European consumer panel were collected from 05/2015 until the end of 04/2017 and include the transaction history of the panelists across multiple product categories. We focus on the same grocery retail chain that provided us with transaction data from its loyalty program (which we analyze later), and we restrict our analysis to the five product categories with the highest number of unique panelists (which we also analyze using the data of a single grocery retail chain). We focus on panelists with enough observations (i.e., six purchases and at least one purchase on promotion in the estimation set, and four purchases in the holdout data set) in the respective category at the focal retailer. As a result, we end up with a final sample of 85 panelists in five product categories (i.e., 117 panelist-category combinations). The panel data also contain information about whether a purchase is made on promotion (although we do not know whether promotions are regular or personalized in the panel data set). We provide summary statistics of the panel data in Table 8.

Table 8 Descriptive statistics including mean and standard deviation of the panel data set (estimation period: 05/2015 until end of 06/2016)

Exploratory analyses To improve our understanding of how price promotions affect customers’ purchase behavior, we conduct a set of exploratory analyses.Footnote 10 We focus on the interpurchase time and purchase quantity of a purchase on promotion at the focal retailer and compare them via t-tests with the directly preceding interpurchase time and purchase quantity or the directly following interpurchase time and purchase quantity (the preceding and following purchase could have been made at any retailer). To ensure an unbiased comparison, we focus on promotions for directly preceding or following purchases that were not on promotion.

We present the results of our exploratory analysis in Table 9. (1) We do not find strong evidence for purchase acceleration, as the interpurchase time of a purchase that directly precedes a purchase on promotion is not significantly different from the interpurchase time of the respective purchase on promotion in four out of five categories. (2) There is no strong and unequivocal evidence for higher purchase quantities when consumers purchase on promotion (preceding purchase: in four out of five categories, there is no significant difference; following purchase: in all categories, there is no significant difference). (3) Our results do not show a significant post-promotion dip in four out of five categories.

Table 9 Exploratory analysis: Impact of redeeming a promotion on true interpurchase time and purchase quantity (estimation period: 05/2015 until end of 06/2016)

The findings regarding promotion incidences at the focal retailer have two implications. First, as we have no strong evidence that purchase quantities at the focal retailer are affected by promotions, this justifies the focus of our proposed model, which is on purchase incidence instead of quantities.

The lack of impact of quantity is in line with our focal retailer’s store format, as the retail chain has rather small-to-midsize neighborhood stores in a big city. Second, we do not find evidence for an impact of promotions on true interpurchase times. This indicates that purchases at the focal retailer would have happened even in the absence of a promotion or would have happened at the competition instead. As the aim of our research is to turn purchases at competitors into a retailer’s own sales, we further explore these reasons.

To do so, we investigate the impact of purchases on promotion at our focal retailer on his/her share-of-transactions. We look at purchases on promotion and the retailer’s share-of-transactions during the time period starting with the purchase on promotion and compare it to his/her share-of-transactions in directly preceding and directly following time periods. We ensure that the time periods directly preceding and following the time period with the purchase on promotion are not affected by other purchases on promotion at the focal retailer. We determine the length of the time periods that we use to calculate the retailer’s share-of-transactions individually using customers’ true interpurchase time.Footnote 11

When comparing the share-of-transactions in the period preceding the promotion with the share-of-transactions in the period starting with the purchase on promotion, we see an increase in share-of-transactions of 48.97 percentage points (from 27.70 to 76.67 percent). In the time period directly following the promotion, we see a drop in share-of-transactions of 45.13 percentage points (to 31.54 percent). This results in an overall increase of 3.84 percentage points in share-of-transactions. Thus, promotions have not only a short-term effect on purchases at the focal retailer but also a longer-lasting (albeit small) positive impact on customers’ share-of-transactions. This supports our proposed model in which we expect promotions to have an immediate effect that gradually levels off.

Appendix 4: Model validation using retailer data

Estimation procedure To estimate our model, we apply a holdout-estimation approach and split the data into an estimation (i.e., 14 months) and a holdout set (i.e., 9 months) to assess the predictive accuracy of the models. All parameter estimates are obtained using the Metropolis–Hastings sampling algorithm with 10,000 iterations and a 20% burn-in (i.e., we keep 8000 iterations; mmax = 50Footnote 12; semi-informed prior) for our proposed model. We fix the decay parameter at ai = 0.1.

Benchmark model To test our model, we benchmark its performance against the performance of a naïve Erlang-2 model.

Retailer data results and discussion Our proposed model estimates customers’ true category-level interpurchase time, share-of-transactions and the increase in share-of-transactions when a personalized price promotion is redeemed. Using data from a single grocery retail chain to validate the estimates proves difficult, as we only know about customers’ observed category-level interpurchase time. Thus, we can only validate our model’s predictions of observed category-level interpurchase time. Table 10 contains the results of our proposed model and provides category-level estimates for seven product categories. To facilitate model evaluation, we aggregate the estimates across all categories using a weighted average. We then calculate MAE to compare expected observed interpurchase times with the actual observed interpurchase times (cf. Jang et al. 2016).

Table 10 Model validation using retailer data based on observed interpurchase time (holdout period: 07/2016 until end of 03/2017)

Our results show that our proposed model provides significantly lower MAE regarding observed interpurchase times than the naïve benchmark model (p < 0.001). Although seemingly small, the magnitude of the difference in MAE is similar to that reported by Chen and Steckel (2012). It is interesting to note that on the level of individual observations, the naïve benchmark model strongly over- and underestimates the interpurchase times; aggregating across these cases then results in an average expected observed interpurchase time that is closer to the actual average observed interpurchase time than that of our proposed model. Taken together our results emphasize the importance of accounting for unobserved purchases and for endogeneity arising from purchases on promotion.

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Wamsler, J., Vuckovac, D., Natter, M. et al. Live shopping promotions: which categories should a retailer discount to shoppers already in the store?. OR Spectrum (2022).

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  • Personalized price promotions
  • Interpurchase times
  • Share-of-transactions
  • Targeting metrics
  • Dynamic targeting