Source: Vindevogel, B, D Van den Poel, and G Wets – Why promotion strategies based on market basket analysis do not work – 2004
The title of Vindevogel et al’s paper is thought-provoking, but also somewhat misleading – their position is not that promotion strategies based on MBA do not (ie never) work, but that the dynamics of sales response to price change are complex and there are identifiable reasons why a particular promotion strategy based on a particular MBA will not/did not work.
Time series analysis may be adapted to MBA to help the market analyst understand these underlying dynamics – and thereby to adopt better promotion strategies.
This paper is a great example of the caution I’d raise about a lot of MBA – too much of the time the use of algorithms is uninformed by real-world knowledge (expressed as hypotheses or at least some a priori notion of how the data may behave). This lack of informed engagement on the part of the subject-matter expert in the analysis leads to various shortcomings with a lot of applied MBA:
- data collection that’s inefficient
- data analysis that amounts to what I call “magical thinking” – others have called it “data dredging” or “conducting a fishing expedition”
- use of biased estimates of association effects
- a flood of “spurious” associations between/among products that amount to Type I errors (ie “false positives”) in the standard theory of statistical inference (that are due to/to be expected from the vast number of effective tests of hypothetical associations)
- most “legitimate” (ie statistically significant, when proper confidence values are used to assess multiple hypotheses) associations are likely to be of no substantive or practical significance – and have little prospect of yielding a marketing strategy that will have any positive impact on sales
Some promising news: this paper suggests some ways of moving forward with MBA – other papers carry these suggestions further, particularly the necessity and possible means of evaluating the impact of your marketing strategies!
FYI – I’ve pushed some of the more technical details of the time-series analysis to the end of the post – the details are not needed to understand the thrust of the argument.
A near-to-next step is to identify a suite of R packages to carry out this analysis.
- positive vs. negative cross-product price elasticities (aka cross-price elasticities)
- short-run vs. long-run (aka persistent) impacts of price promotion on sales
- nature of association between products
- [in another paper we’ll see distinction between complements-in-purchase vs. complements-in-use and ditto substitutes
- consumer-demand effect vs. competitive effect in response to price change
- using a well-defined, customized time-series analysis to determine dynamic (short-run vs. long-run impact) of sales response (none vs. positive vs. negative) to price change as a function of the nature of the association between products + consumer-demand effect + competitive effect
In a recent Journal of Marketing article, Shocker, Bayus, and Kim (2004) call for a better understanding of the connectedness among products. Indeed, it is clear and well known that the purchase of one product can influence purchases of other products. The underlying dynamics of these processes, however, remain less clear.
In the data-mining community, association-rule discovery is a popular technique to analyze the connectedness between sets of products. The framework of association rules was introduced by Agrawal, Imielinski, and Swami (1993) to efficiently mine a large collection of transactions for patterns of consumer purchase behavior. Since the first publications concerning association rules discussed the mining of retail databases, this technique is also referred to as market basket analysis.
The result of a market basket analysis is a set of combinations of products that are purchased together. Since the publication of the paper by Agrawal et al. (1993), literally hundreds of publications followed based on the proposed framework. However, as Hand, Mannila, and Smyth (2001) state: “It is fair to say that there are far more papers published on algorithms to discover association rules than there are papers published on applications of it”.
In scientific publications, there are only a few applications of market basket analysis in a retailing context. Examples of these rare applications include:
- Brijs, Swinnen, Vanhoof, and Wets (2004), who used market basket analysis to create the PROFSET model for optimal product assortment selection
- the use of market basket analysis in cross-sales strategies (see for example Anand, Patrick, Hughes, & Bell (1998); Wang & Shao (2004), or Van den Poel, De Schamphelaere, & Wets (2004).
In the popular business press or text books, however, other, intuitively appealing applications are mentioned when discussing market basket analysis, including the use of market basket analysis to implement more effective price-promotion strategies. The underlying assumption is that associated products exhibit positive cross-price elasticities or, otherwise stated, that a price promotion has a positive impact on the sales of associated products. Market basket analysis is then used to select price promotions that will have a beneficial impact on the sales of full-margin associated products.
A reflection of this belief can be illustrated by the following citation of an article by two data-mining consultants in the popular business press: “Business managers or analysts can use a market basket analysis to plan couponing and discounting. It is probably not a good idea to offer simultaneous discounts on [two products] if they tend to be bought together. Instead, discount one to pull in sales of the other.” (Brand & Gerritsen, 1998).
This belief was also found in text books on data mining. Giudici (2003, p. 209) for example writes: “by promoting just one of the associated products, it should be possible to increase the sales of that product and get accompanying sales increases for the associated products.”
In this paper, we investigate whether the assumption of positive cross-price elasticities between associated products stands firm. We have reasons to believe that associated products do not necessarily show positive cross-price elasticities. Indeed, literature suggests that consumers tend to buy several products from the same category during a single shopping trip. This behavior is known as “horizontal variety seeking“, and can result in association rules between substitute products, which are expected to show negative cross-price elasticities.
Dubé (2004), for example, shows that 31% of shopping trips involving carbonated soft drinks result in the purchase of two or more different products. This behavior can result in association rules between sets of these products. However, as Dubé (2004) shows, these products can be classified as being substitutes, since price changes of a product result in switching behavior. Hence, although these products are associated, a price promotion will result in a negative impact on the sales of the associated product.
In this research, we use the transactional database of a retailer to mine for association rules. In a second phase, we derive the effect of price promotions on the associated products analytically. This enables us to generalize empirically whether market basket analysis can be used effectively to implement a price-promotion strategy.
Figure 1 illustrates the methodological framework of this study. Our analysis proceeds in two phases:
- mining a transactional database of a retailer for association rules
- applying multivariate time-series techniques to measure the dynamic impact of a price promotion
- estimating a vector autoregressive (VAR) model
- deriving the impulse response function, which measures the dynamic impact of a sales promotion on the sales of the associated product
- computing the cross-price elasticity from these responses
- classifying the relationships as being substitutes, complements or independent, depending on the sign of these elasticities
Figure 1. Methodological framework.
Market basket analysis
Market basket analysis is a generic term for methodologies that study the composition of a basket of products purchased by a household during a single shopping trip. Agrawal et al. (1993) first introduced the association-rule framework to study market baskets. Originally, this framework consisted of two parameters: support and confidence. Silverstein, Brin and Motwani (1998) extended this framework by a third parameter: interest. More specifically, the three parameters are defined as follows:
Consider the association rule Y→Z, where Y and Z are two products. Y represents the antecedent and Z is called the consequent.
Support of the rule: the percentage of all baskets that contain both products Y and Z
support = P(Y∧Z)
Confidence of the rule: the percentage of all the baskets containing Y that also contain Z. Hence, confidence is a conditional probability, i.e. P(Z|Y)
confidence = P(Y∧Z)/P(Y)
Interest of the rule: measures the statistical dependence of the rule, by relating the observed frequency of co-occurrence – P(Y∧Z) – to the expected frequency of co-occurrence under the assumption of conditional independence of Y and Z – P(Y)*P(Z)
interest = P(Y∧Z)/(P(Y) * P(Z))
Association-rule discovery is the process of finding strong product associations with a minimum support and/or confidence and an interest of at least one.
Measuring the dynamic effect of a price promotion using multivariate time-series techniques
A rationale for using multivariate time-series techniques
Recent research concerning the effects of price promotions is characterized by an increasing use of multivariate time-series techniques.
(Price promotion) ?⇒? (Short- and Long-run Impact on Sales) – Dekimpe, Hanssens, and Silva-Risso (1999)
- short-run effects of price promotion were found for most cases
- long-run effects were the exception
(Price Promotion) ?⇒? (Category Demand) – Nijs, Dekimpe, Steenkamp, and Hanssens (2001a)
- short-run impact in 58% of the cases, with a duration of 10 weeks on average
- long-run effects are exceptional – observed in 2% of the cases
(Price Promotion) ?⇒? (Category Incidence | Brand Choice | Purchase Quantity) – Pauwels, Hanssens, and Siddarth (2002)
- significant short-term effects for each of the sales components, with durations of up to 8 weeks
- in the long run, however, each sales component lacks a persistent promotion effect
(Temporary | Evolving | Structural Price Change) ?⇒? (Market Share) -Srinivasan, Leszczyc, and Bass (2000)
- temporary price changes and price promotions have only a short-run effect on market share
- structural changes or evolving prices have long-run effects on market share
Although long-term effects of price promotions/changes on sales/sales components are rare, there is still a rationale for the use of multivariate time-series techniques to study these sorts of effects:
- the rare case of a persistent effect of a price promotion on sales may be of high strategic relevance – being able to measure and explain these rare occurrences should be of interest to the marketing community
- time-series techniques are more flexible in measuring the short-run dynamics, which are observed in all studies. Indeed, time-series analysis is able to detect the most irregular fluctuations in the short-run promotional effects, whereas other techniques, like the Koyck model, necessitate an a priori specification of the response, which is usually a gradually decaying response
- in measuring the cross-price elasticity, the use of multivariate time-series techniques shows another benefit – as Nijs, Dekimpe, Steenkamp, and Hanssens (2001b) argue, a cross-sales effect can have two sources:
- a price promotion results in an increase in demand of the promoted product – causing changes in the demand of complement and substitute products = consumer-demand effect
- a price promotion can cause marketing reactions of the associated product, which obviously also results in a change in demand of the associated product = competitive effect
- an advantage of time-series analysis is that it simultaneously accounts for the two underlying sources of a cross-sales effect through the derivation of impulse-response functions
[See below for technical details of study design and analysis]
Figure 2 illustrates an impulse-response function with a short-run effect. It concerns the response of sales of toasted bread to a price promotion of instant soup. The significant responses are labeled with a dot.
Figure 2. Response of the sales of toasted bread to a price promotion of instant soup.
We observe a positive and significant immediate response of 1.31 (period 0). Weeks 1–3 are characterized by a small, be it insignificant, post-promotion dip followed by a period of purchase reinforcement in weeks 4–7. Week 7 is the first week that is followed by four non-significant responses, hence week 7 is the end of the dust-settling period. The short-run cross-price elasticity is derived by the summation of the responses during the dust-settling period, which yields a positive cross-price elasticity of 3.06. Since the responses converge to zero, there is no long-term cross-price effect.
Figure 3 illustrates an impulse-response function with a persistent, long-run effect. It concerns the response of vanilla-flavored ice-cream to a price promotion of chocolate flavored ice-cream. The graphical representation of the impulse-response function clearly shows that the responses converge to a persistent level of –0.97, which is the negative long-run cross-price elasticity. Here, the responses labeled with a dot indicate a response significantly different from the long-run effect. Week 10 is the first week that is followed by four non-significant responses, hence week 10 marks the end of the dust-settling period. The short-run cross-price elasticity is the sum of all the responses in the dust-settling period, which results in this case in a negative cross-price elasticity of –4.85.
Figure 3. Response of the sales of vanilla-flavored ice-cream to a price promotion of a chocolate-flavored ice-cream.
The relationship between the promoted product and the associated product is classified as being independent, substitute or complementary depending on the direction of the cross-price elasticity.
First, we investigate the long-run cross-price elasticity. If this measure appears to be positive, we label the relationship as being complementary, whereas a negative persistent effect indicates a substitution relationship. In the absence of a long-run effect, we use the short-run estimates to classify the relationship. Again, a positive cross-sales effect is classified as being complementary, while a negative effect is classified as substitute. In the absence of a short-run effect, we classify the relationship as being independent.
Applying the aforementioned classification scheme, the 2700 relationships are classified in the following way:
- 1112 relationships are classified as being complements
- 1212 relationships are classified as being substitutes, and
- 376 relationships are classified as being independent.
In Table 1, we give examples of relationships that are classified as complements and substitutes. For both complements and substitutes, we list five relationships that were classified based on their long-run elasticity and five based on their short-run elasticity, resulting in 20 examples.
In 60 instances, a price promotion has a long-run/ persistent positive effect on the sales level of the associated product.
|Persistent effects – complementary products
|Short-run effects – complementary products
|Persistent effects – substitution products
|Short-run effects – substitution products
Table 1. Examples of cross-price elasticities between associated products.
Following our classification scheme, these instances are classified as complements. The mean value of this persistent cross-price elasticity is 0.89. The other 1052 complementary relationships are classified as being complements based on a positive short-run cross-price elasticity. The mean short-run elasticity is 4.56. These short-run dynamics take on average 13 weeks to stabilize.
Forty-two cross-price elasticities exhibit a persistent negative sign, meaning that the price promotion has a persistent negative effect on the sales of the associated product. The mean value of the 42 elasticities is –0.62. The short-run dynamics have a mean value of –4.59. It takes on average 16 weeks for the short-run dynamics to stabilize.
Although we only considered product couples that can be labeled as product associations, it is remarkable that we can classify even more relationships as substitutes (1212) than as complements (1112). This finding denies the intuitively appealing business idea that association rules can be used by retailers to implement more effective promotion strategies. Indeed, the underlying hypotheses that product associations necessarily show positive cross-price elasticities do not seem to hold.
As we have shown, however, there is a bigger probability that the sales of associated products will drop. Indeed, observing that customers tend to buy two products on the same shopping occasion does not imply a complementary relationship between these two products.
Consumers can buy products together for a variety of reasons (see Manchanda, Ansari, & Gupta, 1999, or Böcker, 1978).
Especially, horizontal variety seeking behavior can result in association rules between two products which are actually substitutes. Horizontal variety seeking involves the simultaneous purchase for multiple varieties (Kim, Allenby, & Rossi, 2002). The adjective horizontal is added to make a clear distinction between variety seeking behavior, which describes the process of temporal changes in tastes from purchase occasion to purchase occasion (see for example McAlister & Pessemier, 1982).
Dubé (2004) lists three reasons for the occurrence of horizontal variety seeking
- on a given shopping trip, consumers typically make purchases involving several consumption occasions. If preferences differ across these consumption occasions, this results in the simultaneous purchase of substitutes. A consumer can buy, for example, two flavors of tea, when he prefers flavor A in the morning, whereas he prefers flavor B in the evening.
- the purchase of a variety of products from the same assortment may be a response to the consumer’s uncertainty about his future preferences
- a consumer can make purchases for a complete household. This results in horizontal variety seeking, if preferences differ among the household members
In this research, we have shown empirically that a market basket analysis is not a good technique to implement more efficient promotion strategies. The underlying assumption that associated products are by consequence complements with positive cross-price elasticities cannot be validated. This assumption ignores the occurrence of horizontal variety seeking, which results in the simultaneous purchase of substitutes. We measured the cross-price elasticities of 1350 associated products and conclude that a price promotion has a higher likelihood to result in a decrease of the associated product. For this reason, we advise retailers not to build a promotion expert system based on a market basket analysis. This system should be built on the derivation of cross-price elasticities. Especially, the use of multivariate time series techniques, which account for dynamic effects, can be used to implement more efficient promotion strategies that benefit from positive cross-sales effects.
Technical details of the design and analysis
Unit root tests
The first step of our analysis involves the testing for unit roots. Those tests are necessary, since variables that appear to be non-stationary have to be differenced before entering the model, whereas stationary variables enter the model in levels. Moreover, the presence of a unit root is a necessary condition for the existence of long-run effects (Dekimpe & Hanssens, 1995b).
Augmented Dickey-Fuller tests were used to test for the presence of a unit root. We used the testing scheme proposed by Enders (1995) (see Appendix A). The optimal lag length for the autoregressive part of the test was chosen using the Schwarz Bayesian Criterium (SBC).
This testing procedure classifies each series as a unit-root process, a stationary process or a trend-stationary process.
Vector autoregressive (VAR) models
For each selected product couple, we estimate a four equation VAR model, with the prices and sales of both products as endogenous variables. We thereby control for factors that may influence sales, which are estimated as exogenous variables. More specifically, we estimate the effect of the featuring of the two products in the weekly folder of the retailer and the effect of the total sales per week of the retailer, which controls for external factors that may influence the sales of the two products. When one of the endogenous variables appears to be trend-stationary, a trend variable is included in all equations. Hence, for every product association, the following system is estimated:
As mentioned earlier, endogenous variables that have a unit root enter the system in differences.
Impulse response functions
The effects of a price promotion on the sales of the associated product are estimated by deriving impulse response functions from the estimated VAR systems.
Formally, price promotions are operationalized as onetime unit shocks of the price variable in the VAR model in levels. The impact of a price promotion of product A on the sales of product B, for example, is operationalized by setting the value εPa,t to -1 and measuring the over-time impact on ln(Sb) of this one-time unit shock. From each VAR model we derive two impulse-response functions, measuring cross-price elasticities. Firstly, we estimate the response of the sales of product B to a price promotion of product A, and, secondly, we estimate the response of the sales of product A to a price promotion of product B.
In a VAR system, the instantaneous effects cannot be estimated directly, but are reflected in the variance–covariance matrix of the residuals. We use the method proposed by Evans and Wells (1983) to derive the instantaneous effects (for an explanation of this method, and an argumentation to use this method in this research, we refer to Appendix B).
In order to derive confidence intervals for the estimated responses, we used a bootstrap method. Therefore, elements from the residuals are randomly drawn with replacement. Based on these residuals and the parameters estimated for the VAR model, we create new values for the four endogenous time series. We then re-estimate the parameters of the VAR model using these new time series, and impulse response functions are derived based on this model. This procedure is repeated 500 times. Finally, the sample standard error is computed for these 500 response values. Using this standard error, we compute the t-values of each response. Responses with an absolute t-value higher than 1 are labeled as significant.
We follow Nijs et al. (2001a) in deriving a short-term and a long-term effect from the estimated impulse-response function. A long-term or persistent effect occurs when the asymptotic value of the response (t/N) is significantly different from zero. Short-run effects are the summation of all the impulses over the dust-settling period. The dust-settling period ends at the first period which is followed by four non-significant responses.
Description of the data
For our analysis, we used the transactional database of a large European retailer, which contains the sales transactions of six outlets between July 7th 1999 and March 26th 2003 of 15,017 different SKU’s.
First, we took a sample of all the transactions of 2002, and computed the support and interest measure for all possible combinations of two SKU’s. Since the database covers the sales of more than 15,000 different SKU’s, this results in the estimation of support and interest for more than 112,492,500 SKU pairs. We labeled a combination as a product association if it has an interest larger than two and a support exceeding 0.0157. For the selected product associations we computed six variables on a weekly basis, which results in 194 weekly observations of the price of the two products (Pa and Pb), the sales in units of the two products (Sa and Sb), and the dummy variable that indicates whether the product featured in the folder for both products (Fa and Fb).
Since we are interested in the impact of price promotions on the sales of the associated product, we required that the price series of both products contain at least one price promotion in the 194 weeks. A price promotion was defined following the heuristic procedure in Abraham and Lodish (1993). They define a price promotion if the price is reduced by at least 5%, and then is raised again by at least 3% within the following 8 weeks. If there were weeks where the product was featured in the folder, these weeks do not count in the calculation of the 8 weeks period.
These restrictions result in 1350 selected product associations. As mentioned, we successively simulate a price promotion in both products and measure the impact of the promotion on the sales of the associated product, which results in the estimation of 2700 cross-price elasticities, both for the short and the long run.
Testing for unit roots using ADF-tests – Dolado, Jenkinson, and Sosvilla-Rivero (1990) and Enders (1995).
Testing for unit roots using ADF-tests.
Appendix B- Deriving instantaneous effects – Evans and Wells (1983)
In a VAR system, the instantaneous effects cannot be estimated directly, but are reflected in the variance–covariance matrix of the residuals. For example, if we observe a high covariance between the errors of the sales of products A and B, we can infer that there is a high instantaneous effect between sales of products A and B. A problem, however, remains that we cannot directly observe the direction of these instantaneous effects. In our example, we do not directly know whether it is the sales of product A that have an immediate effect on the sales of product B, or whether it is the other way around, i.e. sales of product B that influence the sales of product A. This problem is traditionally solved by imposing restrictions on the instantaneous effects. These restrictions impose a priori a causal ordering of the instantaneous effects. In a system with n endogenous variables, we need (n2-n)/2 restrictions for identification, which resolves to six restrictions in our four equation model. Imposing these six restrictions in our particular setting seems to be problematic however. While we could reasonably assume that feedback effects from sales to price take some time to materialize, and hence restrict the instantaneous effects from price to sales to zero, this only yields four restrictions (sales A does not have an instantaneous effect on price A and price B, and sales B does not have an instantaneous effect on price A and price B). Imposing further restrictions cannot be done on a theoretical basis. If we observe an instantaneous effect between the price of A and B, for example, there are no theoretical grounds to impose that price A has an instantaneous effect on price B, while price B can only affect price A after one week. To circumvent this problem, we use the method proposed by Evans and Wells (1983) (see Dekimpe & Hanssens, 1999 for an application in marketing) to estimate the instantaneous effects, since this method does not imply to impose restrictions.
This method models instantaneous effects as the expected value of the error term given a particular shock and by assuming a multivariate normal distribution of the error terms. Formally, the expected instantaneous effect of variable j as a result of a shock k of variable i is computed as
E(εj|εj = k) σij=σii
where σij is the corresponding element in the variance–covariance matrix.
Applying this method to our setting, a price promotion of product A is operationalized as a shock in the residual vector of
[-σPa,Sa/σPa,Pa,-σPa,Sb/σPa,Pa, -1, -σPa,Pb/σPa,Pa]‘
Abraham, M. M., Lodish, L. M. (1993). An implemented system for improving promotion productivity using store scanner data. Marketing Science, 12(3), 248–269.
Agrawal, R., Imielinski, T., Swami, A. (1993). Mining association rules between sets of items in large databases. Proceedings of the 1993 AC (pp. 207–216).
Anand, S. S., Patrick, A. R., Hughes, J. G., Bell, D. A. (1998). A data mining methodology for cross-sales. Knowledge-Based Systems, 10(7), 449–461.
Böcker, F. (1978). Die Bestimmung der Kaufverbundenheit von Produkten. Schriften zum Marketing , 7.
Brand, E., & Gerritsen, R. (1998). Associations and Sequencing. http:// www.dbmsmag.com/9807m03.html
Brijs, T., Swinnen, G., Vanhoof, K., Wets, G. (2004). Building an association rules framework to improve product assortment decisions. Data Mining and Knowledge Discovery, 8(1), 7–23.
Brin, S., Motwani, R., Silverstein, C. (1998). Beyond market baskets: Generalizing association rules to dependence rules. Data Mining and Knowledge Discovery, 2(1), 39–68.
Dekimpe, M., Hanssens, D. (1995a). The persistence of marketing effects on sales. Marketing Science, 14(1), 1–21.
Dekimpe, M., Hanssens, D. (1995b). Empirical generalizations about market evolutions and stationarity. Marketing Science, 14(3), G106– G121.
Dekimpe, M., Hanssens, D. (1999). Sustained spending and persistent response: A new look at long-term marketing profitability. Journal of Marketing Research, 36(4), 397–412.
Dekimpe, M., Hanssens, D., Silva-Risso, J. (1999). Long-run effects of price promotions in scanner markets. Journal of Econometrics, 89, 269– 291.
Dolado, J., Jenkinson, T., Sosvilla-Rivero, S. (1990). Cointegration and unit roots. Journal of Economic Surveys, 4, 249–273.
Dubé, J.-P. (2004). Multiple discreteness and product differentiation: Demand for carbonated soft drinks. Marketing Science, 23(1), 66–81.
Enders, W. (1995). Applied econometric time series. New York: Wiley.
Evans, L., Wells, G. (1983). An alternative approach to simulating VAR models. Economic Letters, 12(1), 23–29.
Giudici, P. (2003). Applied data mining. West Sussex, England: Wiley.
Hand, D., Mannila, H., Smyth, P. (2001). Principles of data mining. Massachusetts Institute of Technology.
Kim, J., Allenby, G. M., Rossi, P. E. (2002). Modeling consumer demand for variety. Marketing Science, 21(3), 229–250.
Manchanda, P., Ansari, A., Gupta, S. (1999). The “shopping basket”: A model for multicategory purchase incidence decisions. Marketing Science, 18(2), 95–114.
McAlister, L., Pessemier, E. (1982). Variety seeking behaviour: An interdisciplinary review. Journal of Consumer Research, 9(3), 311–322. Nijs, V. R., Dekimpe, M. G., Steenkamp, J.-B.E.M., Hanssens, D. M. (2001a). The category-demand effects of price promotions. Marketing Science, 20(1), 1–22.
Nijs, V. R., Dekimpe, M. G., Steenkamp, J.-B.E.M., & Hanssens, D. M. (2001b). Tracing the impact of price promotions across categories, Working Paper, Kellogg School of Management.
Pauwels, K., Hanssens, D., Siddarth, S. (2002). The long-term effects of price promotions on category incidence, brand choice, and purchase quantity. Journal of Marketing Research, 39(4), 421–439.
Shocker, A., Bayus, B., Kim, N. (2004). Product complements and substitutes in the real world: The relevance of “other products”. Journal of Marketing, 68(1), 28–40.
Srinivasan, S., Leszczyc, P., Bass, F. (2000). Market share response and competitive interaction: The impact of temporary, evolving and structural changes in prices. International Journal of Research in Marketing, 17(4), 281–305.
Van den Poel, D., De Schamphelaere, J., Wets, G. (2004). Direct and indirect effects of retail promotions. Expert Systems with Applications, 27(1), 53–62.
Wang, F.-S., Shao, H.-M. (2004). Effective personalized recommendation based on time-framed navigation clustering and association mining. Expert Systems with Applications, 27(3), 365–377.