This is the peer reviewed author accepted manuscript (post print) version of a published work that appeared in final form in:

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1 Can the negative binomial distribution predict industrial purchases? This is the peer reviewed author accepted manuscript (post print) version of a published work that appeared in final form in: Wilkinson, John, Trinh, Giang, Lee, Richard & Brown, Neil 2016 'Can the negative binomial distribution predict industrial purchases?' Journal of Business and Industrial Marketing, vol. 31, no. 4, pp This un-copyedited output may not exactly replicate the final published authoritative version for which the publisher owns copyright. It is not the copy of record. This output may be used for noncommercial purposes. The final definitive published version (version of record) is available at: Persistent link to the Research Outputs Repository record: General Rights: Copyright and moral rights for the publications made accessible in the Research Outputs Repository are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognize and abide by the legal requirements associated with these rights. Users may download and print one copy for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the persistent link identifying the publication in the Research Outputs Repository If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.

2 The Library Educating Professionals, Creating and Applying Knowledge, Engaging our Communities This is the accepted manuscript (postprint) version of a published work that will appear in final form in Journal of Business and Industrial Marketing, vol. 31, no. 4, pp , This version has been peer reviewed, but may lack the final formatting of the published version. This article is copyright and may be used for non-commercial purposes.

3 Can the Negative Binomial Distribution Predict Industrial Purchases? Abstract Purpose This paper extends known boundary conditions of the Negative Binomial Distribution (NBD) model, and tests applicability of Conditional Trend Analysis (CTA) a key method to identify whether changes in overall sales are accounted for by previous non-buyers, light buyers or heavy buyers to industrial purchasing situations. Design/methodology/approach The study tested the NBD model and CTA in an industrial marketing context using a 12-month dataset of purchases from an Australian supplier of industrial plastic resins. Findings The purchase data displayed a good NBD fit, the study therefore extending known boundary conditions of the model. Application of CTA provided second-period purchasing frequency estimates showing no significant difference from actual data, indicating applicability of this method to industrial purchasing. Research limitations/implications Data relate to just one supplier. Further research across several industries is required to confirm the generalizability and robustness of NBD and CTA. Practical implications Marketing decisions can be improved through appropriate analysis of customer purchasing data. However, without access to equivalent competitor data, industrial marketers are constrained in benchmarking purchasing patterns of their own customers. The results indicate that use of the NBD model enables valid benchmarking for industrial products, while CTA would enable appropriate analysis of purchases by different classes of customer. Composite version of final draft submitted to Journal of Business and Industrial Marketing and accepted for publication on 22 June 2015.

4 Originality/value This paper extends the known boundary conditions of the NBD model and provides the first published results indicating the appropriateness of CTA to predict purchasing frequencies of different industrial customer classes. Keywords: Industrial marketing; Industrial purchasing; Pareto/NBD model; Customer analysis Article Classification: Research Author Details John W Wilkinson* Ehrenberg-Bass Institute for Marketing Science, University of South Australia Giang Trinh Ehrenberg-Bass Institute for Marketing Science, University of South Australia Richard Lee Ehrenberg-Bass Institute for Marketing Science, University of South Australia Neil Brown, School of Marketing, University of South Australia *Corresponding author: john.wilkinson@unisa.edu.au Acknowledgments: The authors thank the reviewers for their useful suggestions relating to earlier drafts of this article. 2

5 1. Introduction Marketing resource allocation decisions can be improved through appropriate analysis of customer- and sales-related data (Noorizadeh et al., 2013; Shankar, 2012). In particular, business-to-business (B2B) marketing organizations can gain useful insights through evaluation of the levels of (1) support received from existing customers through repeat purchases and (2) business won from new customers (Charlton and Ehrenberg, 1976). However, without access to equivalent information relating to competitors, firms are likely to have some difficulty interpreting or benchmarking information about purchases by their own customers (Ibid.). Unlike the B2B context, the Negative Binomial Distribution (NBD) model has been widely used in consumer marketing for such competitive analyses and benchmarking (Bhattacharya, 1997; Chen et al., 2011; Ehrenberg et al., 2004). Within consumer markets, purchases of fast-moving consumer goods (FMCGs) vary irregularly from one person to another and occur as if at random. Consequently, decision models attempting to explain individual purchase behavior are complex, often perform poorly and are seldom replicated (Ehrenberg et al., 2001). However, aggregating consumer purchases at a market level reveals an underlying statistical distribution or pattern (Bass, 1995; Ehrenberg et al., 2004). This pattern then serves as a benchmark for companies to compare their actual performance against industry norms. Best known among these statistical approaches is the NBD model (Grahn, 1969; Morrison and Schmittlein, 1988). To date, almost all studies using this model have focused on just FMCGs (e.g., Anschuetz, 1997; Bhattacharya, 1997; Decker and Trusov, 2010; Ehrenberg et al., 2004; Nelson- Field et al., 2012; Schwartz et al., 2010; Uncles et al., 1995). Some researchers have suggested that B2B purchase profiles may constitute a boundary condition for the NBD model (Sharp and Wright, 2000; Sharp et al., 2002). A key reason is that NBD modeling is grounded on the 3

6 premise that consumers behavior occurs as if at random (Ehrenberg et al., 2001; Ehrenberg et al., 2004), a characteristic atypical of the decision-making process in industrial markets. Another reason relates to the relatively small numbers of buyers and the closer relationships between buyers and suppliers in business markets compared to consumer markets (Schmittlein and Peterson, 1994). This characteristic also could be expected to result in organizational purchases being less random than the NBD model indicates. This paper argues that the NBD can provide B2B marketing organizations with an adequate measure for such benchmarking by enabling comparison of the distribution pattern of customer orders with the theoretical NBD. In particular, the paper demonstrates the use of conditional trend analysis (Goodhardt and Ehrenberg, 1967) in NBD modeling to benchmark future sales changes based on past performance. Conditional Trend Analysis (CTA) is regarded as a very important method with significant managerial implications (Morrison and Schmittlein, 1988). The technique allows brand or product managers to determine how changes in sales in a later period are due to different types of buyers (light versus heavy) in the previous period. Specifically, the manager can identify sources of growth by comparing (1) the actual sales in the second period with (2) the expected sales predicted by CTA under the stationary or no change condition. Several studies have tested the fit of the NBD model to B2B marketing situations and found that the NBD model provides a reasonably good fit to the data (Bowman and Lele-Pingle, 1997; Charlton and Ehrenberg, 1976; Ehrenberg, 1975; Schmittlein and Peterson, 1994; Uncles and Ehrenberg, 1990). Only one study, relating to surgical supplies, found a poor fit (McCabe et al., 2013). However, there have been no studies applying the NBD model to industrial raw materials or components, and none of the previous studies has used CTA to predict future 4

7 purchases in a B2B marketing context. As noted by Morrison and Schmittlein (1988), fitting the NBD to observed purchase frequency itself provides limited marketing insight. It is the application of CTA that offers the potential of improved decision-making. This study therefore tested the NBD model and its CTA application in an industrial context using a dataset from an Australian supplier of industrial plastic resins. The data comprise a 12-month purchase history of industrial raw material or component products, ranging from general purpose polyolefins to engineering thermoplastics, by a wide range of firms in several industries, including manufacturers of automotive components, building components, whitegoods components, disposable drink ware, electrical accessories, plastic bags, and plumbing fittings. Prior to discussing the study itself and the analysis of results, a brief review is provided of the NBD model, competing models, and prior studies regarding applicability of NBD to B2B marketing. 2. The NBD Model First utilized to assess the recurrence of diseases and accidents (Greenwood and Yule, 1920) and later to analyze consumer behavior (Ehrenberg, 1959), the NBD model is based on two statistical assumptions (Dunn et al., 1983; Uncles et al., 1995). Specifically, within a marketing context, the model assumes that individual buying patterns follow a Poisson distribution, while aggregate population buying patterns follow a Gamma distribution. Collectively, these assumptions imply that consumers possess steady long-run purchase probabilities (e.g., a consumer buys five times in a year), but irregular purchase patterns (i.e., those five purchases can occur randomly within the year). The NBD model also assumes 5

8 stationary markets, in which the number of buyers and the purchase rate in each period of analysis are relatively stable (Morrison and Schmittlein, 1988; Uncles et al., 1995). The NBD model estimates the number of buyers with zero or more purchases in a given base period using two parameters: the K and A parameters, equivalent to the Alpha and Beta parameters of the model s underlying Gamma distribution. The model determines the combination of K and A values that produces the closest fit between theoretical estimates and actual data. Ehrenberg (1959) and colleagues (Chatfield et al., 1966) first provided the mathematical workings of the NBD model for marketing applications. They formulated the probability of a consumer buying r units of a product or category within a period of analysis as follows: (K + r 1)! A P(r) = (1+ A) K (K 1)!r! 1+ A r The K parameter regulates the shape of the purchase data distribution. A high K value means that buyers purchase rates mostly congregate around the mean value. In other words, buyers are homogeneous with respect to the amount purchased. Conversely, a low K value signifies disproportionately high levels of non- or light buyers (Jarvis et al., 2003; Morrison, 1969). The A parameter denotes the overall purchase volume or scale. A larger A parameter implies that data comes from a longer collection period. Figures 1 and 2 illustrate the effects of low and high K values, and Figures 1 and 3 illustrate the effects of low and high A values. The scale parameter A is proportional to the length of the time period, and if the length doubles then so does parameter A. 6

9 Figure 1. NBD model with parameters K=1, A=3 Figure 2. NBD model with parameters K=2, A=3 Figure 3. NBD model with parameters K=1, A=6 7

10 One method of fitting the NBD to observed data involves specifying two inputs: purchase frequency and market penetration (Lam and Mizerski, 2009; Uncles et al., 1995). These inputs are derived from the K and A parameters (Chatfield et al., 1966; Jarvis et al., 2003). Market penetration is the proportion of consumers buying the category or brand at least once in the relevant period. This method requires knowledge of the values of purchase frequency and penetration, and also requires penetration to be less than 100%. An alternative method, maximum likelihood estimation, utilizes raw data of purchase incidence to derive values of K and A (Habel and Riebe, 2004; Rungie, 2003). This method is particularly useful when market penetration is unknown (because the number of non-buyers in the base period is unknown), or when a dataset comprises the purchase incidence of just one brand, thereby implying a penetration of 100% for the brand in the dataset. As the data in this study do not relate to non-buyers, the maximum likelihood technique has been employed. Figure 4 illustrates an (hypothetical) example of an NBD fit between theoretical estimates and actual data for consumer goods. Figure 4. Hypothetical example of an NBD model 70% 60% Percentage of Buyers 50% 40% 30% 20% 10% 0% NBD Estimated Actual > 6 Frequency of Buying 8

11 Since the original article by Ehrenberg (1959), the NBD model has been shown to work well in numerous product categories including FMCGs, petrol, cars, mobile telephone services, magazines, and gambling products, across a wide range of consumer markets in Australia (Lam and Mizerski, 2009), China (Uncles et al., 2010), Greece (Krystallis and Chrysochou, 2010), Italy (Corsi et al., 2011), Japan (Fader and Schmittlein, 1993), New Zealand (Sharp and Sharp, 1997), Singapore (Lee et al., 2011), the United Kingdom (Ehrenberg, 1988), and the United States (Uncles et al., 1995). 2.1 Pareto relationships between light and heavy buyers The NBD model also provides insight into the distribution of buyers of a category or brand. The model predicts that a typical market has many light buyers and few heavy buyers, and that the distribution of light and heavy buyers follows a reverse J-curve (Ehrenberg et al., 2004; Jarvis et al., 2003). Anschuetz (1997) uses the term Pareto relationship to describe situations in which 80% of the sales volume of a category or brand comes from 20% of buyers. However, there is clear evidence that for many products, this 80/20 categorization is somewhat incorrect. For instance, Schmittlein et al. (1993) have examined product categories such as yoghurt, catsup and detergent, and found that the top 20% of consumers account for 50% to 60% of category purchases. Sharp (2010, p. 46) provides a summary of research findings covering many dozens of brands within consumer markets, revealing that the top 20% of buyers typically account for about 50% of annual purchases of a brand, this proportion varying from 45% to 65% for most brands in a range of countries. While relating to consumer markets, this evidence is consistent 9

12 with the prediction by the NBD model of a market comprising many light buyers and few heavy buyers. 2.2 Conditional trend analysis In 1967, Goodhardt and Ehrenberg introduced Conditional Trend Analysis (CTA) as an extension to the NBD model to investigate variations in purchase patterns over time. CTA first examines different classes of buyer, such as non-, light and heavy buyers, in a period. The model then predicts the likelihood of each class of buyer purchasing in the next period. In doing so, CTA addresses questions such as: (1) How likely are consumers, who do not purchase a brand or category in a period, to purchase in the next period? (2) What is the average purchase rate and purchase rate distribution of these buyers in the second period? Based on the parameters A and K of the NBD model, Goodhardt and Ehrenberg (1967) show that the expected mean purchase frequency in Period 2 by buyers who made r purchases in Period 1 is: m 2 r = A (K + r) 1+ A Understanding how buyers should behave from one period to the next is useful for companies wishing to track the purchase patterns of different classes of buyer over time. For example, CTA allows managers to determine which class of customer causes most change in a particular performance metric, such as monthly sales turnover. Armed with this knowledge, managers could determine whether upswings are real (e.g., new buyers, or light buyers purchasing more than usual) or borrowed (i.e., heavy buyers purchasing at the expense of 10

13 previous or future periods), thereby correctly attributing changes in sales volumes to marketing efforts or normal period-to-period fluctuations. Without CTA, companies could interpret periodic changes incorrectly; for example, attributing observed declines in purchases by heavy users to ineffective marketing activities when the declines actually are normal period-to-period fluctuations. Similarly, companies could erroneously credit upswings to promotional events when CTA would show that the additional purchases came from previous buyers who did not purchase in preceding periods; that is, from existing users replenishing their stocks. Schmittlein et al. (1985, p. 255) therefore conclude that predicting future purchases from past purchases in a given period is the most managerially relevant use of the NBD model. 3. Competing Models Since Goodhardt and Ehrenberg s (1967) seminal work, the CTA-NBD approach has been utilized and extended by other researchers. The majority of the extensions focus on the distributions of the model. For example, Morrison (1969) extended the CTA-NBD model to include hard-core non-buyers (buyers who never buy the product). Morrison s rationale is that hard-core non-buyers might cause model bias since these buyers are not appropriate for the gamma distribution that underpins the NBD model. Similarly, Schmittlein et al. (1987) generalized the original model to the Pareto-NBD model to estimate the dead or drop out customers. Schmittlein and Morrison (1983) further applied the condensed NBD to CTA as an Erlang-2 distribution and allowed the inter-purchase times to be more regular than the Poisson distribution. Schmittlein et al. (1985) also extended the CTA to beta binomial/nbd as the beta binomial distribution is shown to be reasonable for modeling purchasing for a particular brand. 11

14 Recently, work has been undertaken within the context of customer base analysis and customer life-time value (Abe, 2009; Batislam et al., 2007; Bemmaor and Glady, 2012; Jerath et al., 2011; Reinartz and Kumar, 2000, 2002, 2003). Although these extended models provide further theoretical support to the robustness of NBD modeling, parsimony in the simpler NBD model, including CTA, has a clear advantage over more complex models for marketing practitioners. Indeed, there is evidence in the literature that the simpler NBD is just as effective in predicting future behavior (e.g., Ehrenberg, 1988; Fader and Hardie, 2002; Morrison and Schmittlein, 1988; Schmittlein et al., 1985). Schmittlein et al. (1985, p. 264) concluded that the NBD is a tough model to beat. 4. The Business-to-Business Marketing Context While the NBD model has successfully fitted data across various consumer domains, its application in a B2B marketing context has been tested in very few studies. Further research is required to test the applicability of the NBD model across different industrial product-markets and buyer-seller situations. For example, it is unclear whether the model is applicable to situations involving either contractual or transactional supply arrangements. Given the importance of supply contracts and the range of different types of contractual arrangements available to industrial buyers (Gundlach et al., 2006; Talluri and Lee, 2010), this is an important issue for consideration within a B2B marketing context. Two studies have been reported regarding distribution of contracts between oil companies and airlines for the supply of aviation fuel at selected international airports (Ehrenberg, 1975; Uncles and Ehrenberg, 1990). In both studies, distribution of the numbers of contracts the airlines awarded to suppliers followed the NBD. A study by Charlton and 12

15 Ehrenberg (1976) of the numbers of participants sponsored by firms over a two-year period to attend residential courses on general management found a reasonably good fit between the distribution of the numbers of participants from each firm and the NBD. A study by Schmittlein and Peterson (1994) on the purchasing of office products by business customers also found a good fit between the actual distribution of buyers and the NBD. Another study, relating to foreign exchange contracts, found that purchasing patterns of large corporations in four different countries displayed a good fit with the NBD (Bowman and Lele-Pingle, 1997). However, findings of a study of members of a public health collaborative purchasing organization, relating to two types of surgical supplies, provided a rather poor fit with the NBD with respect to purchase frequency (McCabe et al., 2013). In summary, five of six published studies relating to business markets have identified purchasing patterns with reasonably good levels of fit with the NBD. The studies focused on three product and two service categories, none covering industrial components or raw materials. Therefore, there is some evidence that the NBD model is applicable to business markets, but further studies are necessary to confirm this situation. In addition, no studies have been published testing the applicability of CTA to business markets. From a research viewpoint, this study extends the assessment of the applicability of the NBD model to business markets by analyzing purchases of a range of industrial raw materials (plastic resins) by manufacturers in Australia. In addition, the study provides a test of the applicability of CTA to forecast purchase patterns within a business market. In turn, this extends our understanding of the generalizability of the model to different markets. There also is agreement that an understanding of purchase frequency within a business market would be useful to practitioners. For example, Pick (2010) argues that information about 13

16 purchase frequency can enable proper estimation of business customer inactivity. Mark et al. (2012) argue that such information would assist evaluation of a business customer s preference toward a supplier. 5. Method and Results A dataset from an Australian supplier of plastic resins was used to test the proposition regarding the utility of the NBD and CTA in predicting organizational purchases. The dataset includes all purchases made by 197 industrial customers during a 12-month period (July 2011 to June 2012). The data comprise (disguised) customer identifier, invoice date, product type and order quantity for each separate purchase event. The data relate to purchases of a reasonably broad industrial product category, ranging from general purpose polyolefins to engineering thermoplastics, by a wide range of firms from a diverse range of industries, including manufacturers of automotive components, building components, whitegoods components, disposable drink ware, electrical accessories, plastic bags, and plumbing fittings. The customers represented in the data set had a mix of supply arrangements with the marketing organization. About 30% of customers had a long-term supply contract, 40% had a short-term contract for a specific purchase volume, 20% had no formal contract but also had no alternative supply option, and 10% bought periodically to meet requirements for particular projects or bought on an opportunistic, one-off basis. Therefore, the dataset contains a mix of customers covering a wide range of supply arrangements, consistent with the situation experienced by many B2B marketing organizations. Entering the purchase data into an NBD model using the maximum likelihood technique yielded the NBD theoretical (estimated) versus actual distributions illustrated in Figure 5. A chi- 14

17 square test found no significant difference between observed and NBD-predicted purchases of resin products (χ2 = 13, df = 11, p = 0.3). Data were truncated at 12 so that all expected frequencies are five or more a general rule for the chi-square analysis (Malhotra et al., 1996). A Pearson s two-tailed test recorded a correlation coefficient of 0.96 (p < 0.001). The results indicate no statistically significant difference between theoretical and actual values. Also, determining the buyer concentration shows the top 20% of customers accounted for 63% of purchases by number of transactions and 68% by volume (quantity of resin). These result are consistent with consumer studies that have found disproportionate purchases by the top buyers (Habel and Riebe, 2004; Schmittlein et al., 1993). Next, the dataset was divided into two components, comprising purchases for the first and second six-month periods. Based on data for the first period, CTA was undertaken to predict purchase patterns for the second period. Comparisons of predicted and actual purchase patterns for the second period are provided in Table 1 and Figure 6. A chi-square test found no significant Figure 5. Results of NBD modeling 20% Percentage of customers 18% 16% 14% 12% 10% 8% 6% 4% 2% 0% Actual NBD (Estimated) Number of purchases 15

18 difference between the predicted and actual purchase frequencies for the second period (χ2 = 4.1, df = 8, p = 0.9). A Pearson s two-tailed test recorded a correlation coefficient of 0.94 (p < 0.001) between the predicted and actual purchase frequencies. Table 1. Results of conditional trend analysis (CTA) Buyer Class in Period 1 Actual Mean Purchase Frequency in Period 2 Predicted Mean Purchase Frequency in Period 2 Difference between Predicted and Actual Means Figure 6. Results of conditional trend analysis (CTA) Average number of purchases in period CTA Predicted Actual Buyer class in Period 1 16

19 To test the robustness of the NBD model, a holdout sample check was undertaken by dividing the data into two six-month periods, estimating the purchase frequency distribution from the data in the first six-month period, and then comparing this distribution with that from the holdout data in the second six-month period. The results are shown in Figure 7. Clearly, the first six-month estimates are very close to the holdout distribution. A chi-square test found no significant difference (χ2 = 4.9, df = 8, p = 0.8). A Pearson s two-tailed test provided a correlation coefficient of 0.98 (p < 0.001). 6. Discussion 6.1. Implications for theory The dataset of plastic-resin purchases displays good NBD fit and, in doing so, extends known boundary conditions of the NBD model. The results further reinforce assertions by Ehrenberg et al. (2004) that these stochastic phenomena are law-like. Figure 7. Results of hold-out analysis 30% Percentage of customers 25% 20% 15% 10% 5% 0% Number of purchases Actual NBD (Estimated) 17

20 Regarding the Pareto relationship, the top 20% of customers accounted for 63% to 68% of purchases, as mentioned above. This finding is unsurprising. In business markets, there are large differences in size of organization, large organizations typically requiring greater quantities of products and services than small organizations in the same sector (Polo Redondo and Cambra Fierro, 2007). For example, General Motors, which sold almost ten million vehicles in 2013 (General Motors, 2014), represents a very much larger sales opportunity for suppliers such as Bosch or Bridgestone than Ferrari, with annual sales of only seven thousand vehicles (Vijayenthiran, 2014). However, some business markets may have a heavy concentration of light buyers, and the collective potential of these light buyers may exceed that of the few heavy buyers. Such a situation implies that these light buyers are a key to improving market share, consistent with findings in consumer research that reaching out to new or light buyers, rather than enhancing loyalty by concentrating on top customers, would yield market share gains (Anschuetz, 1997, 2002; Ehrenberg et al., 2004). The fit of period by period CTA application to B2B data suggests that industrial purchasing involves stochastic change behavior. An individual firm s rate of purchasing is as if random over time (Poison process). In a given time period, an industrial firm may purchase the product once, in the next period the firm may purchase twice, three times, or even more. But this does not constitute a real change; rather, it is a stochastic change around a stable long-run purchasing rate. Some frequent buyers in one period could become infrequent buyers in the next period, and vice versa. Therefore, classifying organizational customers into light versus heavy buyers based on data for one period could be misleading, as customers may have just happened to purchase more or less frequently than their usual rate. Within this context, use of the NBD 18

21 model would enable identification of real changes in long-term purchasing rates, perhaps due to successful marketing activities such as advertising or sales promotion, in contrast to stochastic changes. Managerial implications are discussed in the following section Managerial implications Confirmation of a good NBD fit indicates that B2B marketing firms can use the model to benchmark their performance despite the lack of access to competitive sales data. Such benchmarking would allow companies to detect and possibly explain any abnormalities, which then would enable them to develop appropriate strategies to address identified problems. Benchmarking using the NBD model also would allow firms to predict customer purchase patterns from one period to the next, which would be particularly useful when attempting to track customer purchases over multiple periods. Allowing managers to determine which class of customer causes change enables them to develop marketing actions appropriate to the actual causes of the changes in purchase patterns. For example, if a manager allocates a larger budget for promotion this year and sales then increase, he or she can assess whether the increased promotional support has attracted additional new buyers, light buyers or heavy buyers of the brand by using the CTA benchmark. The NBD model also sets a benchmark so that managers can evaluate their sales performance. It would be useful if managers could predict future sales contributed by new customers and existing customers. For example, if a manager finds that new customers contribute to sales less than expected, he or she could respond by adjusting sales and marketing activities to reach more (potential) buyers. In contrast, if the manager finds that current customers do not contribute to sales as much as estimated by the NBD model, the manager could 19

22 review those sales and marketing activities aimed at customer retention or improvement in share of purchases. Should those customers include key accounts (also known as major or national accounts), it may be necessary to review the effectiveness of the firm s key account program or to consider implementing such a program to ensure the most important customers receive required standards of product quality, customer service and sales representation (Boles et al., 1999). This issue is particularly important given recent moves by many firms to reduce their numbers of suppliers for strategic procurement reasons (Eggert et al., 2009) Limitations and future research This study constitutes an initial attempt to test the applicability of NBD modeling in a market (industrial manufacturing) perceived to be a boundary condition. Given the exploratory nature of the study, future research could build upon the findings and address limitations of the study. First, while NBD modeling can be used to track and benchmark brand performance metrics, such as loyalty, researchers criticize the model for not providing information on what drives performance (Ajzen, 1988; Miyazaki et al., 2001). Future research should investigate organizational purchasing patterns by incorporating explanatory factors into NBD modeling (e.g., see Banelis et al., 2005; Lee et al., 2011). One such explanatory variable may be the derived nature of sales of some business products and services. For example, sales of customized automotive components to car manufacturers are directly related to the manufacturers sales of specific car models; therefore, factoring in the sales of cars could provide greater explanatory power to the NBD modelling of the automotive components. 20

23 Second, future research should replicate the modeling using B2B datasets from a wide range of situations. Comparisons could be made between different supply arrangements, such as non-contractual and different types of contractual arrangements; between different process types, such as suppliers manufacturing in response to customer orders and those manufacturing products to stock in anticipation of future demand (Tukel and Dixit, 2013); and between manufacturers and resellers, since specialty distributors often deal with relatively small customers while manufacturers and some commodity distributors usually deal with large customers, their logistics, promotional strategies and sales patterns therefore being quite different (Decker, 1992). Similarly, comparisons could be made based on the nature of demand for the product; organizations making new-task purchases being willing to wait for special orders to obtain customized products, so that high inventory levels are unnecessary, while organizations making straight rebuys often have little brand or dealer loyalty, readily switching supplier if stock-outs occur, in turn requiring suppliers to maintain extensive inventory levels (Holdren and Hollingshead, 1999). This would strengthen the testing of the generalizability and robustness of the NBD model. Further development would be to extend CTA to multiple brands, effectively combining the NBD model with the Dirichlet multinomial distribution of brand choice (Goodhardt et al., 1984; Ehrenberg et al., 2004). Third, although this study found the NBD model to provide a good fit and reasonably good predictions of future industrial purchasing frequency, the Poisson assumption of the model is not free from theoretical criticism. Specifically, some researchers have noted that interpurchase time is usually more regular than the Poisson process (Chatfield and Goodhardt, 1973). This certainly could be the case for industrial purchases as a result of the production cycle. For 21

24 example, inter-purchase time could be regular at a weekly, monthly or quarterly interval, rather than random in nature as assumed by the Poisson distribution. Chatfield and Goodhardt (1973) tested the assumption of regularity by comparing the Poisson assumption with a more regular Erlang-2 assumption of inter-purchase time. Their results, subsequently confirmed by Dunn et al. (1983), negate concerns regarding inter-purchase regularity by showing that the Poisson assumption is robust. However, their research is based on consumer packaged goods data. Future research is required to extend the test to industrial purchasing data. In conclusion, despite apparent differences in decision-making processes between consumer and industrial purchasing situations, the NBD model seems robust in both environments, although further research is required to confirm the findings relating to industrial purchasing. 22

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