Article

# NBD Model of Repeat-Purchase Loyalty: An Empirical Investigation

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## Abstract

This article describes a model for predicting repeat-purchase loyalty based on consumer panel data. A modification of the original model is offered that permits its application to areas in which brands are not purchased as a multiple of a single-unit pack size. Results of the original and modified models are shown.

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... version ratio .39 (5)(6)(7)(8) .37 (5)(6)(7)(8)(9)(10)(11)(12) .45 (5-8) (RI, .,(1)) ...
... version ratio .39 (5)(6)(7)(8) .37 (5)(6)(7)(8)(9)(10)(11)(12) .45 (5-8) (RI, .,(1)) ...
... Often (ii) is measured by the coefficient of determination R 2 • In the present instance R 2 is a misleading measure tending to overstate the degree of fit. 8 Here we take as a measure of general fit a sum of squares based on the difference between actual values of RI and the values obtaining by estimating (10), then regenerating RI via (11), (12), and (3). This is the Root Mean Square Error (RMSE) calculation exhibited in Table 6. ...
Article
A depth of repeat model is presented that can forecast the demand for new consumer products. The relation of the model to other forecasting models is noted. Data analysis, estimation procedures, and the observed accuracy of forecasts are discussed.
... x Since a is restricted to 0 ;::;; a ;::;; 1, we can try different values of a until we satisfy (8), the sample proportion of zeroes equation. 6 We could use a search technique to solve this set of equations, but the problem does not really warrant that degree of sophistication. We could write a short computer program, and in a matter of seconds try (for example) a = .01, ...
... It i; then possible to estimate r' and t' from this truncated distribution. For details of these estimating procedures that neglect the zero term, the mathematically inclined reader is referred to [2] and the references therein, and [6] .. valid means for screening families. Obviously, any kind of conditional trend model must explicitly include these hard core nonbuyers. ...
... See the empirical work on repeat buying in[4,6] and the many references in[5].3 We have used the Raiffa and Schlaifer notation[8] because it makes the updating to Period 2 easier to understand; the formulas are also somewhat simpler. ...
Article
Goodhardt and Ehrenberg have developed a useful stochastic model for analyzing period-to-period fluctuations in sales. In this article we generalize their model to allow for nonbuyers of the product category. A systematic bias in their simple negative binomial distribution (NBD) model is demonstrated. In fact if the proportion of nonbuyers is large, the simple model will be wrong. We also give explicit formulas and directions that allow a moderately sophisticated analyst to perform his own conditional trend analysis.
... Müşteri sadakatinin üç farklı yaklaşımı bulunmaktadır. Bunlar davranışsal sadakat yaklaşımı (Grahn, 1969); tutumsal sadakat yaklaşımı (Bennett vd., 2002;Jacoby, 1971;Jacoby ve Chestnut, 1978) ve tutumsal ve davranışsal sadakat yaklaşımının birleşimidir (Dick ve Basu, 1994;Jacoby, 1971;Jacoby ve Chestnut, 1978;Oliver, 1997). Davranışsal sadakat yaklaşımı kapsamında Grahn (1969), tüketici anket verilerine dayalı olarak tekrar satın alma bağlılığını veya davranışsal bağlılığı öngörmeye yönelik deneysel bir model tanımlamaktadır. ...
... Bunlar davranışsal sadakat yaklaşımı (Grahn, 1969); tutumsal sadakat yaklaşımı (Bennett vd., 2002;Jacoby, 1971;Jacoby ve Chestnut, 1978) ve tutumsal ve davranışsal sadakat yaklaşımının birleşimidir (Dick ve Basu, 1994;Jacoby, 1971;Jacoby ve Chestnut, 1978;Oliver, 1997). Davranışsal sadakat yaklaşımı kapsamında Grahn (1969), tüketici anket verilerine dayalı olarak tekrar satın alma bağlılığını veya davranışsal bağlılığı öngörmeye yönelik deneysel bir model tanımlamaktadır. Davranışsal yaklaşım, ürün veya hizmetlerin mükerrer satın alınmasını, aynı şirketten ek ve çeşitli mal veya hizmetlerin satın alınmasını ve şirketi başkalarına tavsiye etmeyi içermektedir (Joseph vd., 2009). ...
... Customer loyalty has three distinct approachesbehavioural loyalty approach (Grahn, 1969); attitudinal loyalty approach (Bennett & Rundle-Thiele, 2002;Jacoby, 1971;Jacoby & Chestnut, 1978) and integration of attitudinal and behavioral loyalty approach (Dick & Basu, 1994;Jacoby, 1971;Jacoby & Chestnut, 1978;Oliver, 1997). Grahn (1969) describes an empirical model for predicting repeat-purchase loyalty or behavioural loyalty based on consumer panel data. ...
... Customer loyalty has three distinct approachesbehavioural loyalty approach (Grahn, 1969); attitudinal loyalty approach (Bennett & Rundle-Thiele, 2002;Jacoby, 1971;Jacoby & Chestnut, 1978) and integration of attitudinal and behavioral loyalty approach (Dick & Basu, 1994;Jacoby, 1971;Jacoby & Chestnut, 1978;Oliver, 1997). Grahn (1969) describes an empirical model for predicting repeat-purchase loyalty or behavioural loyalty based on consumer panel data. Jacoby and Chestnut (1978) define attitudinal loyalty as the consumer's predisposition towards a brand as a function of psychological processes which includes attitudinal preference and commitment towards the brand. ...
Article
India has the world’s second largest telecom network, surpassed only by China. In the year 2015–16, India crossed the milestone of one billion telecom subscribers. India’s total telecom subscription stands at 1209.96 million as on August 2017. The telecom sector in India is expected to witness a huge growth in the coming future. The Indian telecom sector is characterized by intense competition as a consequence of low switching costs and price sensitivity among customers. This is what makes the study of ‘Customer Loyalty’ very important as it guides the various stakeholders and help formulate effective customer retention strategies. The present study is based on developing a holistic model of ‘Customer Loyalty’ using the data collected from 770 prepaid telecom subscribers from Delhi and Haryana telecom circles in India. The Structural Equation Modelling technique with the aid of Analysis of Moment Structures (AMOS) statistical package is used for the purpose. The comparative impact of each of the drivers of customer loyalty is computed utilizing the standardized regression weights taken from the path model. Net Promoter Scores (NPS) of all the concerned telecom operators are calculated in order to compare customer loyalty amongst them. The study produces various findings and crucial insights that hold vital implication to the various stakeholders concerned. © 2019
... In Grahn's recent article [2] he presents an empirical analysis of the negative binomial distribution (NBD) model of repeat purchase loyalty. Any researcher who does extensive work with this model must estimate the parameters of the NBD many times. ...
... Hence, w = 0.424354, and from (2) we obtain b = 0.638962 and k = 2.26014. Substituting kin (1) we get Po -1 + 2.26014 = -9.35 ...
Article
One parameter of the negative binomial distribution (NBD) model of repeat purchase loyalty is obtained by an iterative search procedure on an implicit equation. This note presents an extremely accurate explicit series approximation for this parameter. When solving for the parameters by hand, one can use some very efficient table to look up procedures. However, when a researcher is solving for many sets of parameter values, our procedure is much easier to program.
... Customer loyalty has been tested in previous research through three main approaches: the attitudinal loyalty approach, behavioral loyalty approaches, and the combined attitudinal and behavioral approach [21,26,27]. While behavioral loyalty denotes actual recurrent purchase behavior, loyalty in attitudes relates to consumer's psychological state [28]. ...
Article
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With globalization and technological advances, the competition in the jewelry market is becoming increasingly fierce. Under the influence of the pandemic, it is even more difficult for brands like Pandora, which is positioned in the mid-market, to compete for market share. The purpose of this study was to explore the impact of Pandora’s brand identity and brand image on customer loyalty during COVID-19. Different from the previous article, it further analyzed the adjustments and improvements made by Pandora in terms of branding when it was in the face of downtown and the pandemic. Through the use of a SWOT analysis, a qualitative study was conducted. The research concluded that the brand identity and image of Pandora can positively and significantly influence the loyalty of its customers, while it is essential to ensure that the brand identity and image are consistent. Therefore, both scholars and companies should be aware of the importance of brand identity and brand image. The market and theoretical implications of the study and future studies are finally discussed.
... However, the previous study analyzed Taylor's law for product sales under the assumption that 2 X ∕ X = 1 . This was based on the general and feasible postulations that the count X of purchased items of a single customer in a given time unit follows a Poisson distribution or that the parameter of such a Poisson distribution follows a gamma distribution [11,[16][17][18]. We did not assume 2 X ∕ X = 1 ; rather, we estimated 2 X ∕ X to find that, for many of the brands in the categories of Japanese Tea and Instant Noodles, the value was significantly greater than 1, indicating that the fluctuation of X is greater than would be expected if a customer purchases an item completely randomly, i.e., where X follows a Poisson distribution. ...
Article
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In recent years, Taylor’s law describing the power function relationship between the mean and standard deviation of certain phenomena has found an increasing number of applications. We studied the characteristics of Taylor’s law for branded product sales using point-of-sale (POS) data for brands sold in 72 grocery stores in the Greater Tokyo area. A previous study found that product sales follow Taylor’s law with a scaling exponent of 0.5 for low sales quantities and 1.0 for large sales quantities. In the current study, we observed Taylor’s law with cross-over for 54 product brands and estimated the value of the two coefficients in the theoretical curve to characterize the cross-over. The coefficients represent the fluctuations in the number of items purchased per consumer and the number of consumers in one store and in all stores. The estimated coefficients suggested the dependence of the features of Taylor’s law on the category to which the brands belong. We found that brands in the same category tend to share similar features under Taylor’s law. However, some brands exhibited specific features that differed from others in the same category. For example, for many brands in the Laundry Detergent and Instant Noodles categories, the number of customers purchasing the products in each store fluctuated significantly, whereas the number of purchased items per customer varied widely in the Japanese Tea category. In the coffee category, our results indicated that the degree of fluctuation in the number of purchasing customers largely depends on the brand.
... A variety of predictive models for air traveler repeat purchasing have been developed over the past decades in traditional businesses. Nonparametric regression models, such as the k-nearest neighbor (KNN) model [16], negative binomial distribution models [17], logistic regression models [18,19], Bayesian neural network learning models [20], time evolution models, such as time series models [21], and artificial bee colony (ABC) models [12], are commonly used. However, those methods and algorithms used to model in the traditional business context have to be modified for mobile commerce in airlines [10]. ...
Article
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How to promote air traveler repurchasing has become an important marketing strategy in airlines. However, because of the growing concern over user privacy, effectively and accurately delivering advertising to promote repurchasing has become more difficult. Here, we propose an effective framework based on machine learning to model the air traveler repurchasing and furthermore employ a field experiment to test the utility of a model framework. Specifically, we collected that this model framework is based on the random forest algorithm and compared with the conclusions of the other four algorithms, K-nearest neighbor, decision tree, support vector machine, and ExtraTree algorithms. The results show that the proposed model framework is better than the prediction results of the other algorithms. In addition, the proposed model framework was verified through a real case of an airline in China. This study will serve as a guide to analyze the repurchase behaviors of an air traveler and help airlines build a loyal air traveler base.
... Loyalitas menghubungkan keberhasilan dan profitabilitas suatu perusahaan (Eakuru & Mat, 2008). Loyalitas pelanggan umumnya dibedakan dalam tiga pendekatan termasuk pendekatan loyalitas perilaku (Grahn, 1969); pendekatan loyalitas sikap (Bennett & Rundle-Thiele, 2002;Jacoby et al., 1978), dan integrasi sikap dan pendekatan loyalitas perilaku (Dick & Basu, 1994;Jacoby et al., 1978;Oliver, 1999). Loyalitas sikap membantu untuk memeriksa faktor-faktor loyalitas, untuk menghindari perilaku beralih dan untuk memprediksi berapa lama pelanggan akan tetap setia (Jacoby et al., 1978). ...
Article
Full-text available
JRMB Jurnal Riset Manajemen dan Bisnis CC BY: This license allows reusers to distribute, remix, adapt, and build upon the material in any me dium or format, so long as attribution is given to the creator. The license allows for commercial use. The purpose of this study is to determine whether food quality, price, environmental location and service quality affect customer satisfaction, and whether customer satisfaction affects customer loyalty as well, and to determine whether brand image strengthens or weakens customer satisfaction and customer loyalty. This study uses a survey method with an questionnaire for data collection. This research method uses multiple linear analysis test, the population and sample of this research are customers who are located around Tangerang. The total number of samples in this study were 150 respondents. The results of this study explain that food quality has a positive and significant effect on customer satisfaction, and price has a significant positive effect on customer satisfaction, and location and environment have a positive and significant effect on customer satisfaction, and service quality has a positive and significant effect on customer satisfaction, and customer satisfaction has a positive and significant effect on customer loyalty, and brand image moderates customer satisfaction and customer loyalty.
... In the late 60's an important change occurred -the unit of analysis moved from the individual SKUs of a brand and the number of units purchased (purchase quantity) to simply the purchase occasion (purchase incidence) (Ehrenberg, 1968(Ehrenberg, , 1969Grahn, 1969). The difference is subtle, yet powerful. ...
Article
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We present a review of Gerald Goodhardt's most famous contribution to marketing science—the NBD‐Dirichlet model. This provides a powerful illustration of the complex pathway and useful associated discoveries that over 25 years lead to the specification and application of a key marketing model. We identify the process that started with the negative binomial distribution (NBD) applied to purchase incidence, examined alternatives such as the logarithmic series distribution (LSD) and the beta binomial distribution (BBD), and along the way developed conditional trend analysis (CTA). We then explore the development of brand choice beginning with duplication of purchase as a method for understanding the underlying patterns, before moving into various approaches to modelling choice including a multivariate NBD, and eventually a multivariate BBD—the Dirichlet multinomial distribution (DMD). We discuss key events in modelling consumer behaviour and outline the model's implications for how marketers should think about consumers, or more specifically the Dirichlet consumer. Finally, we provide a survey of the model's applications uncovering a rich recent history and bright future for Goodhardt's legacy.
... Other authors have distinguished the concept in form of three approaches. For instance Grahn (1969) In most of these studies, the direct relationship between customer trust and customer loyalty has been a major point of focus. However, it can be assumed that if companies strive to develop a consistent and trustworthy relationship with their customers over time, such relationship might likely be transformed into a positive reputation and brand image for the company which will consequently lead to a repurchase commitment from the customers. ...
Article
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With the intense competition in the Nigerian mobile telecom industry coupled with high switching rate among subscribers, companies have been directing their marketing expenditure towards the enhancement of those customer relationship tactics which is deemed as capable of providing the much needed customer loyalty base. There are empirical evidences indicating that the perception of trust by customers can act as a precursor to customer loyalty. However, little is known regarding the presence of any mediating variable in this relationship. This study investigates the mediating power of brand image in the trust-customer loyalty relationship among subscribers in the Nigerian Mobile Telecommunication industry. Making use of primary data elicited through close ended and structured questionnaire from three hundred and ninety (390) mobile phone services users who were selected through the multistage sampling technique: cluster sampling, proportionate sampling and convenience sampling, the results from the Pearson product moment correlation and the linear regression analysis indicates that both brand image and trust have a linear relationship with customer loyalty at the 0.001 significant level. However, brand image was found to exercise a stronger effect on customer loyalty in a separate linear regression that considered both trust and brand image as independent variables. In other words, brand image mediates the relationship between trust and customer loyalty. In the light of these findings, companies were advised on the need to equally focus on increasing brand image whenever the objective is increasing customer loyalty from the viewpoint of trust.
... To summarize, Morrison has pointed out that the basis of the conditional trend analysis approach (and of the more general NBD/LSD theory) is that it has been shown to fit purchasing data from numerous products. However, a good many systematic subpatterns or additional factors also occur in practice, many of which have been documented elsewhere [1,2,3,7,8]. Some are of technical (model building) interest only at this stage, others are of direct marketing relevance. ...
... Accordingly, these purchasers not only buy more frequently but buy differently. Grahn (1969) introduced the purchase occasion as the unit of analysis in purchase frequency models. 'Subsequently, Ehrenberg and Goodhardt acknowledged that much of their earlier work with the negative binomial distribution (NBD) had been formulated incorrectly in terms of amounts bought instead of purchase occasions (1968, p. 164), and Ehrenberg adapted the NBD model to account for numbers of purchasing trips, treating the quantity bought per trip as a separate variable (1972, p. 229). ...
Article
The lognormal distribution is shown to account well for purchase frequency heterogeneity in the U.S. dentifrice market, including subgroups of households. Renewal process assumptions are used to define the market population. As the definition would exclude some very infrequent buyers, left-truncated lognormal distributions are fitted to the data.
... Literature review shows that customer loyalty has three distinct approaches. Behavioral loyalty approach (Grahn, 1969); attitudinal loyalty approach (Bennett and Rundle-Thiele, 2002;Jacoby, 1971;Jacoby and Chestnut, 1978) and integration of attitudinal and behavioral loyalty approach (Dick and Basu, 1994;Jacoby, 1971;Jacoby and Chestnut, 1978;Oliver, 1997). The results evidenced the dominance of the 'stable parts' of customer transactions over the 'unexpected incidents' such as fault repairs and new service provision. ...
... Literature review shows that customer loyalty has three distinct approaches. Behavioral loyalty approach (Grahn, 1969); attitudinal loyalty approach (Bennett and Rundle-Thiele, 2002;Jacoby, 1971;Jacoby and Chestnut, 1978) and integration of attitudinal and behavioral loyalty approach (Dick and Basu, 1994;Jacoby, 1971;Jacoby and Chestnut, 1978;Oliver, 1997). The results evidenced the dominance of the 'stable parts' of customer transactions over the 'unexpected incidents' such as fault repairs and new service provision. ...
... Early applications of the NBD to the modeling of customer buying behavior assumed that the number of purchases of a particular pack size of the focal brand made by an individual in a given time period could be characterized by a Poisson distribution. As the model was used by other researchers, its poor fit in some settings, along with the challenges of how to model the purchasing of a brand with multiple pack sizes that may not be integer multiples of the smallest pack size (e.g., Grahn, 1969) or the purchasing of products such as gasoline led to a seemingly minor yet fundamental shift in the nature of the count phenomenon being modeled (Ehrenberg, 1988), from the number of purchases to the number of purchase occasions (or transactions). It is now standard to think of the NBD as the fundamental model for characterizing the distribution of the number of transactions across a group of individuals for a given time period. ...
... Yet when purchase data is aggregated, clear patterns emerge that can be described by well-known statistical distributions (Bass, 1995;Ehrenberg, Uncles and Goodhardt, 2004). Best known among these statistical models is probably the negative binomial distribution or NBD (Ehrenberg, 1959;Grahn, 1969;Morrison and Schmittlein, 1988). However, studies using the NBD to analyse buyer behaviour mostly restrict their analysis to a single period. ...
Article
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This study validates a spreadsheet for conditional trend analysis (CTA). CTA was introduced by Goodhardt and Ehrenberg (1967) as an extension to the negative binomial distribution. It predicts the purchase rate of consumers in a subsequent period, based on their current period purchase class (zero buyers, bought once, twice and so forth). These predictions allow companies who use panel data to benchmark and track buying behaviour over time. For example, how much attrition in purchase rates for "heavy buyers" is to be expected? CTA will provide the answer. There have been no easily available tools to apply CTA, limiting research in this area, until recently an appropriate spreadsheet was developed. In this paper we test the validity of the spreadsheet's calculations, using three datasets reported in Goodhardt and Ehrenberg (1967). We find that the spreadsheet yields similar results to the original study, demonstrating that the spreadsheet can be used with confidence to spur research in this under-developed area.
... Thus, loyalty links the success and profitability of a firm (Eakuru & Mat, 2008). Customer loyalty is commonly distinguished in three approaches including behavioral loyalty approach (Grahn, 1969); attitudinal loyalty approach (Bennett & Rundle-Thiele, 2002;Jacoby, 1971;Jacoby & Chestnut, 1978), and integration of attitudinal and behavioral loyalty approach (Dick & Basu, 1994;Jacoby, 1971;Jacoby & Chestnut, 1978;Oliver, 1997). The attitudinal loyalty helps to examine the factors of loyalty, to avoid switching behavior (Caceres & Paparoidamis, 2007), and to predict how long customers will remain loyal (Jacoby & Chestnut, 1978). ...
Article
Corporate image has been assessed as an important antecedent of customer satisfaction and loyalty. Corporate brand is vital because positive corporate brands help companies achieving higher performance, such as sales. Marketing exists to deliver more value to satisfy customers as well as build a long-term and mutually profitability relationship with customers. If a firm's products or services do not satisfy or meet the customer's needs and wants, all the strategies are insufficient. With loyal customers, companies can have higher market share and reduce the operating cost. An improvement of 5 percent in customer retention leads to an increase of 25 percent to 75 percent in profit. It costs more than five times as much to obtain a new customer than to keep an existing one. This initial study was from relevant literature, then set up research structure and hypotheses. Survey was employed, and respondents were from the customers of Starbucks Coffee in Taipei area. There were 199 usable questionnaires to analyze descriptive statistics, reliability, validity, and SEM model. The research found that corporate brand image significantly affects customer satisfaction and customer loyalty, and customer satisfaction has strong impact on customer loyalty for the sample. Therefore, firms have to specifically focus on these factors in order to build a long-term and mutually profitability relationship with a customer and create loyalty as competitive advantages in the market.
... Marketing theory and practice have over the last several decades developed a number of brand choice models or simulations (Grahn 1969;Dodds 1973;Winer 1986;Labeaga-Azcona et al. 2010;Lee et al. 2011). This research has focused on frequently purchased fast moving consumables and has used large scanner-based datasets to model choice, based on behavioral characteristics and the impact of the firm's marketing strategy. ...
Article
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The current use of 3G technologies has created significant demands for capacity, such as cell TV, and this needs to be balanced with the capital constraints of many firms. Providers face price pressures on margins and the need to update cell networks to 4G in the post-GFC era where capital is scarce. Understanding consumer behavior in this area by use of simulations may be a time and cost efficient method, but how accurate is it? This study demonstrates that the use of a simple, agent-based model can lead to accurate initial prediction of parameters of satisfaction with a cell phone provider, and provides a basis of understanding factors of cell phone subscriber choice in the context of the introduction of new technology.
... Note that the use of simulations in marketing is not new; marketing theory and practice over the last several decades has developed a number of brand choice models or simulations (Dodds, 1973;Grahn, 1969;Labeaga-Azcona et al., 2010;Lee et al., 2011;Winer, 1986). Discrete choice models can also be seen as another type of simulation. ...
Article
The study of complex systems through agent based modelling present opportunities for marketing researchers to develop time and space explanations of interactions that occur in the marketplace and determine emergent phenomena, such as the adoption of new technology or successful business networks. The use of simulations and the ideas of complex systems though may appear baffling to many and the acceptance of simulations, especially agent based models has a long way to go given concerns about the validity and realism of many models. In this special issue we aim to present a number of papers which show a wide range of applications of agent based models to study business environments and consumer behaviour. There are also theoretical and methodological papers dealing with this new research paradigm. The validation of simulation models both by competing programs and with real world data is discussed in this special issue. Chinese abstract. 通过基于主体建模而对复杂系统进行的研究使市场研究人员可以从时间和空间方面解释在市场上所出现的各种 相互作用, 以及预测比如采用新的技术或成功的商业网络等现象的出现。模拟的应用以及复杂系统的思路在很 多场合下会令人捉摸不透, 而且考虑到众多的这些模拟– 特别是基于主体建模– 还有有效性和现实性的疑问, 该模拟能够获得认可是任重而道远的。在本专辑中, 我们致力呈现基于主体建模在商业环境和消费者行为方面 的广泛应用。同时还为这个新的研究范例提供理论和方法的论文资料。本专辑也会探讨如何透过其他非基于主 体建模的模型以及分析实际数据对该基于主体建模的模拟模型进行验证。
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Repeat purchasing, i.e., a customer purchasing the same product multiple times, is a common phenomenon in retail. As more customers start purchasing consumable products (e.g., toothpastes, diapers, etc.) online, this phenomenon has also become prevalent in e-commerce. However, in January 2014, when we looked at popular e-commerce websites, we did not find any customer-facing features that recommended products to customers from their purchase history to promote repeat purchasing. Also, we found limited research about repeat purchase recommendations and none that deals with the large scale purchase data that e-commerce websites collect. In this paper, we present the approach we developed for modeling repeat purchase recommendations. This work has demonstrated over 7% increase in the product click through rate on the personalized recommendations page of the Amazon.com website and has resulted in the launch of several customer-facing features on the Amazon.com website, the Amazon mobile app, and other Amazon websites.
Article
Purpose Despite the growing availability of scanner-panel data, surveys remain the most common and inexpensive method of gathering marketing metrics. The purpose of this paper is to explore the size, direction and correction of response errors in retrospective reports of category buying. Design/methodology/approach Self-reported purchase frequency data were validated using British household panel records and the negative binomial distribution (NBD) in six packaged goods categories. The log likelihood theory and the fit of the NBD model were used to test an approach to adjusting the errors post-data collection. Findings The authors found variations in systematic response errors according to buyer type. Specifically, lighter buyers tend to forward telescope their buying episodes. Heavier buyers tend either to over-use a rate-based estimation of once-a-month buying and over-report purchases at multiples of six or to use round numbers. These errors lead to overestimates of penetration and average purchase frequency. Adjusting the aggregate data for the NBD, however, improves the accuracy of these metrics. Practical implications In light of the importance of purchase data for decision making, the authors describe the inaccuracy problem in frequency reports and offer practical suggestions regarding the correction of survey data. Originality/value Two novel contributions are offered here: an investigation of errors in different buyer groups and use of the NBD in survey accuracy research.
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The study of complex systems through agent based modelling present opportunities for marketing researchers to develop time and space explanations of interactions that occur in the marketplace and determine emergent phenomena, such as the adoption of new technology or successful business networks. The use of simulations and the ideas of complex systems though may appear baffling to many and the acceptance of simulations, especially agent based models has a long way to go given concerns about the validity and realism of many models. In this special issue we aim to present a number of papers which show a wide range of applications of agent based models to study business environments and consumer behaviour. There are also theoretical and methodological papers dealing with this new research paradigm. The validation of simulation models both by competing programs and with real world data is discussed in this special issue.
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When the underlying responses are discrete, the interval estimation of the intraclass correlation derived from the normality assumption is not strictly valid for use. This paper focuses the interval estimation on the intraclass correlation under the negative binomial distribution, that has been commonly applied in epidemiological or consumer purchasing behaviour studies. This paper develops two simple asymptotic interval estimation procedures in closed forms for the intraclass correlation. To evaluate the performance of these procedures, a Monte Carlo simulation is carried out for a variety of situations. An example about consumer purchasing behaviors is also included to illustrate the use of the two proposed interval estimation procedures.
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The concept of loyalty is not new in marketing; in fact, it has been one of the most investigated topics. Nevertheless it has not managed to unify criteria on its definition for being a complex phenomenon. Initially, the study of the loyalty was approached from two different ways: As an attitude, where they give themselves fitted feelings and positive affections in favour of a brand; and as an effective behaviour materialized in purchases repeated of the same brand. Then, it was considered to be a current that rises that the measurement of the loyalty does not concern exclusively the valuation of the behaviour of repurchase or the commitment, both of them. The aim of this article is to describe the most relevant aspects of the concept of brand loyalty, from the review and theoretical analysis, specifically its definition, approaches, methods of measurement and types, to present some final considerations.
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A method of analyzing the components of a trend in consumer purchasing is described. An empirically-based mathematical model is first used to predict the purchasing pattern in the absence of a trend. Comparison between the observed data and these predicted norms permits a detailed evaluation of the trend. Two examples of practical applications of the technique are presented.
Article
Of the people who buy a brand or product in a given period of time, a certain number—the “loyal” buyers—will buy again in a later one. The proportion of buyers who are loyal in both can be predicted from a mathematical model, using observed data relating to one period only. In verifying the predictions against the actually observed loyalty proportion for the following period, the goodness of fit has, with one exception, averaged about half a percentage point for loyalty percentages ranging from less than one percent to over 25 percent. Practical applications of developments of this kind are also discussed.
Article
In this article Mr Ehrenberg shows how data on purchases of non-durable consumer goods can be fitted by the negative binomial distribution, and discusses applications of this finding. He also considers a simple model for purchases made in different periods of time and some quick and easy methods for calculating standard errors.
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Two closely related stochastic models are described: The two-parameter NBD or negative binomial distribution model, and the simpler LSD or logarithmic series distribution model.
Article
Of the people who buy a brand or product in a given period of time, a certain number-the "loyal" buyers-will buy again in a later one. The proportion of buyers who are loyal in both can be predicted from a mathematical model, using observed data relating to one period only. In verifying the predictions against the actually observed loyalty proportion for the following period, the goodness of fit has, with one exception, averaged about half a percentage point for loyalty percentages ranging from less than one percent to over 25 percent. Practical applications of developments of this kind are also discussed.
New Dimensions in Analysis of Brand Switching
• Alfred E Kuehn
• Albert C Rohloff
Alfred E. Kuehn and Albert C. Rohloff, "New Dimensions in Analysis of Brand Switching," New Directions in Marketing, Chicago: American Marketing Association, 1965, 297-308.