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The beta-geometric (BG) distribution and the Pareto distribution of the second kind (P(II)) are two basic models for duration-time data that share some underlying characteristics (i.e., continuous ...

Background Critical stakeholder-identified gaps in current health research engagement strategies include the exclusion of voices traditionally less heard and a lack of consideration for the role of trauma in lived experience. Previous work has advocated for a trauma-informed, intersectional, and critical reflexive approach to patient and public involvement in health research. The Valuing All Voices Framework embodies these theoretical concepts through four key components: trust, self-awareness, empathy, and relationship building. The goal of this framework is to provide the context for research teams to conduct patient engagement through the use of a social justice and health equity lens, to improve safety and inclusivity in health research. The aim of this study was to revise the proposed Valuing All Voices Framework with members of groups whose voices are traditionally less heard in health research. Methods A qualitative descriptive approach was used to conduct a thematic analysis of participant input on the proposed framework. Methods were co-developed with a patient co-researcher and community organizations. Results Group and individual interviews were held with 18 participants identifying as Inuit; refugee, immigrant, and/or newcomer; and/or as a person with lived experience of a mental health condition. Participants supported the proposed framework and underlying theory. Participant definitions of framework components included characterizations, behaviours, feelings, motivations, and ways to put components into action during engagement. Emphasis was placed on the need for a holistic approach to engagement; focusing on open and honest communication; building trusting relationships that extend beyond the research process; and capacity development for both researchers and patient partners. Participants suggested changes that incorporated some of their definitions; simplified and contextualized proposed component definitions; added a component of “education and communication”; and added a ‘how to’ section for each component. The framework was revised according to participant suggestions and validated through member checking. Conclusions The revised Valuing All Voices Framework provides guidance for teams looking to employ trauma-informed approaches, intersectional analysis, and critical reflexive practice in the co-development of meaningful, inclusive, and safe engagement strategies. Plain English Summary Patient engagement in health research continues to exclude many people who face challenges in accessing healthcare, including (but not limited to) First Nations, Inuit, and Metis people; immigrants, refugees, and newcomers; and people with lived experience of a mental health condition. We proposed a new guide to help researchers engage with patients and members of the public in research decision-making in a meaningful, inclusive, and safe way. We called this the Valuing All Voices Framework, and met with people who identify as members of some of these groups to help define the key parts of the framework (trust; self-awareness; empathy; and relationship building), to tell us what they liked and disliked about the proposed framework, and what needed to be changed. Input from participants was used to change the framework, including clarifying definitions of the key parts, adding another key part called “education and communication”, and providing action items so teams can put these key parts into practice.

Additional file 2: Appendix 2. Participant Interview Guide

The growth of subscription-based commerce has changed the types of data that firms report to external shareholders. More than ever, companies are discussing and disclosing information on the number of customers acquired and lost, customer lifetime value, and other data. This has fueled an increasing interest in linking the value of a firm's customers to the overall value of the firm, with the term “customer-based corporate valuation” being used to describe such efforts. Although several researchers in the fields of marketing and accounting have explored this idea, their underlying models of customer acquisition and retention do not adequately reflect the empirical realities associated with these behaviors, and the associated valuation models do not meet the standards of finance professionals. The authors develop a framework for valuing subscription-based firms that addresses both issues, and they apply it to data from DISH Network and Sirius XM Holdings.

We address a critical question that many firms are facing today: Can customer data be stored and analyzed in an easy-to-manage and scalable manner without significantly compromising the inferences that can be made about the customers’ transaction activity? We address this question in the context of customer-base analysis. A number of researchers have developed customer-base analysis models that perform very well given detailed individual-level data. We explore the possibility of estimating these models using aggregated data summaries alone, namely repeated cross-sectional summaries (RCSS) of the transaction data. Such summaries are easy to create, visualize, and distribute, irrespective of the size of the customer base. An added advantage of the RCSS data structure is that individual customers cannot be identified, which makes it desirable from a data privacy and security viewpoint as well. We focus on the widely used Pareto/NBD model and carry out a comprehensive simulation study covering a vast spectrum of market scenarios. We find that the RCSS format of four quarterly histograms serves as a suitable substitute for individual-level data. We confirm the results of the simulations on a real dataset of purchasing from an online fashion retailer.

In today’s turbulent business environment, customer retention presents a significant challenge for many service companies. Academics have generated a large body of research that addresses part of that challenge – with a particular focus on predicting customer churn. However, several other equally important aspects of managing retention have not received similar level of attention, leaving many managerial problems not completely solved, and a program of academic research not completely aligned with managerial needs. Therefore, our goal is to draw on previous research and current practice to provide insights on managing retention and identify areas for future research. This examination leads us to advocate a broad perspective on customer retention. We propose a definition that extends the concept beyond the traditional binary retain/not retain view of retention. We discuss a variety of metrics to measure and monitor retention. We present an integrated framework for managing retention that leverages emerging opportunities offered by new data sources and new methodologies such as machine learning. We highlight the importance of distinguishing between which customers are at risk and which should be targeted – as they aren’t necessarily the same customers. We identify tradeoffs between reactive and proactive retention programs, between short-term and long-term remedies, and between discrete campaigns and continuous processes for managing retention. We identify several areas of research where further investigation will significantly enhance retention management.

We investigate the increasingly common business setting in which companies face the possibility of both observed and unobserved customer attrition (i.e., “overt” and “silent” churn) in the same pool of customers. This is the case for many online-based services where customers have the choice to stop interacting with the firm either by formally terminating the relationship (e.g., canceling their account) or by simply ignoring all communications coming from the firm. The standard contractual versus noncontractual categorization of customer–firm relationships does not apply in such hybrid settings, which means the standard models for analyzing customer attrition do not apply. We propose a hidden Markov model (HMM)-based framework to capture silent and overt churn. We apply our modeling framework to two different contexts—a daily deal website and a performing arts organization. In contrast to previous studies that have not separated the two types of churn, we find that overt churners in these hybrid settings tend to interact more, rather than less, with the firm prior to churning; that is, in settings where both types of churn are present, a high level of activity—such as customers actively opening emails received from the firm—is not necessarily a good indicator of future engagement; rather it is associated with higher risk of overt churn. We also identify a large number of “silent churners” in both empirical applications—customers who disengage with the company very early on, rarely exhibit any type of activity, and almost never churn overtly. Furthermore, we show how the two types of churners respond very differently to the firm’s communications, implying that a common retention strategy for proactive churn management is not appropriate in these hybrid settings. Data and the online appendix are available at https://doi.org/10.1287/mksc.2017.1057 .

Cohort-level retention rates typically increase over time, and the beta-geometric (BG) distribution has proven to be a robust model for capturing and projecting these patterns into the future. According to this model, the phenomenon of increasing cohort-level retention rates is purely due to cross-sectional heterogeneity; an individual customer’s propensity to churn does not change over time. In this paper we present the beta-discrete-Weibull (BdW) distribution as an extension to the BG model, which allows individual-level churn probabilities to increase or decrease over time. In addition to capturing the phenomenon of increasing cohort-level retention rates, this new model can also accommodate situations in which there is an initial dip in retention rates before they increase (i.e., a U-shaped cohort-level retention curve). A key finding is that even when aggregate retention rates are monotonically increasing, the individual-level churn probabilities are unlikely to be declining over time, as conventional wisdom would suggest. We carefully explore these connections between heterogeneity, duration dependence, and the shape of the retention curve, and draw some managerially relevant conclusions, e.g., that accounting for cross-sectional heterogeneity is more important than accounting for any individual-level dynamics in churn propensities.

In today’s turbulent business environment, customer retention presents a significant challenge for many companies. Academics have generated a large body of research that addresses part of that challenge – with a particular focus on predicting customer churn. However, several other equally important aspects of managing retention have not received similar level of attention. This suggests a managerial problem not completely solved, and a program of academic research not completely aligned with managerial needs. Therefore, our goal is to draw on previous research and current practice to provide insights on managing retention and identify areas for future research. This examination leads us to advocate a broad perspective on customer retention. We propose a definition that extends the concept beyond the traditional binary retain/not retain view of retention. We discuss a variety of metrics to measure and monitor retention. We develop a framework for managing retention that leverages emerging opportunities offered by new data sources and new methodologies such as machine learning. We highlight the importance of distinguishing between which customers are at risk and which should be targeted – as they aren’t necessarily the same customers. We identify trade offs between reactive and proactive retention programs, between short-term and long-term remedies, and between discrete campaigns and continuous processes for managing retention. We identify several areas of research where further investigation will significantly enhance retention management.

A customer-centric firm takes the view that there are three key drivers of (organic) growth and overall profitability: Customer acquisition , customer retention , and customer development (i.e., increasing the value of each existing customer (per unit of time) while they remain a customer). In this chapter we review the key data-based tools and methods that have been developed by marketing scientists (and researchers and practitioners in related fields such as operations research, statistics, and computer science) to assist firms in their understanding and implementing these activities more effectively.

High voltage station and line insulators are vulnerable to volcanic ash-induced flashover, yet little quantitative data exists on the environmental, volcanological and electrical parameters most influential in reducing their flashover voltage. This paper presents the results from clean-fog rapid flashover tests for 5 different suspension insulators of ceramic, non-ceramic, or RTV-coated design under different environmental and volcanic ash contamination scenarios. Results suggest that moderate accumulations (up to 3 mm) of volcanic ash can accumulate on insulator surfaces without critically reducing the flashover voltage, provided >40% of the creepage distance remains clean and dry. Composite polymer insulators have higher dielectric strength than ceramic equivalents under light to heavy pollution severities, however, all insulators tested here perform comparably when critically contaminated (i.e. both top and bottom surfaces coated in ash). Based on these and other findings, some basic discussion of optimal insulator selection in ashy environments is provided.

While accurate point estimation of customer lifetime value (CLV) has been the target of a large body of academic research, few have focused on the variance of CLV (V(CLV)), which represents the degree of uncertainty associated with a customer's expected CLV. This is ironic because academics have long known that V(CLV) is one of the most important characteristics that defines and differentiates customers from one another, affecting firms on many fundamental levels. No closed-form, forward-looking statistical procedures have been derived to estimate individual-level V(CLV). For the first time, the authors derive, predict, and validate V(CLV) using a powerful combination of stochastic models for the flow of transactions over time and the company's profit on each transaction. They provide these estimates for 561,100 customers of an omnichannel retailer tracked over a 2.25-year period, making this one of the largest-scale CLV analyses to date. They highlight the importance of V(CLV), analyze its relationship to observable summary statistics such as recency, frequency, and monetary value, and uncover many substantive variance-related insights regarding customer segmentation, scoring, targeting, and more.

Objective: To explore prisoners’ views on their own health, health promotion and harm reduction measures, prior to a period of significant change in the way these services are delivered in the prison setting. Design: Structured interviews with prisoners as part of a wider Health Needs Assessment of a local prison. Setting: A high security prison in the West of Scotland with capacity for 700 male prisoners. Methods: A structured questionnaire with prisoners recruited from education, regular wings, and protection wings. Responses were analysed using thematic analysis and statistical techniques. Results: Seventy-nine prisoners were interviewed. Most prisoners reported their health as good or excellent, despite reporting high levels of risk-taking behaviour. Nearly half thought their health had improved since incarceration, citing reduced drug and alcohol use and healthier lifestyles. Prisoners expressed mixed views on harm reduction initiatives, with concerns around confidentiality, bullying, and being exposed to drug use or sexual activity in their ‘home’ environment. Conclusion: This study indicates the importance of listening to prisoners’ views about health promotion and harm reduction initiatives, and also of challenging their perceptions of what constitutes ‘good health’ and risk-taking behaviour. It also highlights the importance of environmental factors on prisoners’ health both within the prison and upon release.

Many businesses track repeat transactions on a discrete-time basis. These include (1) companies for whom transactions can only occur at fixed regular intervals, (2) firms that frequently associate transactions with specific events (e.g., a charity that records whether supporters respond to a particular appeal), and (3) organizations that choose to utilize discrete reporting periods even though the transactions can occur at any time. Furthermore, many of these businesses operate in a noncontractual setting, so they have a difficult time differentiating between those customers who have ended their relationship with the firm versus those who are in the midst of a long hiatus between transactions. We develop a model to predict future purchasing patterns for a customer base that can be described by these structural characteristics. Our beta-geometric/beta-Bernoulli (BG/BB) model captures both of the underlying behavioral processes (i.e., customers' purchasing while “alive” and time until each customer permanently “dies”). The model is easy to implement in a standard spreadsheet environment and yields relatively simple closed-form expressions for the expected number of future transactions conditional on past observed behavior (and other quantities of managerial interest). We apply this discrete-time analog of the well-known Pareto/NBD model to a data set on donations made by the supporters of a nonprofit organization located in the midwestern United States. Our analysis demonstrates the excellent ability of the BG/BB model to describe and predict the future behavior of a customer base.

In this article, we discuss the state of the art of models for customer engagement and the problems that are inherent to calibrating and implementing these models. The authors first provide an overview of the data available for customer analytics and discuss recent developments. Next, the authors discuss the models used for studying customer engagement, where they distinguish the following stages: customer acquisition, customer development, and customer retention. Finally, they discuss several organizational issues of analytics for customer engagement, which constitute barriers for introducing analytics for customer engagement.

The past few years have seen increasing interest in taking the notion of customer lifetime value (CLV) and extending it to value a customer base (with subsequent links to corporate valuation). The application of standard textbook discussions of CLV leads to calculations based on a single retention rate. However, at the cohort level, retention rates typically increase over time. It has been suggested that these observed dynamics are due, in large part, to a sorting effect in a heterogeneous population. We show that failing to recognize these dynamics yields a downward-biased estimate of the residual value of the customer base (compared to an aggregate analysis that ignores these dynamics). We also explore the implications of failing to account for retention dynamics when computing retention elasticities and find that the frequently reported values underestimate the true effect of increases in underlying retention rates in a heterogeneous world.

As more firms begin to collect (and seek value from) richer customer-level datasets, a focus on the emerging concept of customer-base analysis is becoming increasingly common and critical. Such analyses include forward-looking projections ranging from aggregate-level sales trajectories to individual-level conditional expectations (which, in turn, can be used to derive estimates of customer lifetime value). We provide an overview of a class of parsimonious models (called probability models) that are well-suited to meet these rising challenges. We first present a taxonomy that captures some of the key distinctions across different kinds of business settings and customer relationships, and identify some of the unique modeling and measurement issues that arise across them. We then provide deeper coverage of these modeling issues, first for noncontractual settings (i.e., situations in which customer “death” is unobservable), then contractual ones (i.e., situations in which customer “death” can be observed). We review recent literature in these areas, highlighting substantive insights that arise from the research as well as the methods used to capture them. We focus on practical applications that use appropriately chosen data summaries (such as recency and frequency) and rely on commonly available software packages (such as Microsoft Excel).

The Tuscan Lifestyles case (Mason, 2003) offers a simple twist on the standard view of how to value a newly acquired customer, highlighting how standard retention-based approaches to the calculation of expected customer lifetime value (CLV) are not applicable in a noncontractual setting. Using the data presented in the case (a series of annual histograms showing the aggregate distribution of purchases for two different cohorts of customers newly “acquired” by a catalog marketer), it is a simple exercise to compute an estimate of “expected 5 year CLV.” If we wish to arrive at an estimate of CLV that includes the customer's “life” beyond five years or are interested in, say, sorting out the purchasing process (while “alive”) from the attrition process, we need to use a formal model of buying behavior that can be applied on such coarse data. To tackle this problem, we utilize the Pareto/NBD model developed by Schmittlein, Morrison, and Colombo (1987). However, existing analytical results do not allow us to estimate the model parameters using the data summaries presented in the case. We therefore derive an expression that enables us to do this. The resulting parameter estimates and subsequent calculations offer useful insights that could not have been obtained without the formal model. For instance, we were able to decompose the lifetime value into four factors, namely purchasing while active, dropout, surge in sales in the first year and monetary value of the average purchase. We observed a kind of “triple jeopardy” in that the more valuable cohort proved to be better on the three most critical factors.

As modern economies become predominantly service-based, companies increasingly derive revenue from the creation and sustenance of long-term relationships with their customers. In such an environment, marketing serves the purpose of maximizing customer lifetime value (CLV) and customer equity, which is the sum of the lifetime values of the company’s customers. This article reviews a number of implementable CLV models that are useful for market segmentation and the allocation of marketing resources for acquisition, retention, and cross-selling. The authors review several empirical insights that were obtained from these models and conclude with an agenda of areas that are in need of further research.

The authors present a new model that links the well-known RFM (recency, frequency, and monetary value) paradigm with customer lifetime value (CLV). Although previous researchers have made a conceptual link, none has presented a formal model with a well-grounded behavioral ”story.” Key to this analysis is the notion of ”iso-value” curves, which enable the grouping of individual customers who have different purchasing histories but similar future valuations. Iso-value curves make it easy to visualize the interactions and trade-offs among the RFM measures and CLV. The stochastic model is based on the Pareto/NBD framework to capture the flow of transactions over time and a gamma-gamma submodel for spend per transaction. The authors conduct several holdout tests to demonstrate the validity of the model's underlying components and then use it to estimate the total CLV for a cohort of new customers of the online music site CDNOW. Finally, the authors discuss broader issues and opportunities in the application of this model in actual practice.

Today’s managers are very interested in predicting the future purchasing patterns of their customers, which can then serve as an input into “lifetime value” calculations. Among the models that provide such capabilities, the Pareto/NBD “counting your customers” framework proposed by Schmittlein et al. (1987) is highly regarded. However, despite the respect it has earned, it has proven to be a difficult model to implement, particularly because of computational challenges associated with parameter estimation. We develop a new model, the beta-geometric/NBD (BG/NBD), which represents a slight variation in the behavioral “story” associated with the Pareto/NBD but is vastly easier to implement. We show, for instance, how its parameters can be obtained quite easily in Microsoft Excel. The two models yield very similar results in a wide variety of purchasing environments, leading us to suggest that the BG/NBD could be viewed as an attractive alternative to the Pareto/NBD in most applications.

SUMMARY In this paper, we develop the idea of a ‘simple model’}defined as one that a good business student can build and implement on his/her notebook PC using readily available software. We explore how such models have the potential to bridge the gap between what marketing academics create and what marketing managers seek in a model. We provide specific examples from the areas of new product sales forecasting and customer-base analysis, using spreadsheet-based models that provide good forecasts and insights about actual buyer behaviour. Copyright # 2005 John Wiley & Sons, Ltd.

We present two everyday applications of a new bivariate beta-binomial distribution. Although the applications are familiar, they share unique characteristics that cannot be handled adequately by existing bivariate discrete distributions. These features are high levels of between- and within-trial correlation for the bivariate random variables. Our model is derived from a broad class of bivariate models based on a versatile, but little-known, family of distributions due to Sarmanov. For the applications presented, we show that our model fits observed data very well. In addition, for the bacon and eggs application, the model can be used to help improve the management of inventory in grocery stores.

At the heart of a new product sales-forecasting model for consumer packaged goods is a multiple-event timing process. Even after controlling for the effects of time-varying marketing mix covariates, this timing process is not a stationary one, which means the standard interpurchase time models developed within the marketing literature are not suitable for new products. In this paper, we develop a dynamic changepoint model that captures the underlying evolution of the buying behavior associated with the new product. This extends the basic changepoint framework, as used by a number of statisticians, by allowing the changepoint process itself to evolve over time. Additionally, this model nests a number of the standard multiple-event timing models considered in the marketing literature. In our empirical analysis, we show that the dynamic changepoint model accurately tracks (and forecasts) the total sales curve as well as its trial and repeat components and other managerial diagnostics (e.g., percent of triers repeating).

A number of researchers have developed models that use test market data to generate forecasts of a new product’s performance. However, most of these models have ignored the effects of marketing covariates. In this paper we examine what impact these covariates have on a model’s forecasting performance and explore whether their presence enables us to reduce the length of the model calibration period (i.e. shorten the duration of the test market). We develop from first principles a set of models that enable us to systematically explore the impact of various model ‘components’ on forecasting performance. Furthermore, we also explore the impact of the length of the test market on forecasting performance. We find that it is critically important to capture consumer heterogeneity, and that the inclusion of covariate effects can improve forecast accuracy, especially for models calibrated on fewer than 20 weeks of data. Copyright © 2003 John Wiley & Sons, Ltd.

To date, Bayesian inferences for the negative binomial distribution (NBD) have relied on computationally intensive numerical methods (e.g., Markov chain Monte Carlo) as it is thought that the posterior densities of interest are not amenable to closed-form integration. In this article, we present a “closed-form” solution to the Bayesian inference problem for the NBD that can be written as a sum of polynomial terms. The key insight is to approximate the ratio of two gamma functions using a polynomial expansion, which then allows for the use of a conjugate prior. Given this approximation, we arrive at closed-form expressions for the moments of both the marginal posterior densities and the predictive distribution by integrating the terms of the polynomial expansion in turn (now feasible due to conjugacy). We demonstrate via a large-scale simulation that this approach is very accurate and that the corresponding gains in computing time are quite substantial. Furthermore, even in cases where the computing gains ...

Research addressing the diffusion of successive generations of technological innovations has generally ignored the impact of marketing-mix variables. As a result, there have been several calls for the development of multiple-generation models that incorporate marketing-mix variables. The authors develop a model of first-time sales and subscriptions for successive generations of a technological innovation, which explicitly captures the effects of marketing-mix variables through a proportional hazards framework. The empirical analysis estimates the impact of price for two generations of cellular telephones in a European country. The results suggest that there are important substantive insights to be gained from the parameter estimates for this marketing-mix variable when intergenerational interdependencies are considered. For example, although the time path of the estimated price elasticities in a multiple-generation setting closely follows those reported previously for single generations, the authors find evidence of an important interaction in price response across generations. Therefore, empirical estimates in single-generation models may be missing an important part of the pricing equation.

We conducted a modeling exercise in conjunction with the online music retailer CDNOW to develop a simple stochastic model of buyer behavior capable of forecasting medium-term aggregate CD purchasing by a cohort of new customers. We modeled weekly sales using a finite mixture of beta-geometric distributions with a separate time-varying component to capture nonstationarity in repeat buying. The resulting model can easily be implemented within a standard spreadsheet environment (for example, Microsoft Excel). It does a good job of describing the underlying sales patterns and produces an excellent medium-term forecast.

In this paper we present a parsimonious model for the analysis of underreported Poisson count data. In contrast to previously developed methods, we are able to derive analytic expressions for the key marginal posterior distributions that are of interest. The usefulness of this model is explored via a re-examination of previously analysed data covering the purchasing of port wine (Ramos, 1999).

While numerous researchers have proposed diAerent models to forecast trial sales for new products, there is little systematic understanding about which of these models works best, and under what circumstances these findings change. In this paper, we provide a comprehensive investigation of eight leading published models and three diAerent parameter estimation methods. Across 19 diAerent datasets encompassing a variety of consumer packaged goods, we observe several systematic patterns that link diAerences in model specification and estimation to forecasting accuracy. Major findings include the following observations: (1) when dealing with consumer packaged goods, simple models that allow for relatively limited flexibility (e.g. no S-shaped curves) in the calibration period provide significantly better forecasts than more complex specifications; (2) models that explicitly accommodate heterogeneity in purchasing rates across consumers tend to oAer better forecasts than those that do not; and (3) maximum likelihood estimation appears to oAer more accurate and stable forecasts than nonlinear least squares. We elaborate on these and other findings, and oAer suggested directions for future research in this area. #1998 John Wiley & Sons, Ltd. Almost every textbook discussion of the new product development process includes a call to conduct some form of market test before actually launching the new product. Such an exercise serves several objectives, including the desire to produce an accurate forecast of the new product’s sales performance over time. These forecasts can help lead to a final go/no-go decision and can also assist in the marketing and production planning activities associated with the product launch. In the case of consumer packaged goods, conducting a market test historically saw the company’s sales force selling the product into retail distribution in one or more markets for one to two years, after which a decision of whether or not to go national with the new product was

This article reports new research on price promotions in grocery products. The results are striking and taken with other evidence they suggest that few consumers benefit from deep-discount price promotions. The study raises big questions about how manufacturers and retailers allocate their marketing budgets - and even about whether companies' management accounting and remuneration practices may be leading to reduced profits.

A conceptual distinction is offered between amplifying versus simplifying technological innovations. This distinction is shown to have value in explaining intended adoption. The results of the study indicate the need for further conceptualization and research regarding the role of innovation characteristics in adoption-decision processes.

Recently Power Quality Guidelines have been produced for the Electricity Engineers' Association of New Zealand. Among the various power quality issues, this paper specifically presents the development of voltage harmonic planning levels in the medium voltage networks by applying the concept of voltage droop. These planning levels are used to determine how much harmonic current can be allocated to a customer. These levels are shown to be comparable with values from international standards.