This note provides a clarification regarding the conditional and marginal likelihood functions in the BG/BB model, as published in Marketing Science by Fader, Hardie, and Shang (2010). Their Equations 4 and 5 do not include normalizing constants which, if included, would equate these likelihood functions with their corresponding joint probability functions. While these expressions are valid, because likelihood functions need only be correct up to a constant of proportionality, they are not joint probability functions, which may be a source of potential confusion for users who mistakenly equate the one for the other. Assuming the likelihood functions in Equations 4 and 5 are equal to their respective joint probability functions will lead to an incorrect joint probability distribution over recency and frequency data, resulting in incorrect goodness-of-fit metrics and managerially relevant expressions. We provide formal derivations of the joint probability functions that correspond to the likelihood functions in Equations 4 and 5 to remove this potential source of confusion for users of the BG/BB model.
{"title":"The Normalizing Constant in the BG/BB Model","authors":"D. McCarthy, Michael Braun, Arun Gopalakrishnan","doi":"10.2139/ssrn.3241680","DOIUrl":"https://doi.org/10.2139/ssrn.3241680","url":null,"abstract":"This note provides a clarification regarding the conditional and marginal likelihood functions in the BG/BB model, as published in Marketing Science by Fader, Hardie, and Shang (2010). Their Equations 4 and 5 do not include normalizing constants which, if included, would equate these likelihood functions with their corresponding joint probability functions. While these expressions are valid, because likelihood functions need only be correct up to a constant of proportionality, they are not joint probability functions, which may be a source of potential confusion for users who mistakenly equate the one for the other. Assuming the likelihood functions in Equations 4 and 5 are equal to their respective joint probability functions will lead to an incorrect joint probability distribution over recency and frequency data, resulting in incorrect goodness-of-fit metrics and managerially relevant expressions. We provide formal derivations of the joint probability functions that correspond to the likelihood functions in Equations 4 and 5 to remove this potential source of confusion for users of the BG/BB model.","PeriodicalId":237599,"journal":{"name":"SMU Cox: Marketing (Topic)","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121110485","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Enabled by modern interaction-logging technologies, managers increasingly have access to data on quality levels in customer interactions. We consider the direct marketing targeting problem in situations where 1) the customer's experience quality level varies randomly and independently from occasion to occasion, 2) the firm has measures of the quality levels experienced by each customer on each occasion, and 3) the firm can customize marketing according to these measures and the customer's behaviors. A primary contribution of this paper is a framework and methodology to use data on customer experience quality data to model a customer's evolving beliefs about the firm's quality and how these beliefs combine with marketing to influence purchase behavior. Thereby, this paper allows the manager to assess the marketing response of a customer with any specific experience and behavior history, which in turn can be used to decide which customers to target for marketing. This research develops a novel, tractable way to estimate and introduce flexible heterogeneity distributions into Bayesian learning models. The model is estimated using data from the casino industry, an industry which generates more than $60 billion in U.S. revenues but has surprisingly little academic, econometric research. The counterfactuals offer interesting findings on gambler learning and direct marketing responsiveness and suggest that casino profitability can increase substantially when marketing incorporates gamblers' beliefs and past outcome sequences into the targeting decision.
{"title":"Incorporating Experience Quality Data into CRM Models: The Impact of Gambler Outcomes on Casino Return Times","authors":"Wayne J. Taylor, Anand V. Bodapati","doi":"10.2139/ssrn.3455460","DOIUrl":"https://doi.org/10.2139/ssrn.3455460","url":null,"abstract":"Enabled by modern interaction-logging technologies, managers increasingly have access to data on quality levels in customer interactions. We consider the direct marketing targeting problem in situations where 1) the customer's experience quality level varies randomly and independently from occasion to occasion, 2) the firm has measures of the quality levels experienced by each customer on each occasion, and 3) the firm can customize marketing according to these measures and the customer's behaviors. A primary contribution of this paper is a framework and methodology to use data on customer experience quality data to model a customer's evolving beliefs about the firm's quality and how these beliefs combine with marketing to influence purchase behavior. Thereby, this paper allows the manager to assess the marketing response of a customer with any specific experience and behavior history, which in turn can be used to decide which customers to target for marketing. This research develops a novel, tractable way to estimate and introduce flexible heterogeneity distributions into Bayesian learning models. The model is estimated using data from the casino industry, an industry which generates more than $60 billion in U.S. revenues but has surprisingly little academic, econometric research. The counterfactuals offer interesting findings on gambler learning and direct marketing responsiveness and suggest that casino profitability can increase substantially when marketing incorporates gamblers' beliefs and past outcome sequences into the targeting decision.","PeriodicalId":237599,"journal":{"name":"SMU Cox: Marketing (Topic)","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125111637","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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