New Perspectives on Customer "Death" Using a Generalization of the Pareto/NBD Model
New Perspectives on Customer "Death" Using a Generalization of the Pareto/NBD Model
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DOI：
10.1287/mksc.1110.0654
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发表时间：
2011-09
期刊：
影响因子：
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通讯作者：
Kinshuk Jerath;P. Fader;Bruce G. S. Hardie
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文献类型：
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作者：
Kinshuk Jerath;P. Fader;Bruce G. S. Hardie
一些研究人员提出了非契约环境下的购买者行为模型，假设客户在一段时间内“活着”，然后变得永久不活跃。最著名的这种模型是帕累托/NBD，它假设客户流失（流失或“死亡”）可能发生在日历时间的任何一点。最近的一个替代模型，BG/NBD，假设客户流失遵循伯努利“抛硬币”过程，发生在“交易时间”（即，每次购买后）。虽然修改后的模式更容易实施，但这意味着重度买家有更多的机会“死亡”。在本文中，我们开发了一个模型，与日历时间的离散时间辍学过程。具体来说，我们假设每个客户定期“抛硬币”，以确定她是否“退出”或继续作为客户。对于活着时购买的部分，我们保持Pareto/NBD和BG/NBD模型的假设。这个周期性死亡机会（PDO）模型使我们能够更仔细地研究客户死亡的假设如何影响模型拟合以及管理人员通常用于描述客户群的各种指标。当每个客户做出她的辍学决定（我们称之为周期长度）的时间段非常小时，我们分析表明，PDO模型减少到帕累托/NBD。当周期长度长于校准周期时，丢弃过程被“关闭”，并且PDO模型崩溃为负二项分布（NBD）模型。通过系统地改变这些限制之间的周期长度，我们可以探索“连续时间死亡”帕累托/NBD和天真的“无死亡”NBD之间的全谱模型。在覆盖这个频谱，PDO模型执行至少以及这些模型中的任何一个;我们的实证分析表明，两个数据集上的PDO模型的上级性能。我们还表明，不同的模型提供了显着不同的估计购买相关的和死亡相关的指标为两个数据集，这些差异可以是相当戏剧性的死亡相关的指标。随着越来越多的研究人员和管理人员做出与死亡过程直接相关的管理判断，我们认为应该仔细选择用于生成这些指标的模型。
Several researchers have proposed models of buyer behavior in noncontractual settings that assume that customers are “alive” for some period of time and then become permanently inactive. The best-known such model is the Pareto/NBD, which assumes that customer attrition (dropout or “death”) can occur at any point in calendar time. A recent alternative model, the BG/NBD, assumes that customer attrition follows a Bernoulli “coin-flipping” process that occurs in “transaction time” (i.e., after every purchase occasion). Although the modification results in a model that is much easier to implement, it means that heavy buyers have more opportunities to “die.” In this paper, we develop a model with a discrete-time dropout process tied to calendar time. Specifically, we assume that every customer periodically “flips a coin” to determine whether she “drops out” or continues as a customer. For the component of purchasing while alive, we maintain the assumptions of the Pareto/NBD and BG/NBD models. This periodic death opportunity (PDO) model allows us to take a closer look at how assumptions about customer death influence model fit and various metrics typically used by managers to characterize a cohort of customers. When the time period after which each customer makes her dropout decision (which we call period length) is very small, we show analytically that the PDO model reduces to the Pareto/NBD. When the period length is longer than the calibration period, the dropout process is “shut off,” and the PDO model collapses to the negative binomial distribution (NBD) model. By systematically varying the period length between these limits, we can explore the full spectrum of models between the “continuous-time-death” Pareto/NBD and the naive “no-death” NBD. In covering this spectrum, the PDO model performs at least as well as either of these models; our empirical analysis demonstrates the superior performance of the PDO model on two data sets. We also show that the different models provide significantly different estimates of both purchasing-related and death-related metrics for both data sets, and these differences can be quite dramatic for the death-related metrics. As more researchers and managers make managerial judgments that directly relate to the death process, we assert that the model employed to generate these metrics should be chosen carefully.