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The analysis of customer value in direct marketing combines customer timing and quantity data into a single statistic used to compute lifetime values, rank-order customers for selection, and identify prospects for cross-selling. However, current models assume that purchase timing and quantity decisions are independently realized (i.e., uncorrelated) over time given individual-level parameters. In this article, the authors show that customer value calculations can be severely biased in these models when timing and quantity are dependently related.

The authors develop a hierarchical model of purchase timing and quantity that allows for the covariation of these quantities over time and among respondents. The authors propose a parameterization of a model for timing and quantity that overcomes restrictive conditions typically encountered when modeling heterogeneous covariances and show that this parameterization leads to improved prediction and inference.

The analysis of two direct-marketing data sets illustrates the benefits of the proposed model. In both data sets, the authors find a positive association between purchase timing and purchase quantity, indicating that customers engage in compensating behavior such that smaller order amounts are more likely to occur when interpurchase times are shorter. The presence of compensating customer behavior is ignored in conventional scoring models. Neglecting this behavior leads to an overvaluation of customer value.

Predictive results for a business-to-business data set indicate an increase in revenues of $14 million for the top 20% of customers based on the proposed score versus one that assumes timing and quantity are independent. Similar results are found in a business-to-consumer data set—namely, the loss due to employing a conventional model that ignores dependence is approximately $16 million.

Biography
Lichung Jen is Professor of Marketing in the Department of International Business at the National Taiwan University, Taipei, Taiwan. Professor Jen received his PhD from Ohio State University in 1995. His current research interests include database marketing, customer relationship marketing, and modeling consumer behavior using hierarchical Bayesian statistical models.

Chien-Heng Chou is Associate Professor of Marketing in the Department of International Trade at the Chinese Culture University, Taipei, Taiwan. Professor Chou received his PhD from Chinese Culture University in 2001. His current research interests include customer participation, customer lifetime value, experiential marketing, and quantitative research methodology.

Greg M. Allenby is a professor and Helen C. Kurtz Chair in Marketing in the Department of Marketing and Logistics, Fisher College of Business, Ohio State University. Professor Allenby specializes in the study of economic and statistical issues in marketing. He is coauthor of Bayesian Statistics and Marketing (John Wiley & Sons, 2005) and is an associate editor of Journal of Marketing Research, Marketing Science, and Quantitative Marketing and Economics.

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