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Statistical Methods in Customer Relationship Management by J. Andrew Petersen, V. Kumar

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4.4 Order Quantity and Order Size

4.4.1 How Much (in $) Will a Customer Order?

Loyalty programs are designed to increase the level of customer loyalty and encourage customers to make more purchases or use more services. Bolton et al. [22] investigated whether loyalty programs increase customers' satisfaction and their usage levels of products/services. Since the data used had customers' transactions, these authors directly modeled the number of transactions during a certain period using a Tobit model. Bolton and Lemon [13] modeled customers' usage level in a dynamic model. These authors argued that there is some minimum unobserved level of usage (threshold) associated with use of the service at all, say c. The amount of usage actually observed can be written as

(4.30) equation

The independent variables in the future usage equation are overall satisfaction, price, and a vector of cross-sectional economic variables. This specification is easily captured by a Tobit model. Following Borle et al. [23], the authors assumed that the amount expended by customer img on purchase occasion img, img, followed a log-normal ...

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