Prediction of purchase timing and quantity decisions of a household
is an important element for success of any retailer. This is
especially so for an online retailer, as the traditional
brick-and-mortar retailer would be more concerned with total sales.
A number of statistical models have been developed in the marketing
literature to aid traditional retailers in predicting sales and
analyzing the impact of various marketing activities on sales.
However, there are two important differences between traditional
retail outlets and the increasingly important online retail/delivery
companies, differences that prevent these firms from using models
developed for the traditional retailers: 1) the profits of the
online retailer/delivery company depend on purchase frequency and on
purchase quantity, while the profits of traditional retailers are
simply tied to total sales, and 2) customers in the tails of the
frequency distribution are more important to the delivery company
than to the retail outlet. Both of these differences are due to the
fact that the delivery companies incur a delivery cost for each
sale, while customers themselves travel to retail outlets when
buying from traditional retailers. These differences in costs
translate directly into needs that a model must address. For a model
intended to be useful to online retailers the dependent variable
should be a bivariate distribution of frequency and quantity, and
frequency distribution must accurately represent consumers in the
tails. In this article we develop such a model and apply it to
predicting the consumer?s joint decision of when to shop and how
much to spend at the store. Our approach is to model the marginal
distribution of purchase timing and the distribution of purchase
quantity conditional on purchase timing. We propose a hierarchical
Bayes model that disentangles the weekly and daily components of the
purchase timing. The daily component has a dependence on the weekly
component thereby accounting for strong observed periodicity in the
data. For the purchase times, we use the Conway-Maxwell-Poisson
distribution, which we find useful to fit data in the tail regions
(extremely frequent and infrequent purchasers).
Keywords: Conway-Maxwell-Poisson distribution; Hierarchical Bayes; Online
retailers/delivery companies.