Predicting the amount individuals withdraw at cash machines using a random effects multinomial model

Retail finance organizations use data on past behaviour to make predictions for customer value management strategies. Random-effects models, where each individual has a behavioural pattern drawn from an overall population distribution, are a natural statistical form in this context. The random effects models in this paper are used to predict how much individuals withdraw at a single cash machine visit. A multinomial distribution is taken for the distribution of amounts and the random effects are modelled by a Dirichlet distribution or the empirical distribution of individual maximum likelihood fits. A third model extends the multinomial distribution by incorporating a form of serial dependence and uses an empirical distribution for the random effects. Several prediction tests on a sample of 5000 UK high-street bank accounts find that the greatest benefit from the models is for accounts with a small number of past transactions; that little information may be lost by binning and that the Dirichlet distribution might overestimate the probability of previously unobserved withdrawal amounts. The empirical distribution of random effects is found to perform well because there are a large number of individual accounts.