Improving response prediction in direct marketing by optimizing for specific mailing depths

Response modeling is a very important application field of classification methods in direct marketing because the success of a direct-mail campaign is highly dependent on who is being targeted. To date, standard classification models are applied to predict future purchasing behaviour for the complete customer file. In practice, however, companies use mailing budgets, i.e. only a subset of customers will be sent mail. Just those customers with sufficiently high-expected response rates are mailed to. The percentage of the total population that will actually receive the mailing is referred to as mailing depth. Hence, the real classification problem is not to classify all potential recipients as well as possible, but rather to find those customers, within the budget limitation, with the highest probability of response. Therefore, we propose an innovative alternative route to improved overall performance by tailoring the classification method to fit the problem at hand. We adapt binary logistic regression by iteratively changing the true values of the dependent variable during the maximum-likelihood estimation procedure. Those customers who rank lower than the cutoff in terms of predicted purchase probability, imposed by the mailing-depth restriction, will not contribute to the total likelihood. We illustrate our procedure on a real-life direct-marketing dataset comparing traditional response models to our innovative approach optimising for a specific mailing depth. The results show that for mailing depths up to 48% our method achieves significant and substantial profit increases.