Estimating promotion effects in email marketing using a large-scale cross-classified Bayesian joint model for nested imbalanced data

Abstract

We consider a large-scale, cross-classified nested (CRON) joint model for modeling customer responses to opening, clicking, and purchasing from promotion emails. Our logistic regression-based joint model contains crossing of promotions and customer effects and allows estimation of the heterogeneous effects of different promotion emails, after adjusting for customer preferences, attributes, and historical behaviors. Using data from an email marketing campaign of an apparel retailer, we exhibit the varying effects of promotions not only based on the contents of the email but also across the three different stages, viz. open, click, and purchase of the conversion funnel. We conduct Bayesian estimation of the parameters in the joint model by using a block Metropolis–Hastings algorithm that not only incorporates nested subsampling to tackle the severe imbalance between conversions and no conversions but also uses additive transformation-based modifications of random walk Metropolis to scale estimation for large numbers of customers. We extend our approach to a segmented cross-classified nested (SCRON) joint model that encompasses the possibility of varying promotion effects across different customer segments. The resultant high-dimensional model is estimated using spike-and-slab priors on the promotion and customer segment interactions. Our nested joint model accounts for the correlations in customer preferences across the conversion funnel. Based on the promotion estimates from the model, we demonstrate how marketers can use different priced, nonpriced, and combination of price and nonprice promotions to increase brand awareness or increase purchases. Comparing estimates from CRON and SCRON models, we display the benefits of targeted marketing by using email promotion lists which are separately optimized for the different customer segments.