Path to Purchase: A Mutually Exciting Point Process Model for Online Advertising and Conversion

This paper studies the effects of various types of online advertisements on purchase conversion by capturing the dynamic interactions among advertisement clicks themselves. It is motivated by the observation that certain advertisement clicks may not result in immediate purchases, but they stimulate subsequent clicks on other advertisements, which then lead to purchases. We develop a novel model based on mutually exciting point processes, which consider advertisement clicks and purchases as dependent random events in continuous time. We incorporate individual random effects to account for consumer heterogeneity and cast the model in the Bayesian hierarchical framework. We construct conversion probability to properly evaluate the conversion effects of online advertisements. We develop simulation algorithms for mutually exciting point processes to compute the conversion probability and for out-of-sample prediction. Model comparison results show the proposed model outperforms the benchmark models that ignore exciting effects among advertisement clicks. Using a proprietary data set, we find that display advertisements have relatively low direct effect on purchase conversion, but they are more likely to stimulate subsequent visits through other advertisement formats. We show that the commonly used measure of conversion rate is biased in favor of search advertisements and underestimates the conversion effect of display advertisements the most. Our model also furnishes a useful tool to predict future purchases and advertisement clicks for the purpose of targeted marketing and customer relationship management.