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

This paper studies the e ects 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 stochastic model based on mutually exciting point processes, which model advertisement clicks and purchases as dependent random events in continuous time. We incorporate individual random e ects to account for consumer heterogeneity and cast the model in the Bayesian hierarchical framework. We propose a new metric of conversion probability to measure the conversion e ects of online advertisements. Simulation algorithms for mutually exciting point processes are developed to evaluate the conversion probability and for out-of-sample prediction. Model comparison results show the proposed model outperforms the benchmark model that ignores exciting e ects among advertisement clicks. We nd that display advertisements have relatively low direct e ect 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 e ect of display advertisements the most. Our model also furnishes a useful tool to predict future purchases and clicks on online