  Marketers employ various online advertising channels to reach customers, and
they are particularly interested in attribution for measuring the degree to
which individual touchpoints contribute to an eventual conversion. The
availability of individual customer-level path-to-purchase data and the
increasing number of online marketing channels and types of touchpoints bring
new challenges to this fundamental problem. We aim to tackle the attribution
problem with finer granularity by conducting attribution at the path level. To
this end, we develop a novel graphical point process framework to study the
direct conversion effects and the full relational structure among numerous
types of touchpoints simultaneously. Utilizing the temporal point process of
conversion and the graphical structure, we further propose graphical
attribution methods to allocate proper path-level conversion credit, called the
attribution score, to individual touchpoints or corresponding channels for each
customer's path to purchase. Our proposed attribution methods consider the
attribution score as the removal effect, and we use the rigorous probabilistic
definition to derive two types of removal effects. We examine the performance
of our proposed methods in extensive simulation studies and compare their
performance with commonly used attribution models. We also demonstrate the
performance of the proposed methods in a real-world attribution application.
