Uncovering Characteristic Response Paths of a Population

We propose an approach for uncovering characteristic response paths of a population from an individual-level multivariate time series data set. The approach is based on a model that accommodates a set of arbitrary distributions for endogenous variables and interstep intervals and variables. The model enables reliable estimation of individual-level parameters by uncovering and statistically pooling clusters of similar individuals. We show that using such a model one can distribute the response of an outcome variable to an impulse over all possible preceding activity sequences. When a few such sequences explain most of the response, they describe the population's characteristic response paths from the impulse to the outcome. We apply the proposed approach to a customer touchpoint data set from a large multichannel specialty retailer. This application uncovers six customer segments, each with unique characteristic paths to purchase. These paths provide insights into the behavior of customers and the optimal over-time communication strategy for different customer segments. Summary of Contribution: Uncovering users' paths through physical and virtual spaces has been of considerable interest in the computing and operations research domain. The existing research suggests a demand for visualizing the primary paths of agents through geographic, online, and activity spaces. Thus far, most of the research have developed approaches that are unique to specific domains providing insight into the domain in the process. There is a need for a general statistically robust approach that can be applied to a broad range of domains to uncover variable sequences that lead to outcomes of interest. We propose a computational approach to uncover characteristic response paths of a population from an individual-level multivariate time series data set. The approach is based on a statistical model that accommodates arbitrary and mixed set of distributions for the endogenous variables, accommodates intersession intervals and variables, and reliably estimates individuals' parameters through statistical pooling by uncovering clusters of similar members. These features make the proposed model suitable for a large variety of real-world datasets. We show that using such a model one can extract characteristic paths over possible activity sequences starting from an impulse leading up to a target variable of interest.