A Representative Sampling Method for Peer Encouragement Designs in Network Experiments

Music City Center 

Firms are increasingly interested in conducting network experiments through peer encouragement designs to causally quantify the potentially heterogeneous effects of social marketing programs. For example, researchers randomly sample ego networks (where each ego network consists of one ego and the alters who are directly connected to the ego) for assignment to treatment and control conditions, and then estimate the direct treatment effects based on responses of egos and the indirect treatment effects based on responses of alters. To satisfy the Stable Unit Treatment Value Assumption (SUTVA), researchers have typically adopted the excluding approach by removing those contaminated ego networks defined by some criteria. However, this practice often results in two problems documented in the literature: underrepresentation (i.e., the post-exclusion samples are not representative of the population on key network attributes such as degree and clustering coefficient), and undersupply (i.e., the post-exclusion samples consist of a limited number of ego networks). We propose a method that directly addresses the underrepresentation and undersupply problems, and efficiently generates proper and representative treatment and control samples satisfying SUTVA. We employ the Metropolis-Hastings algorithm to obtain optimal samples that minimize the distance between the samples and the population network based on the joint distribution of some key network attributes that may significantly influence the general properties of networks and the magnitudes of treatment effects. Our method comprises three key input modules: the selection of key network attributes upon which the sample and population distributions will be compared, the definition of the distance between the sample and population distributions, and the specification of desired sample sizes. By adjusting these three modules, researchers can flexibly generate proper and representative samples across a variety of network conditions as needed to facilitate causal inferences in network experiments employing peer encouragement designs. Through extensive simulations using both simulated and real population network data, our results collectively demonstrate that underrepresentation and undersupply become more pronounced for the post-exclusion samples when the required sample size of ego networks is large, the population network is not of large scale, the population network is dense, and when both first- and second-degree contamination are considered. We demonstrate the usefulness and boundary conditions of the proposed method in generating larger and more representative samples. We also demonstrate that the representative samples generated by our proposed method effectively improve the efficacy of the estimation and statistical inference. The proposed representative sampling method can be adapted and incorporated into many applications to help firms improve designs of social marketing programs.

Peer Encouragement Designs, Network Experiments, Sampling, Metropolis-Hastings, Targeting, Social Influences