A Weighted Statistical Network Modeling

10 Statistical network models have been used to study the competition among different prod11 ucts and how product attributes influence customer decisions. However, in existing research 12 using network-based approaches, product competition has been viewed as binary (i.e., whether 13 a relationship exists or not), while in reality, the competition strength may vary among prod14 ucts. In this paper, we model the strength of the product competition by employing a statistical 15 network model, with an emphasis on how product attributes affect which products are consid16 ered together and which products are ultimately purchased by customers. We first demonstrate 17 how customers’ considerations and choices can be aggregated as weighted networks. Then, we 18 propose a weighted network modeling approach by extending the valued Exponential Random 19 Graph Model to investigate the effects of product features and network structures on product 20 competition relations. The approach that consists of model construction, interpretation, and val21 idation is presented in a step-by-step procedure. Our findings suggest that the weighted network 22 model outperforms commonly used binary network baselines in predicting product competition 23 as well as market share. Also, traditionally when using binary network models to study product 24 competitions, and depending on the cut-off values chosen to binarize a network, the resulting es25 timated customer preferences can be inconsistent. Such inconsistency in interpreting customer 26