Publication Detail

Relationships Between the Online and In-Store Shopping Frequency of Davis, California Residents: a Copula-Linked Bivariate Ordinal Response Model


Research Report

Suggested Citation:
Sener, Ipek N., Richard Lee, Patricia L. Mokhtarian, Susan L. Handy (2015) Relationships Between the Online and In-Store Shopping Frequency of Davis, California Residents: a Copula-Linked Bivariate Ordinal Response Model. Institute of Transportation Studies, University of California, Davis, Research Report UCD-ITS-RR-15-42

The growth of online shopping is transforming the retail marketplace. In 2007, approximately half of U.S. residents reported purchasing a product online, and by 2012 online retail sales had reached $227 billion, nearly an order of magnitude higher than in 2000. With growing retail market share, it is reasonable to expect that online shopping will have an effect on the frequency of in-store shopping trips. This could result in significant transportation implications because shopping trips accounted for approximately 15 percent of vehicle miles traveled in the United States in 2009.

In general, online shopping can influence shopping trips through one of three mechanisms: complementarity, substitution, or modification. It would be simplistic to assume that online shopping purchases substitute for in-store purchases on a one-to-one basis. Complementarity would result, for example, if online purchasers were to exploit the time savings resulting from avoiding a trip to the store by conducting additional shopping trips. The interrelationship between online and in-store shopping is a complex phenomenon, and accurately assessing the travel impacts of online shopping will require an understanding of its relationship with in-store shopping trips. Therefore, the objective of this paper is to uncover the factors influencing the decisions to shop online and in stores, and to describe the relationship between these two shopping modes.

This study will use a copula-based approach to jointly model the online and in-store shopping choice decisions. The model will be built using two ordered response models with frequency of engagement in each form of shopping being the dependent variables in their respective equations, and will relax the assumption of independence between these two shopping forms using a copula. The concept of a copula, though widely recognized in the statistics field, has a relatively newer history in the field of transportation choice modeling. A copula is a device or tool that generates a stochastic dependence form among random variables with pre-specified marginal distributions. The copula-based approach generates dependency through a multivariate functional form for the joint distributions of random variables. It jointly models the dependent variables as distinct choices, while simultaneously describing their relationship in terms of how they are influenced by a shared set of observed and unobserved factors. While doing that, copula models greatly enhance the flexibility in capturing the influences across different choice dimensions by allowing the analyst to test the presence, type and level of correlation without pre-imposing any particular direction. It is likely that the typical bivariate normal distribution assumption might not accurately describe the dependency form between in-store and online shopping, which might result in inefficient and inconsistent parameter estimates.

Presented at International Choice Modelling Conference 2015, Austin, TX, May 10-13, 2015