International Choice Modelling Conference, International Choice Modelling Conference 2015

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Relationships between the online and in-store shopping frequency of Davis, California residents: A copula-linked bivariate ordinal response model
Ipek N. Sener, Richard J. Lee, Patricia L. Mokhtarian, Susan L. Handy

Last modified: 18 May 2015


The growth of online shopping is transforming the retail marketplace. In 2007, approximately half of U.S. residents reported purchasing a product online (Horrigan 2008), and by 2012 online retail sales had reached $227 billion, nearly an order of magnitude higher than in 2000 (U.S. Census Bureau 2014). 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 (Santos et al. 2011).

In general, online shopping can influence shopping trips through one of three mechanisms: complementarity, substitution, or modification (Mokhtarian 2002). 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.

The results of several studies indicate that online shopping is positively associated with in-store shopping, even after controlling for income and other socioeconomic characteristics. Using a linear regression model, Ferrell (2004) demonstrated a positive association between online shopping and in-store shopping trip frequency. These results were supported by Cao et al. (2010), who used ordered probit models to isolate the effects of online purchasing on shopping travel. Circella and Mokhtarian (2010) reported a similar result, though the relationship was not statistically significant. Other researchers have used structural equation modeling (SEM) to examine the association between online and in-store shopping. Rather than assuming that the relationship is unidirectional, this technique can be used to test interactions from multiple directions. Using SEM, Cao et al. (2012) found that online shopping positively influenced in-store shopping frequency, and both were influenced by online research. Farag et al. (2007) also uncovered potential complementary effects between online and in-store shopping, but in the opposite direction. Unexpectedly, SEM indicated that the frequency of in-store shopping trips had a positive effect on online shopping frequency but not vice versa. While the findings of these studies suggest complementarity, it cannot be assumed that the relationship is direct as online shoppers could simply be more prone to conducting shopping trips (Mokhtarian 2004). In addition, while these SEM-based studies provide important insights by allowing bi-directional influences between choices, they significantly suffer from the multivariate normality assumption, which “will often be incorrect” in practice as noted by Bentler and Dudgeon (1996). For instance, in their study, Cao et al. (2012) were forced to remove significant exogenous variables from their SEM for this very reason.

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.

The data used in this study will be drawn from a two-part online survey characterizing the shopping behavior of Davis, California, residents (Lovejoy et al. 2013). The survey was first conducted in 2009 before the opening of a Target store (n = 1018) and again the following year using a separate sample (n = 1025). The split-survey design allows for an examination of the effect of a big-box store—the first of its kind in Davis—on shopping behavior. For online and offline shopping venues, survey participants were asked for their shopping frequency and whether they had shopped for any of 17 product categories in the previous year. Respondents also provided information on their most recent purchases for each shopping venue and answered questions regarding shopping-related attitudes and opinions. The detailed surveys provide a rich dataset through which to analyze shopping behavior in Davis.

By jointly modeling the sociodemographic, built environment, and attitudinal factors influencing online and in-store shopping, this paper aims to provide an enhanced understanding of shopping choices and how they are linked. Based on the literature, it is evident that a link exists between online shopping and in-store shopping, but the nature of the relationship is uncertain, as are the relationships between their predictive factors. Specific attention will be given to develop a detailed understanding of the built environment (through expanded measures) as well as attitudes and perceptions, which are likely to play a significant role in scaling the trade-off effects between online and in-store shopping trips. The accurate characterization of these interactions based on this flexible approach can then be used to enhance the estimation of the travel-related impacts of online shopping.


Annual Retail Trade Survey - 2012. 2014. United States Census Bureau.

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