A copula-based approach to accommodate residential self-selection effects in travel behavior modeling

Abstract

The dominant approach in the literature to dealing with sample selection is to assume a bivariate normality assumption directly on the error terms, or on transformed error terms, in the discrete and continuous equations. Such an assumption can be restrictive and inappropriate, since the implication is a linear and symmetrical dependency structure between the error terms. In this paper, we introduce and apply a flexible approach to sample selection in the context of built environment effects on travel behavior. The approach is based on the concept of a "copula", which is a multivariate functional form for the joint distribution of random variables derived purely from pre-specified parametric marginal distributions of each random variable. The copula concept has been recognized in the statistics field for several decades now, but it is only recently that it has been explicitly recognized and employed in the econometrics field. The copula-based approach retains a parametric specification for the bivariate dependency, but allows testing of several parametric structures to characterize the dependency. The empirical context in the current paper is a model of residential neighborhood choice and daily household vehicle miles of travel (VMT), using the 2000 San Francisco Bay Area Household Travel Survey (BATS). The sample selection hypothesis is that households select their residence locations based on their travel needs, which implies that observed VMT differences between households residing in neo-urbanist and conventional neighborhoods cannot be attributed entirely to the built environment variations between the two neighborhoods types. The results indicate that, in the empirical context of the current study, the VMT differences between households in different neighborhood types may be attributed to both built environment effects and residential self-selection effects. As importantly, the study indicates that use of a traditional Gaussian bivariate distribution to characterize the relationship in errors between residential choice and VMT can lead to misleading implications about built environment effects.1

A Copula-Based Sample Selection Model of Telecommuting Choice and Frequency

“…shown visually in Bhat and Eluru (2009), the dependence surface of Frank's copula shows very strong central dependency (stronger than the Gaussian copula) and very weak tail dependence (weaker than the Gaussian copula). In the current empirical context, this means that, due to unobserved factors, individuals are likely to be substantially clustered around the medium-medium levels of the two-dimensional (latent) telecommuting propensity-frequency inclination spectrum, and less so at the low-low end or the high-high end of the spectrum.…”

Change of Scale and Forecasting with the Control-Function Method in Logit Models

“…(2) corresponds to a structural equation and to treat ξ as a latent variable (Guevara, 2010). With some modifications, this approach is also equivalent to the methods used by Zimmer and Trivedi (2006) or by Bhat and Eluru (2009) to address endogeneity in discrete choice models.…”

A copula-based closed-form binary logit choice model for accommodating spatial correlation across observational units

“…This provides substantial flexibility in correlating random variables, which may not even have the same marginal distributions. The effectiveness of a copula approach has been recognized in the statistics field for several decades now (see Schweizer and Sklar, 1983, Chapter 6), but it is only recently that Copula-based methods have been explicitly recognized and employed in the financial risk analysis and econometrics fields (see, for example, Smith, 2005, Zimmer and Trivedi, 2006, Cameron et al, 2004, Embrechts et al, 2003, Cherubini et al, 2004, Junker and May, 2005, Quinn, 2007, and Bhat and Eluru, 2008). …”