A multi-level cross-classified model for discrete response variables

Abstract

In many spatial analysis contexts, the variable of interest is discrete and there is spatial clustering of observations. This paper formulates a model that accommodates clustering along more than one dimension in the context of a discrete response variable. For example, in a travel mode choice context, individuals are clustered by both the home zone in which they live as well as by their work locations. The model formulation takes the form of a mixed logit structure and is estimated by maximum likelihood using a combination of Gaussian quadrature and quasiMonte Carlo simulation techniques. An application to travel mode choice suggests that ignoring the spatial context in which individuals make mode choice decisions can lead to an inferior data fit as well as provide inconsistent evaluations of transportation policy measures.

Valuation of environmental and social functions of the multifunctional Cypriot agriculture

“…For the estimation, Halton draws are preferred, in order to minimize variance (Bhat, 1999(Bhat, , 2000. The choice of random coefficients and distributional forms depends on the researcher.…”

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

“…2 Another possible approach is to maintain a relatively restrictive spatial correlation structure that allows a constant correlation within observational units in pre-specified spatial regions, but no correlation in observational units in different spatial regions. Bhat (2000) and Dugundji and Walker (2005) address unordered multinomial discrete choices in this manner. Specifically, Bhat (2000) examines work travel mode choice, allowing for error correlation across decision-makers based on residential location as well as work location.…”

“…Bhat (2000) and Dugundji and Walker (2005) address unordered multinomial discrete choices in this manner. Specifically, Bhat (2000) examines work travel mode choice, allowing for error correlation across decision-makers based on residential location as well as work location. Dugundji and Walker (2005) also examine work mode choice, but allow for spatial error correlation only among decision-makers in the same residential location.…”

“…As discussed in Bhat (2000), and more recently in Páez (2007), much of the spatial analysis literature to date has focused on accommodating spatial effects in models with continuous dependent variables or proportions. In contrast, and as indicated by Páez (2007), "…the explicit incorporation of spatial effects in discrete choice models is still in its infancy".…”

“…The pervasive nature of spatial effects has spawned a vast literature on accommodating spatial effects in different fields such as earth sciences, epidemiology, transportation, land use analysis, geography, and ecology (see Páez and Scott, 2004 for a relatively recent review). The studies in these fields have focused on one or more of three spatial analytic issues in analyzing the dependent variable of interest: spatial dependency, spatial heterogeneity, and spatial heteroscedasticity (see Bhat, 2000).…”