Spatial dependence in data may occur because of several reasons, including diffusion effects, social interaction effects, or unobserved location-related effects influencing the level of the dependent variable. Accommodating such spatial dependence has been an active area of research in spatial statistics and spatial econometrics. However, while this literature abounds in techniques to address spatial dependence in continuous dependent variable models, there has been much less research on techniques to accommodate spatial dependence in discrete choice models. Further, almost all of these efforts are focused on the binary spatial probit model, which is predicated on a multivariate normality assumption to characterize the spatial dependence structure. This assumption imposes the restriction that the dependence between the spatial error terms is radially symmetric about the center point in the Gaussian copula. That is, for a given correlation, the level of dependence is equal in the upper and lower tails. On the other hand, asymmetric tail dependence may be important characteristics in spatial data (even after conditioning each marginal variable in terms of observed covariates). For instance, closely located neighborhoods may simultaneously experience high crime rates or high trip rates, but not necessarily low crime rates or low trip rates. This is the case of strong right tail dependence (strong correlation at high values) but weak left tail dependence (weak correlation at low values).

An approach referred to as the "Copula" approach has recently revived interest in a whole set of alternative couplings that can allow non-linear and asymmetric dependencies. A copula is essentially a multivariate functional form for the joint distribution of random variables derived purely from pre-specified parametric marginal distributions of each random variable. Under the copula approach, the multivariate normal distribution adopted in the spatial binary probit model is but one of a suite of different types of error term couplings that can be tested.

In terms of estimation of discrete choice models with a general spatial correlation structure, the traditional simulation methods to approximate a multi-dimensional integral (of the order of the number of observational units in the estimation sample) over a multivariate normal distribution becomes practically infeasible for moderate-to-large samples. In the current paper, we combine a copula-based formulation for spatial dependence with a pseudo-likelihood estimation technique based on a composite marginal likelihood (CML) inference approach to propose a simple and practical approach to estimate ordered-response discrete choice models with spatial correlation across observational units. The approach is applicable to data sets of any size, provides standard error estimates for all parameters, and does not require any simulation machinery. Another associated contribution of this paper is to construct a new generalized multivariate version of the Gumbel copula that, to our knowledge, has not appeared in the statistical or mathematical literature. This generalized version of the Gumbel copula is useful for accommodating spatial correlation, though it should have other wide-ranging applications too. The approach is applied to study the daily episode frequency of teenagers' social activity participation, a subject of considerable interest in the transportation, sociology, and adolescence development fields.