A hierarchical Bayesian logit model for spatial multivariate choice data

Spatial perceptions mediate human–environment interaction, and understanding spatial perceptions of humans can play a key role in the planning of activities. This study aims to analyze spatial multivariate binary choice data representing if an individual perceives a spatial unit to belong to a certain category (e.g., her neighborhood or set of potential activity places). To reasonably analyze such data, we present a spatial autoregressive mixed logit (SAR-MXL) model that accounts for both inter-individual heterogeneity and spatial dependence. We rely on the Bayesian approach for posterior inference of model parameters, where Pólya-Gamma data augmentation (PG-DA) is adopted to address the non-conjugacy of the logit kernel. The PG-DA technique eliminates the need for the Metropolis–Hastings step during the Markov Chain Monte Carlo process and allows for fast and efficient posterior inference. The high efficiency of the Bayesian SAR-MXL model is demonstrated through a numerical experiment. The proposed framework is applied to street-based neighborhood perception data, and we empirically analyzed the factors associated with the street perception probability of individuals. The result suggests a clear improvement of the model fit by incorporating spatial dependence and random parameters.