Spatial Random Slope Multilevel Modeling Using Multivariate Conditional Autoregressive Models: A Case Study of Subjective Travel Satisfaction in Beijing

Abstract

This article explores how to incorporate a spatial dependence effect into the standard multilevel modeling (MLM). The proposed method is particularly well suited to the analysis of geographically clustered survey data where individuals are nested in geographical areas. Drawing on multivariate conditional autoregressive models, we develop a spatial random slope MLM approach to account for the within-group dependence among individuals in the same area and the spatial dependence between areas simultaneously. Our approach improves on recent methodological advances in the integrated spatial and MLM literature, offering greater flexibility in terms of model specification by allowing regression coefficients to be spatially varied. Bayesian Markov chain Monte Carlo (MCMC) algorithms are derived to implement the proposed model. Using two-level travel satisfaction data in Beijing, we apply the proposed approach as well as the standard nonspatial random slope MLM to investigate subjective travel satisfaction of residents and its determinants. Model comparison results show strong evidence that the proposed method produces a significant improvement against a nonspatial random slope MLM. A fairly large spatial correlation parameter suggests strong spatial dependence in district-level random effects. Moreover, spatial patterns of district-level random effects of locational variables have been identified, with high and low values clustering together.