Inferring neighbourhood quality with property transaction records by using a locally adaptive spatial multi-level model

Social and physical processes often exhibit both macro-level geographic smoothness – implying positive spatial dependence – and micro-level discontinuities – suggesting implicit step changes or boundaries in the data. However, a simultaneous treatment of the two features in a unified statistical model poses great challenges. This study extends an innovative locally adaptive spatial auto-regressive modelling approach to a multi-level modelling framework in order to explore multiple-scale geographical data. It develops a Bayesian locally adaptive spatial multi-level model that takes into account horizontal global spatial dependence and local step changes, as well as a vertical group dependency effect imposed by the multiple-scale data structure. At its heart, the correlation structures of spatial units implied by a spatial weights matrix are learned along with other model parameters using an iterative estimation algorithm, rather than being assumed to be invariant and exogenous. A Bayesian Markov chain Monte Carlo (MCMC) sampler for implementing this new spatial multi-level model is derived. The developed methodology is applied to infer neighbourhood quality using property transaction data, and to examine potential correlates of neighbourhood quality in Liverpool. The results reveal a complex and fragmented geography of neighbourhood quality; besides an overall smoothness trend, boundaries delimiting neighbourhood quality are scattered across Liverpool. Socio-economics, built environment, and locational characteristics are statistically significantly associated with neighbourhood quality.