Bayesian Inference in Large Hierarchical Spatial Data Structures

In processing discrete-choice spatially referenced data evolving from large hierarchical structures, investigators typically encounter three imposing difficulties. One difficulty is the evaluation of a large-scale determinant resulting from the Jacobian of the transformation from the error structure to the latent variables used to simulate the discrete choices. A second difficulty results from an imposing inversion of an N×N matrix resulting from the need to simulate conditionally truncated draws. And, third, where investigator choice is involved, there is the over-arching need to evaluate and identify sets of preferred modelling substructures. When N is large, these problems often impart formidable computational demands on investigators, raising scope for the search for alternatives to conventional implementation. This paper demonstrates how each of the difficulties can be mitigated by exploiting hierarchical substructures embedded within the sampling framework. We demonstrate the procedures within a rich set of data sampled from 13000 professional (large economic size) farm households in some 4,000 municipalities throughout Italy collected during the 2005 production year. The empirical investigation explores the factors affecting the adoption of organic production and certification, and the depiction of so-called ‘neighbourhood effects.’ An important phenomenon affecting adoption decision-making is the decision of a “similar” farm household, where similarity is measured in terms of “location”/municipality. The hierarchical spatial model estimated in this paper allows the investigator to analyze the differences in the neighbourhood effects among regions that can be caused by the different infrastructures and the different social capital endowments available within regions.