Flexible dependence modeling using convex combinations of different types of connectivity structures

There is a great deal of literature regarding use of non-geographically based connectivity matrices or combinations of geographic and non-geographic structures in spatial econometrics models. We explore alternative approaches for constructing convex combinations of different types of dependence between observations. Pace and LeSage (2002) as well as Hazır et al. (2016) use convex combinations of different connectivity matrices to form a single weight matrix that can be used in conventional spatial regression estimation and inference. An example for the case of two weight matrices, W1,W2 reflecting different types of dependence between a cross-section of regions, firms, individuals etc., located in space would be: Wc=γ1W1+(1−γ1)W2,0≤γ1≤1. The matrix Wc reflects a convex combination of the two weight matrices, with the scalar parameter γ1 indicating the relative importance assigned to each type of dependence. We explore issues that arise in producing estimates and inferences from these more general cross-sectional regression relationships in a Bayesian framework. We propose two procedures to estimate such models and assess their finite sample properties through Monte Carlo experiments. We illustrate our methodology in an application to CEO salaries for a sample of nursing homes located in Texas. Two types of weights are considered, one reflecting spatial proximity of nursing homes and the other peer group proximity, which arise from the salary benchmarking literature.