15: A Dimension Reduction Approach to Edge Weight Estimation for Use in Spatial Models

Music City Center 

Models for areal data are traditionally defined using the neighborhood structure of the regions on which the data are observed. The unweighted adjacency matrix of a graph is commonly used to characterize relationships between locations, resulting in the implicit assumption that all pairs of neighboring regions interact similarly, an assumption which may not be true in practice. It has been shown that more complex spatial relationships between graph nodes may be represented when edge weights are allowed to vary. Christensen and Hoff (2024) introduced a covariance model for data observed on graphs which is more flexible than traditional alternatives, parameterizing covariance as a function of an unknown edge weights matrix. However, their treatment of each edge weight as a unique parameter presents computational issues as graph sizes increase. In this work we propose a framework for estimating edge weight matrices that reduces their effective dimension via a basis function representation of the edge weights. We show that this method may be used to enhance the performance and flexibility of covariance models parameterized by such matrices in a series of simulations and data examples.