Clustering Random Curves Under Spatial Interdependence With Application to Service Accessibility

Service accessibility is defined as the access of a community to the nearby site locations in a service network consisting of multiple geographically distributed service sites. Leveraging new statistical methods, this article estimates and classifies service accessibility patterns varying over a large geographic area (Georgia) and over a period of 16 years. The focus of this study is on financial services but it generally applies to any other service operation. To this end, we introduce a model-based method for clustering random time-varying functions that are spatially interdependent. The underlying clustering model is nonparametric with spatially correlated errors. We also assume that the clustering membership is a realization from a Markov random field. Under these model assumptions, we borrow information across functions corresponding to nearby spatial locations resulting in enhanced estimation accuracy of the cluster effects and of the cluster membership as shown in a simulation study. Supplementary materials including the estimation algorithm, additional maps of the data, and the C++ computer programs for analyzing the data in our case study are available online.