WEB APPENDIX Bayesian Spatio-Temporal Analysis of Imitation Behavior Across New Buyers at an Online Grocery Retailer

Web Appendix A. Low-rank spatial smoothing of the broadband access variable Our measure of the Internet access availability has a few known imperfections: there are some missing data for some zip codes, and in some cases services are under-reported. To improve the quality of this variable, we implement a low-rank thin plate spline smoother (Wand 2003) to correct for measurement errors. Here, we provide an outline for our implementation; readers are encouraged to see Wand (2003) for more details. Step 1. Choose knots: We obtain " knots " based on centroids of a k-d tree (Molenberghs and Verbeke 2006). Starting with the entire set of zip codes, the k-d tree partitions the space until all partitions contain at most 300 regions. The region nearest to the centroid of each partition is chosen as a knot which creates 117 knots in our application, as shown in the figure below.