Interpretation and Computation of Estimates from Regression Models using Spatial Filtering

<title>Abstract</title> Spatial filtering in various forms has become a popular way to address spatial dependence in statistical models (Griffith, 2003; Tiefelsdorf & Griffith, 2007). However, spatial filtering faces computational challenges for large <italic>n</italic> as the current method requires order of n-super-3 operations. This manuscript demonstrates how using iterative eigenvalue routines on sparse weight matrices can make filtering feasible for data sets involving a million or more observations and empirically estimates an operation count on the order of n-super- <italic>1.1</italic> . Moreover, we show that filtering performs better, both statistically and numerically, for spatial weight matrices with more neighbours. Finally, we show that although filtering out spatial aspects of the data reduces bias in parameter estimates for the spatially lagged dependent variable DGP, it also filters out spatial aspects of interest such as spillovers.