An Adaptive Filter for Estimating Spatially-Varying Parameters: Application to Modeling Police Hours Spent in Response to Calls for Service

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Abstract
The Spatial Adaptive Filter (SAF), introduced in this paper, uses generalized damped negative feedback to estimate spatially-varying parameters for multivariate models. Previous adaptive filters have been designed to estimate time-varying parameters and process data recursively in time sequence. SAF processes all data simultaneously in an iterative algorithm. Monte Carlo studies show that SAF is successful in automatically identifying and estimating step-jump and continuous spatial variation in the parameters of causal variables. A case study on census-tract data from Columbus, Ohio, relating police-vehicle hours spent in responding to calls to socio-economic indicators, has systematic spatial variation in estimated parameters. Independent variables that are significant in inner-city areas of Columbus become progressively less significant in moving to outlying areas.

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