Weighted Spatial Adaptive Filtering: Monte Carlo Studies and Application to Illicit Drug Market Modeling

Abstract

This paper introduces a pattern recognizer, similar to weighting schemes used in combining time series forecasts, for use in spatial adaptive filtering applied to estimating multivariate cross-sectional models. The pattern recognizer enhances the ability to automatically detect and estimate parameters with discontinuous or sharp gradient changes over geographic contexts. Results from Monte Carlo studies suggest that the weighted spatial adaptive filter is at least as accurate as the unweighted filter for cases having smoothly changing parameters, but superior for cases having discontinuous, step-jump parameters. A case study on illicit drugmarket activities using census tract-level data from Pittsburgh, Pennsylvania, further illustrates the advantages of the weighted filter.

Geographical Analysis: Its First 40 Years

“…As Fotheringham and Brunsdon (, p. 340) remark: “ Geographical Analysis has published many of the significant contributions in this field.” Notable in this regard is GWR, which extends the regression model to address problems where the regression parameters cannot be assumed invariant across a geographic landscape (e.g., Brunsdon, Fotheringham, and Charlton ). This attention to local effects also underpins the expansion method first introduced by Casetti (), as well as the subject of wider consideration by Jones and Hanham () and of spatial adaptive filtering (Gorr and Olligschlaeger ).…”

Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity

“…The method of spatial adaptive filtering (SAF) has also been proposed to handle spatially varying relationships (Foster and Gorr 1986;Gorr and Olligschlaeger 1994). However, this approach incorporates spatial relationships in a rather ad hoc manner and produces parameter estimates that cannot be tested statistically so that it is of limited applicability.…”

Exploring Scale Effect Using Geographically Weighted Regression on Mass Dataset of Urban Robbery

“…According to socioeconomic findings of many ecology studies since 1960s, crimes are highly correlated with poverty (Gorr & Olligschlaeger, 1994;Olligschlaeger, 1997;Cahill & Mulligan, 2003;Ceccato et al, 2002;Gruenewald et al, 2006), unemployment (Schmid, 1960;Ackerman, 1998;Ceccato et al, 2002;Gruenewald et al, 2006), lower income (Schmid, 1960;Ackerman, 1998), education levels (Schmid, 1960;Ackerman, 1998;Cahill & Mulligan, 2003;Cozens, 2002;Gruenewald et al, 2006), being a renter (Ackerman, 1998), population density (Ackerman, 1998;Cahill & Mulligan, 2003;Ceccato et al, 2002;Cozens, 2002;Malczewski & Poetz, 2005), migration (Ackerman, 1998;Ceccato et al, 2002), minority (Ackerman, 1998;Gruenewald et al, 2006), marital status (Ackerman, 1998), number of children (Ackerman, 1998;Olligschlaeger, 1997;Gruenewald et al, 2006), youth (Olligschlaeger, 1997;Gruenewald et al, 2006), family structure (Cahill & Mulligan, 2003;Ceccato et al, 2002;Malczewski & Poetz, 2005), ethnicity (Ergün & Yirmibeşoğlu, 2005;Gruenewald et al, 2006) and commercial land uses (Olligschlaeger, 1997;Cozens, 2002;…”

“…Some of them focused on street level crime explanation like Gorr & Olligschlaeger (1994) and Ayhan (2007), whereas some of them studied on city or district level like Schmid (1960) and Ackerman (1998).…”

“…Above cited studies aim to understand crime occurrences by using spatial analysis techniques such as weighted spatial adaptive filtering (Gorr & Olligschlaeger, 1994), chaotic cellular forecasting (Olligschlaeger, 1997), Getis-Ord statistics (Murray et al, 2001;Ceccato et al, 2002;Gruenewald et al, 2006), Geographically Weighted Regression (GWR) (Malczewski & Poetz, 2005) or non-spatial analysis techniques such as linear regression (Ackerman, 1998;Ayhan, 2007) and correlation analysis (Ergün & Yirmibeşoğlu, 2005;Salleh et al, 2012). Some of them focused on street level crime explanation like Gorr & Olligschlaeger (1994) and Ayhan (2007), whereas some of them studied on city or district level like Schmid (1960) and Ackerman (1998).…”