Comparing spatially varying coefficient models: A case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests

Journal of Geographical Systems

Volumn 11, Issue 1, 2009, Pages 1-22

  Wheeler, David C ^a,b   Waller, Lance A ^c  

^a HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

^b NATIONAL CANCER INSTITUTE   (United States)

^c EMORY UNIVERSITY   (United States)

Author keywords

Bayesian regression; Collinearity; GWR; Penalization methods

Indexed keywords

ALCOHOL; BAYESIAN ANALYSIS; CRIME; DRUG; ESTIMATION METHOD; MODELING; SPATIAL ANALYSIS; SPATIAL DATA; VIOLENCE;

HOUSTON; NORTH AMERICA; TEXAS; UNITED STATES;

EID: 60649107800     PISSN: 14355930     EISSN: 14355949     Source Type: Journal    
DOI: 10.1007/s10109-008-0073-5     Document Type: Article

References (24)

1. Banerjee S, Carlin BP, Gelfand AE (2004) Hierarchical modeling and analysis for spatial data. Chapman & Hall/CRC, Boca Raton
2. Belsley DA (1991) Conditioning diagnostics: Collinearity and weak data in regression. Wiley, New York
3. Brantingham PL, Brantingham PJ (1993) Nodes, paths and edges: considerations on the complexity of crime and the physical environment. J Environ Psychol 13:3-28. doi: 10.1016/S0272-4944(05)80212-9
4. Brantingham PL, Brantingham PJ (1999) A theoretical model of crime hot spot generation. Stud Crime Crime Prev 8:7-26
5. Brunsdon C, Aitkin M, Fotheringham S, Charlton M (1999) A comparison of random coefficient modelling and geographically weighted regression for spatially non-stationary regression problems. Geogr Environ Model 3:47-62
6. Fotheringham AS, Brunsdon C, Charlton M (2002) Geographically weighted regression: The analysis of spatially varying relationships. Wiley, West Sussex
7. Gelfand AE, Kim H, Sirmans CF, Banerjee S (2003) Spatial modeling with spatially varying coefficient processes. J Am Stat Assoc 98:387-396. doi: 10.1198/016214503000170
8. Goldstein M (1976) Bayesian analysis of regression problems. Biometrika 63(1):51-58. doi: 10.1093/biomet/63.1.51
9. Gorman D, Speer PW, Gruenewald PJ, Labouvie EW (2001) Spatial dynamics of alcohol availability, neighborhood structure and violent crime. J Stud Alcohol 62:628-636
10. Griffith D (2008) Spatial filtering-based contributions to a critique of geographically weighted regression (GWR). Environ Plant A (in press)
11. Group 1 Software (2003) Centrus Desktop, Version 4.01.01. Boulder, CO
12. Gruenewald PJ, Freisthler B, Remer L, LaScala EA, Treno A (2006) Ecological models of alcohol outlets and violent assaults: Crime potentials and geospatial analysis. Addiction 101:666-677. doi: 10.1111/ j.1360-0443.2006.01405.x
13. Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning: Data mining, inference and prediction. Springer, New York
14. Hoerl AE, Kennard RW (1970) Ridge regression: Biased estimation for non-orthogonal problems. Technometrics 12:55-67. doi: 10.2307/1267351
15. Lindley DV, Smith AFM (1972) Bayes estimates for the linear model. J Roy Statist Soc Ser B Methodol 34(1):1-41
16. Lipton R, Gruenewald PJ (2002) The spatial dynamics of violence and alcohol outlets. J Stud Alcohol 63:187-195
17. Nelson AL, Bromley RDF, Thomas CJ (2001) Identifying micro and temporal patterns of violent crime and disorder in the British city center. Appl Geogr 21:249-274. doi: 10.1016/S0143-6228(01)00008-X
18. Roncek DW, Maier PA (1991) Bars, blocks, and crimes revisited: Linking the theory of routine activities to the empiricism of "hot spots". Criminology 29:725-753. doi: 10.1111/ j.1745-9125.1991.tb01086.x
19. Sampson RJ, Lauritsen JL (1994) Violent victimization and offending: individual-, situational- and community-level risk factors. In: Reiss AJ Jr, Roth J (eds) Understanding and preventing violence: Social influences, volume 3. National Academy Press, Washington, DC, pp 1-114
20. Scribner RA, MacKinnon DP, Dwyer JH (1995) The risk of assaultive violence and alcohol availability in Los Angeles County. Am J Public Health 85:335-340
21. Waller L, Zhu L, Gotway C, Gorman D, Gruenewald P (2007) Quantifying geographic variations in associations between alcohol distribution and violence: A comparison of geographically weighted regression and spatially varying coefficient models. Stochastic Environ Res Risk Assess 21(5):573-588. doi: 10.1007/s00477-007-0139-9
22. Wheeler D (2007) Diagnostic tools and a remedial method for collinearity in geographically weighted regression. Environ Plant A 39(10):2464-2481. doi: 10.1068/a38325
23. Wheeler D, Calder C (2007) An assessment of coefficient accuracy in linear regression models with spatially varying coefficients. J Geogr Syst 9:145-166. doi: 10.1007/s10109-006-0040-y
24. Wheeler D, Tiefelsdorf M (2005) Multicollinearity and correlation among local regression coefficients in geographically weighted regression. J Geogr Syst 7:161-187. doi: 10.1007/s10109-005-0155-6