Abstract
Exploratory spatial data analysis (ESDA) plays a key role in research that includes geographic data. In ESDA, analysts typically need to visualize observations and local relationships on a map. However, software dedicated to visualizing local degrees of association between multiple variables in high-dimensional geospatial datasets remains undeveloped. This paper introduces gwpcorMapper, a newly developed software application for mapping geographically weighted (GW) correlation and partial correlation statistics in high-dimensional datasets. gwpcorMapper facilitates ESDA by giving researchers the ability to interact with map components that describe local correlative relationships. gwpcorMapper is an open source and is built using the R Shiny framework. The software inherits its algorithm logic from GWpcor, an R library for calculating the geographically weighted correlation and partial correlation statistics. We demonstrate the application of gwpcorMapper by using it to investigate census data to find meaningful relationships that describe the work-life environment in the 23 special wards of Tokyo, Japan. gwpcorMapper is useful in both variable selection and parameter tuning for GW statistics.
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References
Anselin L (1988a) Spatial econometrics: methods and models. Stud Oper R. https://doi.org/10.1007/978-94-015-7799-1
Anselin L (1988b) Lagrange multiplier test diagnostics for spatial dependence and spatial heterogeneity. Geogr Anal 20:1–17. https://doi.org/10.1111/j.1538-4632.1988.tb00159.x
Anselin L, Rey S (1991) Properties of tests for spatial dependence in linear regression models. Geogr Anal 23:112–131. https://doi.org/10.1111/j.1538-4632.1991.tb00228.x
Anselin L (1999) The future of spatial analysis in the social sciences. Ann Gis 5:67–76. https://doi.org/10.1080/10824009909480516
Anselin L (2005) Interactive techniques and exploratory spatial data analysis. In: Longley PA, Goodchild MF, Maguire DJ, Rhind D (eds) Geographical Information Systems: Principles, Techniques, Management and Applications, 2nd edn. Wiley, pp 253–266
Anselin L, Syabri I, Kho Y (2006) GeoDa: an introduction to spatial data analysis. Geogr Anal 38:5–22. https://doi.org/10.1111/j.0016-7363.2005.00671.x
Bibri SE, Krogstie J Kärrholm M (2020) Compact city planning and development: emerging practices and strategies for achieving the goals of sustainable development. Dev Built Environ. https://doi.org/10.1016/j.dibe.2020.100021
BioMedware (2020) Spacestat. https://www.biomedware.com/software/spacestat/. Accessed 22 February 2021
Bivand RS (2010) Exploratory Spatial Data Analysis. In: Fishcer M, Getis A (eds) Handbook of applied spatial analysis: software tools, methods and applications. Springer, Heidelberg, pp 219–254
Bivand R, Yu D (2020) spgwr: geographically weighted regression. R package version 0.6–34. https://CRAN.R-project.org/package=spgwr. Accessed 22 February 2021
Brunsdon C, Fotheringham AS, Charlton ME (1996) Geographically weighted regression: a method for exploring spatial nonstationarity. Geogr Anal 28(4):281–298. https://doi.org/10.1111/j.1538-4632.1996.tb00936.x
Brunsdon C (1998) Exploratory spatial data analysis and local indicators of spatial association with XLISP-STAT. J Royal Statistical Soc Ser D Statistician 47(3):471–484. https://doi.org/10.1111/1467-9884.00148
Brunsdon C, Fotheringham AS, Charlton M (2002) Geographically weighted summary statistics — a framework for localised exploratory data analysis. Comput Environ Urban Syst 26(6):501–524. https://doi.org/10.1016/s0198-9715(01)00009-6
Brunsdon C, Fotheringham S, Charlton M (2007) Geographically weighted discriminant analysis. Geogr Anal. 39(4):376–396. https://doi.org/10.1111/j.1538-4632.2007.00709.x
CARTO (2021) CARTO. https://carto.com/. Accessed 25 February 2021
Chang W, Cheng J, Allaire JJ, Xie Y, McPherson J (2020) Shiny: web application framework for R. R package version 1.5.0. https://CRAN.R-project.org/package=shiny. Accessed 4 December 2020
Cliff AD, Ord JK (1973) Spatial Autocorrelation. Pion, London
Comber A, Brunsdon C, Charlton M, Dong G, Harris R, Lu B, LuY, Murakami,D, Nakaya T, Wang Y, Harris P (2022) A route map for successful applications of geographically weighted regression. Geogr Anal. https://doi.org/10.1111/gean.12316
Dantzig G, Saaty TL (1973) Compact city: a plan for a livable urban environment. Freeman, W. H
Dykes J (1998) Cartographic visualization. J Royal Statistical Soc Ser D Statistician 47(3):485–497. https://doi.org/10.1111/1467-9884.00149
Dykes J, Brunsdon C (2007) Geographically weighted visualization: interactive graphics for scale-varying exploratory analysis. IEEE Trans Visual Comput Graphics 13(6):1161–1168. https://doi.org/10.1109/tvcg.2007.70558
Eddelbuettel D, François R (2011) Rcpp: seamless R and C++ integration. J Stat Softw. 40(8). https://doi.org/10.18637/jss.v040.i08
ESRI (2020) ArcGIS desktop: release 10.8. Redlands, CA: Environmental Systems Research Institute. https://www.esri.com/en-us/arcgis/about-arcgis/overview. Accessed 22 February 2021
Farber S, Páez A (2007) A systematic investigation of cross-validation in GWR model estimation: empirical analysis and Monte Carlo simulations. J Geogr Syst 9(4):371–396. https://doi.org/10.1007/s10109-007-0051-3
Fotheringham A (1992) Exploratory spatial data analysis and GIS. Environ Plan A 12(24):1675–1678
Fotheringham AS, Charlton M, Brunsdon C (1997) Recent developments in spatial analysis, spatial statistics, behavioural modelling, and computational intelligence. Adv Spat Sci. 60–82. https://doi.org/10.1007/978-3-662-03499-6_4
Fotheringham SA, Brunsdon C, Charlton M (2003) Geographically weighted regression—the analysis of spatially varying relationships. John Wiley & Sons
Garnier S (2018) viridis: default color maps from ‘matplotlib’. R package version 0.5.1. https://CRAN.R-project.org/package=viridis. Accessed 25 February 2021
Getis A (1994) Spatial dependence and heterogeneity and proximal databases. Spatial analysis and GIS. 105–120.
Gollini I, Lu B, Charlton M, Brunsdon C, Harris P (2015) GWmodel: an R package for exploring spatial heterogeneity using geographically weighted models. J Stat Softw. 63(17). https://doi.org/10.18637/jss.v063.i17
Guo L, Ma Z, Zhang L (2008) Comparison of bandwidth selection in application of geographically weighted regression: a case study. Can J Forest Res 38(9):2526–2534. https://doi.org/10.1139/x08-091
Haining R, Wise S, Ma J (1998) Exploratory spatial data analysis. J Royal Statistical Soc Ser D Statistician 47(3):457–469. https://doi.org/10.1111/1467-9884.00147
Harris P, Brunsdon C (2010) Exploring spatial variation and spatial relationships in a freshwater acidification critical load data set for Great Britain using geographically weighted summary statistics. Comput Geosci 36(1):54–70. https://doi.org/10.1016/j.cageo.2009.04.012
Harris P, Brunsdon C, Charlton M (2011) Geographically weighted principal components analysis. Int J Geogr Inf Sci 25(10):1717–1736. https://doi.org/10.1080/13658816.2011.554838
Hong Z, Hao H, Li C, Du W, Wei L, Wang H (2018) Exploration of potential risks of hand, foot, and mouth disease in Inner Mongolia Autonomous Region, China Using Geographically Weighted Regression Model. Sci Rep-Uk 8(1):17707. https://doi.org/10.1038/s41598-018-35721-9
Irigoien X, Klevjer TA, Røstad A, Martinez U, Boyra G, Acuña JL, Bode A, Echevarria F, Gonzalez-Gordillo JI, Hernandez-Leon S, Agusti S, Aksnes DL, Duarte CM, Kaartvedt S (2014) Large mesopelagic fishes biomass and trophic efficiency in the open ocean. Nat Commun 5(1):3271. https://doi.org/10.1038/ncomms4271
Kalogirou S (2020) lctools: local correlation, spatial inequalities, geographically weighted regression and other tools. R package version 0.2–8. https://CRAN.R-project.org/package=lctools. Accessed 29 March 2022
Kim S, Kim Y, Lim S-S, Ryoo J-H, Yoon J-H (2019) Long commute time and sleep problems with gender difference in work–life balance: a cross-sectional study of more than 25,000 workers. Saf Heal Work 10(4):470–475. https://doi.org/10.1016/j.shaw.2019.08.001
Lee S-I (2009) Neighborhood Effects. In: Kitchin R, Thrift N (eds) International encyclopedia of human geography. Elsevier, Oxford, pp 349–353
Li Z, Fotheringham SA, Li W, Oshan T (2019) Fast geographically weighted regression (FastGWR): a scalable algorithm to investigate spatial process heterogeneity in millions of observations. Int J Geogr Inf Sci 33(1):155–175. https://doi.org/10.1080/13658816.2018.1521523
Lloyd CD (2010) Analysing population characteristics using geographically weighted principal components analysis: a case study of Northern Ireland in 2001. Comput Environ Urban Syst 34(5):389–399. https://doi.org/10.1016/j.compenvurbsys.2010.02.005
Lu B, Harris P, Charlton M, Brunsdon C (2014) The GWmodel R package: further topics for exploring spatial heterogeneity using geographically weighted models. Geo-Spatial Information Sci 17(2):85–101. https://doi.org/10.1080/10095020.2014.917453
Luo J, Du P, Samat A, Xia J, Che M, Xue Z (2017) Spatiotemporal pattern of PM2.5 concentrations in Mainland China and analysis of its influencing factors using geographically weighted regression. Sci Rep-uk 7(1):40607. https://doi.org/10.1038/srep40607
Mapbox (2021) Mapbox. https://www.mapbox.com/. Accessed 25 February 2021
Open Source Geospatial Foundation, GeoServer Contributors (2021) GeoServer; Version 2.18.2. http://geoserver.org/download/. Accessed on 25 February 2021
Pebesma E (2018) Simple features for R: standardized support for spatial vector data. R J 10(1):439–446. https://doi.org/10.32614/rj-2018-009
Penrose R (1955) A generalized inverse for matrices. Math Proc Cambridge 51(3):406–413. https://doi.org/10.1017/s0305004100030401
Percival J, Tsutsumida N (2017) Geographically weighted partial correlation for spatial analysis. GI_Forum. 1:36–43. https://doi.org/10.1553/giscience2017_01_s36
QGIS Development Team (2021) QGIS geographic information system. Open Source Geospatial Foundation. http://qgis.org. Accessed 22 February 2021
R Core Team (2020) R. A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.: https://www.r-project.org/. Accessed on 4 December 2020
Schafer J, Opgen-Rhein R, Zuber V, Ahdesmaki M, Silva A P D, Strimmer K (2017) corpcor: efficient estimation of covariance and (partial) correlation. R package version 1.6.9. https://CRAN.R-project.org/package=corpcor. Accessed on 4 December 2020
Sievert C (2020) Interactive web-based data visualization with R, plotly, and shiny. Chapman and Hall/CRC, Florida
Thomas JJ, Cook KA (2006) A visual analytics agenda. IEEE Comput Graphics Appl 26(1):10–13. https://doi.org/10.1109/mcg.2006.5
Unwin A, Unwin D (1998) Exploratory spatial data analysis with local statistics. J Royal Statistical Soc Ser D Statistician 47(3):415–421
Yu D, Wei YD, Wu C (2007) Modeling spatial dimensions of housing prices in Milwaukee. WI Environ Plan B Plan Des 34(6):1085–1102. https://doi.org/10.1068/b32119
Funding
This research was funded by the Joint Support Center for Data Science Research at Research Organization of Information and Systems (ROIS-DS-JOINT) under Grant 006RP2018, 004RP2019, 003RP2020, and 005RP2021.
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NT conceived the original idea behind gwpcorMapper and both JEHP and NT developed the software with JEHP being the main contributor. JEHP prepared the initial draft of the manuscript and produced the visualizations. All authors contributed to the writing of the paper. All authors have read and agreed to the published version of the manuscript.
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Percival, J.E.H., Tsutsumida, N., Murakami, D. et al. Exploratory Spatial Data Analysis with gwpcorMapper: an Interactive Mapping Tool for Geographically Weighted Correlation and Partial Correlation. J geovis spat anal 6, 17 (2022). https://doi.org/10.1007/s41651-022-00111-3
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DOI: https://doi.org/10.1007/s41651-022-00111-3