Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology
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We study point patterns of events that occur on a network of lines, such as road accidents recorded on a road network. Okabe and Yamada developed a 'network K function', analogous to Ripley's K function, for analysis of such data. However, values of the network K-function depend on the network geometry, making interpretation difficult. In this study we propose a correction of the network K-function that intrinsically compensates for the network geometry. This geometrical correction restores many natural and desirable properties of K, including its direct relationship to the pair correlation function. For a completely random point pattern, on any network, the corrected network K-function is the identity. The corrected estimator is intrinsically corrected for edge effects and has approximately constant variance. We obtain exact and asymptotic expressions for the bias and variance of under complete randomness. We extend these results to an 'inhomogeneous' network K-function which compensates for a spatially varying intensity of points. We demonstrate applications to ecology (webs of the urban wall spider Oecobius navus) and criminology (street crime in Chicago). © 2011 Board of the Foundation of the Scandinavian Journal of Statistics.
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Rakshit, Suman; Nair, G.; Baddeley, Adrian (2017)© 2017 Elsevier B.V. The analysis of clustering and correlation between points on a linear network, such as traffic accident locations on a street network, depends crucially on how we measure the distance between points. ...
Baddeley, Adrian; Nair, G.; Rakshit, Suman; McSwiggan, G. (2017)Statistical methodology for analysing patterns of points on a network of lines, such as road traffic accident locations, often assumes that the underlying point process is “stationary” or “correlation-stationary.” However, ...
Baddeley, Adrian; Jammalamadaka, A.; Nair, G. (2014)© 2014 Royal Statistical Society. We develop methods for analysing the spatial pattern of events, classified into several types, that occur on a network of lines. The motivation is the study of small protrusions called ...