Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology
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 th...
| Main Authors: | , , |
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| Format: | Journal Article |
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WILEY-BLACKWELL
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/16050 |
| _version_ | 1848749062330777600 |
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| author | Ang, Q. Baddeley, Adrian Nair, G. |
| author_facet | Ang, Q. Baddeley, Adrian Nair, G. |
| author_sort | Ang, Q. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T07:14:58Z |
| format | Journal Article |
| id | curtin-20.500.11937-16050 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:14:58Z |
| publishDate | 2012 |
| publisher | WILEY-BLACKWELL |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-160502017-09-13T15:44:33Z Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology Ang, Q. Baddeley, Adrian Nair, G. 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. 2012 Journal Article http://hdl.handle.net/20.500.11937/16050 10.1111/j.1467-9469.2011.00752.x WILEY-BLACKWELL restricted |
| spellingShingle | Ang, Q. Baddeley, Adrian Nair, G. Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology |
| title | Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology |
| title_full | Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology |
| title_fullStr | Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology |
| title_full_unstemmed | Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology |
| title_short | Geometrically Corrected Second Order Analysis of Events on a Linear Network, with Applications to Ecology and Criminology |
| title_sort | geometrically corrected second order analysis of events on a linear network, with applications to ecology and criminology |
| url | http://hdl.handle.net/20.500.11937/16050 |