Estimation of relative risk for events on a linear network

Adrian Baddeley, Gopalan Nair, Gregory McSwiggan

Research output: Contribution to journal › Article

Abstract

Motivated by the study of traffic accidents on a road network, we discuss the estimation of the relative risk, the ratio of rates of occurrence of different types of events occurring on a network of lines. Methods developed for two-dimensional spatial point patterns can be adapted to a linear network, but their requirements and performance are very different on a network. Computation is slow and we introduce new techniques to accelerate it. Intensities (occurrence rates) are estimated by kernel smoothing using the heat kernel on the network. The main methodological problem is bandwidth selection. Binary regression methods, such as likelihood cross-validation and least squares cross-validation, perform tolerably well in our simulation experiments, but the Kelsall–Diggle density-ratio cross-validation method does not. We find a theoretical explanation, and propose a modification of the Kelsall–Diggle method which has better performance. The methods are applied to traffic accidents in a regional city, and to protrusions on the dendritic tree of a neuron.
Original languageEnglish
Pages (from-to)1-16
JournalStatistics and Computing
DOIs
Publication statusE-pub ahead of print - 21 Aug 2019

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Linear networks
Highway accidents
Relative Risk
Cross-validation
Neurons
Accidents
Bandwidth
Spatial Point Pattern
Traffic
Binary Regression
Kernel Smoothing
Bandwidth Selection
Road Network
Heat Kernel
Experiments
Simulation Experiment
Accelerate
Least Squares
Neuron
Likelihood

Cite this

Baddeley, Adrian ; Nair, Gopalan ; McSwiggan, Gregory. / Estimation of relative risk for events on a linear network. In: Statistics and Computing. 2019 ; pp. 1-16.
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Baddeley, A, Nair, G & McSwiggan, G 2019, 'Estimation of relative risk for events on a linear network' Statistics and Computing, pp. 1-16. https://doi.org/10.1007/s11222-019-09889-7

Estimation of relative risk for events on a linear network. / Baddeley, Adrian; Nair, Gopalan; McSwiggan, Gregory.

In: Statistics and Computing, 21.08.2019, p. 1-16.

Research output: Contribution to journal › Article

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AU - Nair, Gopalan

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AB - Motivated by the study of traffic accidents on a road network, we discuss the estimation of the relative risk, the ratio of rates of occurrence of different types of events occurring on a network of lines. Methods developed for two-dimensional spatial point patterns can be adapted to a linear network, but their requirements and performance are very different on a network. Computation is slow and we introduce new techniques to accelerate it. Intensities (occurrence rates) are estimated by kernel smoothing using the heat kernel on the network. The main methodological problem is bandwidth selection. Binary regression methods, such as likelihood cross-validation and least squares cross-validation, perform tolerably well in our simulation experiments, but the Kelsall–Diggle density-ratio cross-validation method does not. We find a theoretical explanation, and propose a modification of the Kelsall–Diggle method which has better performance. The methods are applied to traffic accidents in a regional city, and to protrusions on the dendritic tree of a neuron.

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Baddeley A, Nair G, McSwiggan G. Estimation of relative risk for events on a linear network. Statistics and Computing. 2019 Aug 21;1-16. https://doi.org/10.1007/s11222-019-09889-7

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