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Estimation of relative risk for events on a linear network

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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.

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Acknowledgements

We thank Dr Tilman Davies and the referees for insightful comments.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Hwy, Nedlands, WA, 6009, Australia

    Greg McSwiggan & Gopalan Nair

  2. Department of Mathematics and Statistics, Curtin University, GPO Box U1987, Perth, WA, 6845, Australia

    Adrian Baddeley

  3. Data61, CSIRO Leeuwin Centre, 65 Brockway Rd, Floreat, WA, 6014, Australia

    Adrian Baddeley & Gopalan Nair

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  1. Greg McSwiggan
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  2. Adrian Baddeley
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  3. Gopalan Nair
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Correspondence to Adrian Baddeley.

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Research supported by the Australian Research Council, Discovery Grants DP130102322 and DP130104470.

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McSwiggan, G., Baddeley, A. & Nair, G. Estimation of relative risk for events on a linear network. Stat Comput 30, 469–484 (2020). https://doi.org/10.1007/s11222-019-09889-7

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