TY - JOUR

T1 - Estimation of relative risk for events on a linear network

AU - McSwiggan, Greg

AU - Baddeley, Adrian

AU - Nair, Gopalan

PY - 2020/3

Y1 - 2020/3

N2 - 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.

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.

KW - Bandwidth selection

KW - Cross-validation

KW - Dendritic spines

KW - Density ratio

KW - Heat kernel

KW - Kelsall–Diggle cross-validation

KW - Road traffic accidents

U2 - 10.1007/s11222-019-09889-7

DO - 10.1007/s11222-019-09889-7

M3 - Article

VL - 30

SP - 469

EP - 484

JO - Statistics and Computing

JF - Statistics and Computing

SN - 0960-3174

IS - 2

ER -