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 -