Intensity estimation with log-linear Poisson model on linear networks

Abstract

Purpose: The statistical analysis of point processes on linear networks is a recent area of research that studies processes of events happening randomly in space (or space-time) but with locations limited to reside on a linear network. For example, tra ffi c accidents happen at random places that are limited to lying on a network of streets. This paper applies techniques developed for point processes on linear networks and the tools available in the R-package spatstat to estimate the intensity of tra ffi c accidents in Leon County, Florida. Methods: The intensity of accidents on the linear network of streets is estimated using log-linear Poisson models which incorporate cubic basis spline ( B -spline) terms which are functions of the x and y coordinates. The splines used equally-spaced knots. Ten di ff erent models are fit to the data using a variety of covariates. The models are compared with each other using an analysis of deviance for nested models. Results: We found all covariates contributed significantly to the model. AIC and BIC were used to select 9 as the number of knots. Additionally, covariates have di ff erent e ff ects such as increasing the speed limit would decrease tra ffi c accident intensity by 0.9794 but increasing the number of lanes would result in an increase in the intensity of tra ffi c accidents by 1.086. Conclusion: Our analysis shows that if other conditions are held fixed, the number of accidents actually decreases on roads with higher speed limits. The software we currently use allows our models to contain only spatial covariates and does not permit the use of temporal or space-time covariates. We would like to extend our models to include such covariates which would allow us to include weather conditions or the presence of special events (football games or concerts) as covariates.