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I am working on a spatial analysis of traffic accidents, the goal of which is to estimate the effects of spatial covariates on the intensity function of crashes. The original analysis was an inhomogeneous poisson point process model which treated space as a plane. This approach received criticism because it does not respect the fact that "points" can only occur on the road network. While conducting a literature search, I found some sources related to estimating things like density, the K-function, and other common spatial descriptives for point processes on a network. This paper

“A Network-Constrained Integrated Method for Detecting Spatial Cluster and Risk Location of Traffic Crash: A Case Study from Wuhan, China” Sustainability 2015, 7, 2662-2677

and those it cites are good examples. However, none of these appear to give methods for regression-like point process models restricted to a network. Does anyone have any references for this problem? I can't imagine I'm the first to encounter this.

p.s. While typing the title of this question the following question was suggested:

Are there models for "censored" spatial point processes?

while related, I think I'm asking a very different question (correct me if I'm wrong).

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In shameless self-promotion I can say that a chapter is devoted to this in Spatial Point Patterns: Methodology and Applications with R. The main problem for you would be that it is expected to be available for purchase sometime in November 2015. The relevant methodology is already implemented in the spatstat package for R, so you might find inspiration there. To fit a Poisson model with covariates you would use the function lppm.

Sorry for not being more helpful at this time.

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