# Spatial statistics - Point process on a network of one-dimensional lines

## Main Question or Discussion Point

Hi everyone,

My data consists of road accidents and spatial covariates. Originally i wanted to apply an inhomogenous Poisson process with covariates. Then I realised that the accidents cannot occur everywhere in space, but only on roads. I found an example, that is quite similiar to mine. it is said there, that one may model a Point process on a network of one-dimensional lines. Unfortunately it isn't given any more information. I searched the internet for it, but wasn't able to get information, how to explicitly model this.
The area of interest is 70.000 square kilometers and the coordinates of all roads are given.

I would deeply appreciate it, if somebody gave me a hint and/or name some literature on how to tackle this!

Thank you very much in advance!

Regards
Nemorad

## Answers and Replies

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Stephen Tashi
Science Advisor
If you cited the source of the example you found, someone else might be able to find related material by searching the web. It's not clear to me if you are determined to use a "point process on a network" to model the accidents or whether you are merely looking for a good way to model the accidents. For example, I found this PDF on the web:http://www.google.com/url?sa=t&source=web&cd=4&ved=0CCsQFjAD&url=http://www.easts.info/publications/journal_proceedings/journal2010/100465.pdf&ei=apCTTY2lJ5DUtQOrkuzPBQ&usg=AFQjCNEOQ8kyrbhEJhrVrlEczAWYR1ZT8g

Thank you for the quick reply and the article!

This approach is very interesting.
The example is merely part of a schedule of different scenarios where point processes are applicable. It is found in Gelfand et. al (2010) "Handbook of Spatial Statistics" p 340, but occupies only six lines. I myself am not commited to point processes on networks, yet my professor told me, I should use point processes to model the data. However he isn't that much into the matter. A more practical problem may be, that it would be hard to employ the method in the article you proposed on my data since I would have to divide the road data into segments of say length one kilometer, which may difficult to realise a posteriori.

Thanks again in advance for further hints!

Stephen Tashi
Science Advisor
What is the format of your data?

My guess: Time and GPS location of accidents. Roads given as vectors or as segments with (x,y) data for each end. Will you have trouble with errors in the accident locations that cause them to be off the roads?

To be honest, I'm not sure about that. The data set containing the roads is a shp-file and the one containing the accidents is a Rda-File for use in the statistical programming language R and structured as you said. Up to this point I didn't manage to look at the raw data of the roads using the open source geographical information system GRASS GIS. However I managed to look at the roads data visually: The roads appear to be curved in it, but maybe they are composed of lines. The file is in vector format.
The problem I was thinking about is, that it may hard to divide the roads into segments of same length, since it would be difficult to decide, what to do at crossroads and, if the roads are not represented as lines but as irregular curves, how to measure the lengths of the roads in general.
The latter problem would also be present for the point process on a network except the software would conduct that automatically.

In case nobody has an idea how to realise the point process on a network: May it be possible to neglect the fact, that the points cannot appear everywhere in space and apply an ordinary point process, since there are hardly any bigger "holes" with no roads on the map?

Stephen Tashi
Science Advisor
It's best not to make many plans about how to model data until you can inspect the data in detail. (You are in very real-world situation for an analyst. Someone hands you some files and expects an analysis or model. The data often doesn't live up to the expectations.)

May it be possible to neglect the fact, that the points cannot appear everywhere in space and apply an ordinary point process, since there are hardly any bigger "holes" with no roads on the map?
What is possible depends on how the final simulation will be judged. Who will evaluated it? What is it expected to do? Is the purpose only to demonstrate your knowledge of particular mathematics and skill as a programmer? Or will you do some formal statistical tests to compare the results to real world data?

You're right, I'd better edit the data for final use in the analysis before finally deciding on what to do. However it'll probably take some time before I reach that point since I'm not very familiar with GRASS GIS and the shp-data set has to be merged with the R data set. I'll get some help from a fellow student who has already experience with GRASS.

The data are indeed real world data. I'm not sure whether I will conduct a simulation too to validate the effectiveness of the method I will finally apply, but probably not. The main task is to identify covariates that are very influental on the occurence of (deer) accidents so that the number can be reduced in the future by setting up signs in areas with many accidents (although the programming code must be correct). The analysis will be evaluated by a professor. I guess the validity of using an ordinary point process compared to applying a more suitable method can only be judged by comparing the two methods, right?

Thanks again for your help!

I am also working on this. Any suggestions? I cannot find any detailed references :( Thanks!