[R-sig-Geo] Temporal marked point process with time-varying covariates

Wed Aug 18 09:21:17 CEST 2010

On Tue, 17 Aug 2010, Mayeul KAUFFMANN wrote:

> Dear spatial statisticians and R users,

The following is posted for David Harte:
----------------------------------------------------
Attached is my response to a question raised on your list. My response
to the list was rejected as I am not a member.

David Harte

Dear Mayeul

The structure of the PtProcess package is based on the conditional
intensity function (i.e. is history dependent), and if the user can
specify their ground intensity function, then they can use the provided
framework within the package to fit the model, simulate, and do various
other things. Processes that are just time varying, with no explicit
dependence on the history, can obviously be included with a null history.

I understand that the models fitted by spatstat are somewhat different,
and have no natural definition of past history and are based on a
Papangelou conditional intensity (i.e. conditional on the spatial
locations of other points, with no time ordering).

A marked point process has a structure where the conditional intensity
function is the product of the ground intensity function and the mark
distributions. What sort of functional relationship are you proposing
for your data? Can you write an equation for your ground intensity
function? Can you specify a spatial mark distribution? In particular,
can the spatial distribution be separated from the ground intensity as a
mark? There is no reason why other covariates cannot be part of the
defined ground intensity function, or the mark distribution.

I do not think that the ETAS model will have any relevance for your
situation. The spatial ETAS model is slightly peculiar as it does not
satisfy the simple product of the ground intensity and spatial mark
required for it to be a marked point process. It is a "compounded" mark
point processes, i.e. I mean here the sum of many marked point
processes; which makes it rather interesting. See the cited paper below
for further information.

If you can write an equation that represents your ground intensity
function in terms of your covariates and any other information, and also
for a spatial mark distribution, then I suggest that you look at the
code for the simple time varying conditional intensity functions (see
manual page for simple_gif, it will list the various functions). These
are just non-homogeneous Poisson processes that are various functions of
time. However, given your specification of your conditional intensity as
a function of the covariates, you should be able to mimic the required
structure, and write your own ground intensity function. Similarly, you
will also need to specify your spatial mark distribution. You also
mentioned the magnitude of the event. Is this independent of space? If
not, then it will be part of a spatial-magnitude mark. If independent,
then the spatial-magnitude density would be the product of the two
densities.

I have recently published further explanation about the package in the
Journal of Statistical Software, see: http://www.jstatsoft.org/v35/i08/

Good luck

David Harte

-- 
David Harte
Statistics Research Associates Ltd
PO Box 12 649
Thorndon
Wellington
NEW ZEALAND

Tel:    +64-4-473 1760
Email:  david at statsresearch.co.nz
Web:    www.statsresearch.co.nz

----------------------------------------------------
>
> I am trying to model a temporal marked point process with time-varying
> covariates and I am looking for the most appropriate function among several
> ones.
> (The events are violent events, such as fightings, in African countries). I want
> to model both the time/location of the events and at least one of the mark (the
> intensity of the event, measured for example by the number of persons killed).
>
> Events are collected over a few years. The time-resolution of the events is the
> day, while the covariates vary more slowly. The events have latitude and
> longitude, while the covariates are raster data (1km x 1km grid).
>
> I had a look at the following packages but I'm not sure I found the right
> solution yet:
> spatstat
> splancs
> PtProcess
>
> spatstat seems to have the correct object to handle my dependant variables (the
> ppx class: 2D space + time) but if I'm correct the ppm() model fitting function
> cannot handle this (it only works with ppp). Am I missing something? I saw at
> http://www.spatstat.org/  that this branch is in development. Any news /
> schedule on that?
>
> PtProcess does allow to estimate a time dependent marked point process (using
> etas_spatial()  ). However, apparently, only the history of the point process
> itself can be taken into account (there are marks but they are no covariates:
> there is no data for locations without events). One workaround might be to
> include in the point process dummy events with (near-)zero intensity for all (or
> sampled) time-space cells and to attach the covariates as marks. What do you
> think?
>
> splancs does not seem to support this but has a nice space-time kernel smoothing
> function (kernel3d) and ability to display the result (kerview). I could
> transform the point process into a time-varying surface, but do not know how to
> model it either.
>
> The main aim is to measure the impact of the covariates on the point process.
> Ideally, the model should allow for time and space autocorelation among events
> (clustering is likely), similar to what the etas_spatial() function permits.
>
> Thanks for any comment!
> Regards,
>
> Mayeul KAUFFMANN
>
> PS: for reference, some messages I found close to my problem:
> https://stat.ethz.ch/pipermail/r-sig-geo/2010-March/007909.html
> https://stat.ethz.ch/pipermail/r-sig-geo/2009-September/006438.html
> https://stat.ethz.ch/pipermail/r-sig-geo/attachments/20091023/b33321bb/attachmen
> t.pl
>
> _____________________________________________________
> Dr. Mayeul KAUFFMANN, Conflict Specialist
> European Commission, Joint Research Centre (JRC)
> Institute for the Protection and Security of the Citizen (IPSC)
> Global Security and Crisis Management - ISFEREA
> Via E. Fermi 2749 - I-21027 Ispra (VA), ITALY
> Phone: (+39) 033278 5071
> http://isferea.jrc.ec.europa.eu/Staff/Pages/Kauffmann-Mayeul.aspx
>
> (Office: building 48c, 1st floor, room 123. TP: 483)
>
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-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no