[R-sig-Geo] marked poisson process using a quadrature scheme and covariates in 'spatstat'

[Rolf Turner]

On 04/05/11 23:33, Roman Hornung wrote:
> Hello everyone,
>
> My data consists of marked points and several covariates, whereby the 
> marks are the time points of the observations. The problem is, that 
> one of the covariates is hard to handle as an image. This covariate 
> represents the type of roads. As there aren't roads at every location 
> of the map, one cannot specify the value of the covariate at any point 
> on a grid, which is necessary to specify an image. To tackle this, I 
> wanted to use a quadrature scheme and use points on the roads as dummy 
> points instead of a data point pattern as the outcome variable. The 
> problem I now encounter is, that I can't give marks to the dummy 
> points, since they are no "real" observations (and omitting the marks 
> gives an error).
> Does somebody know, what to do in such a situation?
>
> Thank you very much in advance! Any tips are appreciated much!

I am somewhat puzzled by what you are trying to do.  Covariates may be 
used to
model the intensity of a point pattern.  The intensity is defined at 
every point of
the domain of definition of the pattern; in practice it must be defined 
at every
point of the observation window.

So in your case the objective would be to specify the intensity 
"lambda(u)" in terms
of your covariates at every point "u" of your observation window.  You 
say that
one of your covariates is ``type of road''.  Obviously if no road passes 
through "u"
then there is no ``type of road'' ***at*** "u".  So how does the 
intensity at u depend
on ``type of road''?  Clarify that idea, and all of your problems will 
disappear.

One idea, which you may be subconsciously entertaining, is that the 
intensity at
"u" depends on the type of the road nearest to u.  Or it might depend on the
types of all roads weighted in some way by the distance of the roads 
from "u".
Get it clear in your mind first how you want to model the intensity.  Then
build your image, or images, in terms of your roads data in a manner 
consistent
with your modelling criteria.

Note that the distmap() and distfun() functions in "spatstat" will allow 
you to determine the
distance from a given point to the nearest road (if the roads are 
represented as "psp"
objects).

     cheers,

             Rolf Turner