On 16/04/11 15:50, Gregory Ryslik wrote:
Hi Everyone,
I am trying to figure out the spatstat package for the first time and am having
some trouble. Unfortunately, I can't post my data set but I'll hopefully post
enough details for some help.
I want to model the intensity of a spatial point process using 2 covariates from my data.
After reading through the documentation, I have successfully created 2 "ppp"
objects. The first ppp object is a list of coordinates where people exist and the second
is where people do not exist as follows:
people_exist
planar point pattern: 944 points
window: rectangle = [73, 135] x [18, 54] units
people_empty
planar point pattern: 2828 points
window: rectangle = [73, 135] x [18, 54] units
Now, I also have observed values for two covariates, Z1 and Z2 for both the 944
and 2828 points in dataframe form. Finally, following the documentation, I was
able to create one quadrature Q, with 944 points and 2828 dummy points that
correctly takes the points where we had an event (people_exist) and the points
where we don't have an event (people_empty).
people_quadrature
Quadrature scheme
944 data points, 2828 dummy points
Total weight 1098.64
How do I use the Quadrature to model my intensity based off of those two
covariates and an intercept term alpha? In mathematical terms, if \lambda is my
intensity function, I want to estimate \lambda(s;b) = exp(alpha + b_1 * Z_1 +
b_2 * Z_2).
Thank you for your help! I really appreciate it.
Your procedure seems to evince quite a bit of confusion in your mind about
what you are actually doing. To start with, one gets the impression
that you have
*two* point patterns ("people" and "no people"). But then, from your
quadrature
scheme it appears that you are treating the "no people" pattern as the dummy
points for the quadrature scheme.
*Are* they just dummy points, chosen by you in some more or less arbitrary
manner? Or are they points of an actual *observed* point pattern?
Assuming that they are indeed dummy points (chosen in a reasonably sensible
manner) what you need to do is create a data frame of covariate values
at each
of the points of your quadrature scheme. You indicate that you have
the covariate
values available at each of these points, so that should be alright.
(In respect of "sensible manner" --- 2828 dummy points may be somewhat too
few. The default quadrature scheme that ppm() would create would have 4904
dummy points.)
Anyhow, suppose that you have such a data frame, say "covDf" with two
columns
named "Z1" and "Z2" and with 3772 = 944 + 2828 rows, the i-th row
corresponding
to the i-th point in the quadrature scheme.
You would then execute a command of the form
fit <- ppm(people_quadrature, ~ Z1 + Z2, covariates=covDf)
See the help on ppm().
Life would be much easier for you if you could build *images* providing
the values of
Z1 and Z2 for a fairly fine pixellation of the observation window. See
the help on im().
If you have such images, say IZ1 and IZ2, then you can let ppm() take
care of creating
the dummy points and proceed as follows:
fit <- ppm(people_exist, ~ IZ1 + IZ2, covariates=list(IZ1=IZ1,
IZ2=IZ2))
I.e. you just need the ``real'' point pattern (presumably a point
pattern of human
habitations) and the covariates expressed as (pixellated) images.
cheers,
Rolf Turner
P. S. The foregoing all assumes that the pattern of interest is a
realization of
an inhomogeneous ***Poisson*** process, with intensity depending (log
linearly)
upon the two covariates Z1 and Z2. There could of course be
*interaction* between
the points and the dependence upon covariates could be more complicated than
that proposed.
R. T.
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