How set up spatstat::densityHeat()?

On 14/07/20 1:39 am, Michal Kvasni?ka wrote:

Hello.

I have to find hotspots of road accidents. It seems that
spatstat::densityHeat() implements McSwiggan et al. (2017) algorithm I

want

to use. I plan to follow path of DrHotNet package:

1. estimate the density function
2. lixelize the network
3. calculate the density in the middle point of each lixel from (2) using
function estimated in (1)
4. find clusters of lixels from (3) with sufficiently high density

However, I don't know how to set the function's parameters.

I cannot use the implicit setting (finespacing=TRUE) because it suggests
tens of billions iterations. (I use OSM road maps of Czech districts
converted to Krovak projection. My testing district has about 2,700 km of
roads with an average length of road segments of about 30 meters due to
road curvatures. This is not the largest district I have to

handle---Prague

is much larger.)

I can set finespacing = FALSE and then finetune the parameters myself.
However, I can't find any documentation. Having skimmed the source code,
I'm trying something like this:

density_function <- densityHeat(accident_lpp, sigma, finespacing = FALSE,
eps = 10, fun = TRUE)

This way I get the function I need. However, I'm not certain what I'm
doing. It seems that the densityHeat() uses some grid, based on lixelized
network. My questions are:

* Is it sufficient to set the eps parameter or do I need to set other
parameters too? Which ones?
* Is the parameter in meters (my map is projected with meters as its

units)?

* If eps = 10 means grid of 10x10 meters, what precisely does it mean?

How

is the network lixelized (and why)? How does it affect the estimated
function (not the linim object)?
* What is the (economically/substantially) reasonable value of eps (and
other necessary parameters)?
* Is there any documentation to the function? (I've read chapter 17 of

the

spatstat book but found nothing there. The function help page doesn't

cover

this either.)
* Does it any difference if I lixelize the network myself before running
densityHeat()?

Many thanks for your advice. (And an apology for such a long question.)

Best wishes,
*Ing. Michal Kvasni?ka, Ph.D.*

Dear Michal,

I am replying on behalf of the spatstat authors (and not claiming any
personal competence in the area of point processes on networks).

My co-authors suggest that you:

    * upgrade to the latest development version of spatstat.  You
      could use

      > remotes::install_github("spatstat/spatstat",lib=.Rlib)

      to do this,

    * look at help(densityHeat), in particular the
      section "Discretisation and Error Messages" which explains
      how the discretisation is performed,

    * use densityfun.lpp instead of density.lpp if you want a
      function rather than a pixel image.

Note that if finespacing=FALSE is selected, the discretisation is
determined by the default pixel resolution of the window containing the
network. The arguments eps and dimyx would be passed to as.mask to
determine pixel resolution in the usual way (their interpretation is
explained in the help for as.mask()).

Note also that density.lpp() calls densityHeat() which calls the
internal algorithm. Similarly densityfun.lpp() calls the same internal
algorithm. Consequently they all handle discretisation arguments the
same way.

The spatstat authors know nothing about the package DrHotNet and do not
necessarily endorse whatever they are doing. Definitely *do not*
'lixellate' (discretise) the network before applying density(), because
this will screw up the discretisation procedure.

We are very sceptical about the validity of applying clustering to the
elements of the discretisation.

HTH

cheers,

Rolf Turner

--
Honorary Research Fellow
Department of Statistics
University of Auckland
Phone: +64-9-373-7599 ext. 88276