[R-sig-Geo] Estimating multiStrauss interaction radii

[Rolf Turner]

On 17/08/12 04:23, José M. Blanco Moreno wrote:
> Dear users and experts,
> I know that my question is not strictly R-related, but... Is there any good strategy (preferably already implemented in R) for estimating interaction radii of a MultiStrauss model?
>
> I have been working with  function profilepl in spatstat, but I frequently have to evaluate I too many combinations of interaction radii (1000's) and not even then I am sure that I get the right answer, because either I have likelihood maxima that are very narrow (easy to miss; it is one of the cases that I fave faced), or two local maxima with a large separation among them, leading to very different answers (from inhibition to gamma parameters higher than one, which if I have properly understood, are not "desirable") or changing the evaluation grid slightly I get different (or very different) answers.
>
> Should I just resign, take a deep breath and evaluate a grid of interaction radii of 10,000's?

I think that your problem is a pretty thorny one.

(a) It is not clear to me just how well one can estimate "irregular" 
parameters
such as interaction radii in any circumstances.

(b) Since the parameters are *irregular*, even if you could do full-blown
maximum likelihood it's not clear that the estimators would have 
particularly
good properties.

(c) Gamma parameters greater than 1 are OK for interactions between 
points of
different type.  For points of the same type they are not just 
undesirable, they
are verboten.  The model is undefined if any gamma_{ii} > 1.

(d) I have no idea how to handle the problem of getting two local maxima
which are widely separated (and of similar heights, presumably).  My gut 
feel
is that in such instances the data are simply being recalcitrant and 
refusing
to tell you a clear story about the information they contain, and there is
nothing much you can do about it.  (But then, I am by nature a confirmed
pessimist.  Maybe there *is* something you can do .... but I haven't a clue
as to what.)

Of course if one of the local maxima leads to gamma estimates which make
the model undefined then I think that you can safely rule it out.

(e) In respect of computational strategy:  I experimented a bit, a while 
back,
with using optim() (with the --- default --- Nelder-Meade simplex algorithm
method) to maximise the profile pseudolikelihood, rather than doing a brute
force grid search.  It seemed be quite a bit faster, but I'm not sure 
I'd trust
it.  The problems you describe (a maximum at a very narrow peak, multiple
local maxima) would be even more vexatious with the optim() approach
than with the grid search approach.

I can send you more detail about how I implemented the optim() approach
if you like, but as I said I don't really trust it.

(f) In respect of grid searches, the interaction radii yielding a maximum of
the pseudolikelihood have to occur at interpoint distances  So you can
(should?) search over grids whose values consist of interpoint distances.
Rather than over regularly spaced grids. This *could* cut down the number
of points over which to search.  And it *could* keep you from missing maxima
which occur at very narrow peaks.  I think.

I am cc-ing this email to Adrian in the hope that he may have other ideas
and suggestions.

         cheers,

             Rolf