Thank you Rolf for your very detailed response. As you said, these lists are "bloody amazing", and the people who participate actively much more (I mean, those giving advice, not so much for those of us who can, at most, pose partially interesting questions).
Points a & b understood.

(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.
So if I understand it properly, I can discard any model fitting any gamma_{ii} > 1. However, that seems to be happening to me/my data quite often. If it is not asking too much, should I take it as an indication of what? Recalcitrant data, improperly chosen model, any of the previous?


(d) I have no idea how to handle the problem of getting two local maxima
which are widely separated (and of similar heights, presumably).
Yes, I did not make the point clear enough. Since they are about the same height, changing the grid a bit can indicate one or the other, depending on "alignment". But I wasn't aware (or I did not remember) that they have to accour at interpoint distances (likely that I haven't read enough), so I will check again.

  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.)
OK, so two pessimists on board... perhaps too much for my problem.


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.
Just after sending the e-mail I experimented with optim, but not too much. Anyway, the "preliminary results" were simply discouraging, but yes, I would like to know how you did, because my force brute approach using optim did not work, plainly, it sucks.

Thank you *very much* for the advice. I will try again when I'm back in office on Tuesday.

Cheers,

José M.



--
---------------------------------------
José M. Blanco-Moreno
Dept. de Biologia Vegetal (Botànica)
Facultat de Biologia
Universitat de Barcelona
Av. Diagonal 643
08028 Barcelona
SPAIN
---------------------------------------
phone: (+34) 934 039 863
fax: (+34) 934 112 842
---------------------------------------


The great enemy of clear language is
insincerity. -George Orwell, writer (1903-1950)



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