Dear Rolf,



Thank you very much for your very detailed responses, which are helping me to clarify some "muddy" areas of my "knowledge", though I must confess that the mathematical detail scares me a bit.



That the Strauss model with Gamma parameters > 1 could indicate clustering is something that I was suspecting, since the Geyer model (irrespective of marks) already made me think of that possibility in one of the datasets that I am analysing, and I am trying to get rid of the medium-distance clustering before going into modelling interpoint interactions.



Indeed I have had a half-baked question in the drafts folder for days...



I suspect/observe that there is some degree of clustering in the data, and there seems to be at the same time some degree of short distance repulsion among events (either in the same or different classes). Although departures from pointwise or simultaneous confidence bands are not obvious or present at all, the difference between ppm models which include some polynomial of coordinates vs. those that don't is significant.



However, I do not have any external covariate to model the clustering/trend (usually complex variations in density not easy to be captured by polynomials of the coordinates), what would be the best way to proceed? Could I use variation in general density --as captured by kernel density estimation irrespective of marks, as a surrogate of probability of events ocurring in a certain area-- as a covariate? Is this procedure licit or is this silly?



And last, and all the receivers must excuse my verbose e-mails, using project=TRUE in profiling the pseudolikelihood makes the procedure quite slow (compared to calls to the function profilepl without this argument), so I do not know if daring into evaluating a complete set of interpoint distances with project=TRUE.





Sigh^2!









---------------------------------------
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
---------------------------------------

Currently:
National Wildlife Research Center
Environment Canada
Science & Technology
National Wildlife Research Centre
1125 Colonel By Drive, Raven Rd.
Carleton University
Ottawa, Ontario, Canada K1A

0H3

________________________________
De: Rolf Turner [r.turner@auckland.ac.nz]
Enviat el: dissabte, 18 / agost / 2012 02:48
Per a: José M. Blanco Moreno
Cc: r-sig-geo@r-project.org; Adrian.Baddeley@csiro.au
Tema: Re: [R-sig-Geo] Estimating multiStrauss interaction radii --- CORRECTION


I, uh, mis-spoke in respect of the gamma_{ij} with i != j.

On 17/08/12 14:11, "José M. Blanco Moreno" wrote:
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.

    Actually the model is not defined (or at lease it cannot be *guaranteed* to be defined)
    if ANY of the gamma_{ij} are > 1, irrespective of whether i = j.

    The details seem to be complicated.  It appears to me to difficult to demonstrate
    that the relevant integral fails to converge if (e.g. in a 2 type MultiStrauss model)
    gamma_{12} > 1, but one cannot show that it converges either.

    If gamma_{11} = 1 and gamma_{22} = 1, then one *can* show that the integral
    diverges if gamma_{12} > 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?
    You should discard (project) any model with ANY gamma_{ij} > 1.

    In doing your grid search you should probably set project=TRUE in the
    calls to ppm() (by passing the argument project=TRUE in the call to profilepl()).

    As I said in a previous message, projecting (to a valid model) will reduce the
    reported value of the log pseudolikelihood.

    Also please note that getting values of gamma_{ij} that are > 1 *may* indicate
    that a Strauss (MultiStrauss) model is not appropriate, and that there is some
    sort of clustering going on.   I.e. contrary to what I said previously,
    gamma_{ij} > 1 is not necessarily saying there is no interaction between points
    of type i and type j.  It *could* be saying that, but it could also be trying to tell
    you that there *is* interaction, of the clustering sort, which the MultiStrauss process
    is not capable of modelling.

    Sorry for all the confusion.

    Bottom line: Use project=TRUE.

        cheers,

            Rolf

P. S.  What I said about doing the grid search only over interpoint distances was
correct.  In thinking on it a bit more it seems to me that it might be better to take
the midpoints between pairs of these distances, rather than the distances themselves.
I.e. if these distances are r_1, r_2, r_3, ... then grid search over (r_1)/2, (r_1 + r_2)/2,
(r_2 + r_3)/2, ....

Note that if your patterns are at all large then the number of distances to search
over will be very large.  So doing this sort of search will make sure you get the
"true" maximum log pseudolikelihood, but may increase the computational
burden substantially.  (Which is the last thing you want.  Psigh!!!)

        R.






Aquest correu electrònic i els annexos poden contenir informació confidencial o protegida legalment i està adreçat exclusivament a la persona o entitat destinatària. Si no sou el destinatari final o la persona encarregada de rebre'l, no esteu autoritzat a llegir-lo, retenir-lo, modificar-lo, distribuir-lo, copiar-lo ni a revelar-ne el contingut. Si heu rebut aquest correu electrònic per error, us preguem que n'informeu al remitent i que elimineu del sistema el missatge i el material annex que pugui contenir. Gràcies per la vostra col·laboració.

Este correo electrónico y sus anexos pueden contener información confidencial o legalmente protegida y está exclusivamente dirigido a la persona o entidad destinataria. Si usted no es el destinatario final o la persona encargada de recibirlo, no está autorizado a leerlo, retenerlo, modificarlo, distribuirlo, copiarlo ni a revelar su contenido. Si ha recibido este mensaje electrónico por error, le rogamos que informe al remitente y elimine del sistema el mensaje y el material anexo que pueda contener. Gracias por su colaboración.

This email message and any documents attached to it may contain confidential or legally protected material and are intended solely for the use of the individual or organization to whom they are addressed. We remind you that if you are not the intended recipient of this email message or the person responsible for processing it, then you are not authorized to read, save, modify, send, copy or disclose any of its contents. If you have received this email message by mistake, we kindly ask you to inform the sender of this and to eliminate both the message and any attachments it carries from your account. Thank you for your collaboration.

	[[alternative HTML version deleted]]

