
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.





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