[R-sig-Geo] How to estimate LGCP parameters for replicated point pattern

[Rolf Turner]

Good question!  (And very clearly expressed.)  I think that the answer 
to "Is there
any way ....?" is currently "no".  We have mppm() which will fit a model 
to independent
replicate patterns assumed to arise from a ***Gibbs*** model, but this 
function
does not work for models arising from clustering mechanisms, which get 
fitted via
the method of minimum contrast.  (Using, as you have noted, kppm().)

I'm not sure how hard (or easy!) it would be to add such a facility.  I 
would guess
not ***too*** hard, but my guesses have sometimes been known to be horribly
wrong.  Adrian B., to whom I am cc-ing this message, will know off the 
top of his
head.  In any event I think a substantial amount of effort would be 
required to
add this facility, and it would take time.

     cheers,

     Rolf Turner

On 16/12/13 22:01, hugues Santin-Janin wrote:
> Dear all,
>
>   
>
> Let P1, P2 and P3 to be 3 realizations of a Log Gaussian Cox Process, say:
>
>   
>
> #Setting parameter values
>
> sigma2 <- 1
>
> kappa <- 1
>
> beta0 <-  3
>
> beta1 <-  4.5
>
> beta2 <- -1.5
>
> beta3 <- 2.5
>
>   
>
> ## spatstat_1.33-0
>
> ##R  3.0.1
>
> library(spatstat)
>
>   
>
> m <- as.im(function(x, y){beta0 + beta1 * x + beta2 * (x^2) + beta3 * y},
> W=owin())
>
>   
>
> #Generating replicated point patterns
>
> set.seed(1)
>
> P1 <- rLGCP("matern", m, c(0, variance=sigma2, nugget=0, scale=1/kappa,
> nu=1))
>
> set.seed(2)
>
> P2 <- rLGCP("matern", m, c(0, variance=sigma2, nugget=0, scale=1/kappa,
> nu=1))
>
> set.seed(3)
>
> P3 <- rLGCP("matern", m, c(0, variance=sigma2, nugget=0, scale=1/kappa,
> nu=1))
>
>   
>
>   
>
> Considering either replicate P1, P2 or P3, estimates of the parameters
> beta0, beta1, beta2, eta3, sigma2 and kappa can be obtained using the kppm
> function:
>
>   
>
> Q1 <- quadscheme(P1)
>
> Est1 <- kppm(Q1, trend=~polynom(x, 2) + y, cluster= "LGCP", method="clik",
> covmodel=list(model="matern", nu=1))
>
>   
>
> Is is possible (and if yes how) to use the kppm function, or any other R
> function,  to estimate the parameters beta0, beta1, beta2, beta3, sigma2 and
> kappa based on the whole dataset (i.e., using the three replicates P1, P2
> and P3) ?