Analysing spatial point patterns in R - CSIRO

170 Fitting Gibbs models
ppm(simdat, ~1, interaction = Strauss)
log PL
−17.5 −16.5 −15.5 −14.5
0.0 0.5 1.0 1.5 2.0
To extract the final fitted model,
> pfit$fit
Stationary Strauss process
First order term:
beta
2.583110
Interaction: Strauss process
interaction distance: 0.275
Fitted interaction parameter gamma: 0.5631
Relevant coefficients:
Interaction
-0.5743608
There is a summary method for these objects as well.
27.7 Improvements over maximum pseudolikelihood
r
Maximum pseudolikelihood is quick and dirty. There are statistically more efficient alternatives,
but they are computationally intensive.
Currently we have implemented the easiest of these alternatives, the Huang-Ogata [43] onestep
approximation to maximum likelihood. Starting from the maximum pseudolikelihood estimate
ˆθ PL , we simulate M independent realisations of the model with parameters ˆθ PL , evaluate
the canonical sufficient statistics, and use them to form estimates of the score and Fisher information
at θ = ˆθ PL . Then we take one Newton-Raphson step, updating the value of θ.
The rationale is that the log-likelihood is approximately quadratic in a neighbourhood of the
maximum pseudolikelihood estimator, so that one Newton-Raphson step is almost enough.
To use the Huang-Ogata method instead of maximum pseudolikelihood, add the argument
method="ho".
> fit fit
CopyrightCSIRO 2010