exactMPLEstrauss(X, R, ngrid = 2048, plotit = FALSE)"ppp").TRUE, the log pseudolikelihood is plotted
on the current device. It fits the stationary Strauss point process model
to the point pattern dataset X by maximum pseudolikelihood
(with the border edge correction) using an algorithm with very high accuracy.
This algorithm is more accurate than the
default behaviour of the model-fitting function
ppm because the discretisation is much finer.
Ripley (1988) and Baddeley and Turner (2000) derived the
log pseudolikelihood for the stationary Strauss
process, and eliminated the parameter $\beta$,
obtaining an exact formula for the partial log pseudolikelihood
as a function of the interaction parameter $\gamma$ only.
The algorithm evaluates this expression to a high degree of accuracy,
using numerical integration on a ngrid * ngrid lattice,
uses optim to maximise the log pseudolikelihood
with respect to $\gamma$, and finally recovers
$\beta$.
The result is a vector of length 2, containing the fitted coefficients
$\log\beta$ and $\log\gamma$.
These values correspond to the entries that would be obtained with
coef(ppm(X, ~1, Strauss(R))).
The fitted coefficients are typically accurate to within $10^{-6}$ as shown in Baddeley and Turner (2013).
Baddeley, A. and Turner, R. (2013) Manuscript in preparation.
Ripley, B.D. (1988) Statistical inference for spatial processes. Cambridge University Press.
ppmexactMPLEstrauss(cells, 0.1)
coef(ppm(cells, ~1, Strauss(0.1)))
coef(ppm(cells, ~1, Strauss(0.1), nd=128))Run the code above in your browser using DataLab