
446 Spatial Point Patterns: Methodology and Applications with R
Influence for Poisson point process models
The influence of a point process model is effectively a value attached to each data point (i.e. each
point of the po int pattern to whic h the model was fitted) . It is a discrete measu re on the data points
x
i
with masses
m
i
=
1
p
Z(x
i
)I
ˆ
θ
−1
Z(x
i
)
T
. (11.44)
The influence value m
i
at data point x
i
represents the change in the maximised log-likelihood that
occurs whe n the point x
i
is deleted. A relatively large value of m
i
indicates a data point with a large
influence on the fitted model.
Since the influence measure turns out to be a n atomic measure on the data ...