
Patterns of Several Types of Points 591
where I
θ
is the Fisher information matrix and
P(u,m) = p(m | u)
h
Z(u,m) −
∑
m
′
Z(u,m
′
)p(m
′
| u)
i
R(u,m) = r(m | u)[Z(u,m) −Z(u,m
0
)].
These calculations are performed by relrisk.ppm, the method for the generic relrisk for fitted
Poisson or Gibbs point process models. For example, for the gastric m ucosa data (Figure 14 .1 on
page 561), we might consider the model
> fit <- ppm(mucosa
~
marks * polynom(x,y,3))
Then the sp a tially varying probabilities of each type are computed by
> probs <- relrisk(fit, casecontrol=FALSE)
Figure 14.15 shows the estimated proportion of ECL cells. The spatially varying relative ‘risk’ of
ECL ...