
374 Spatial Point Patterns: Methodology and Applications with R
10.3.3 Wald test for single parameter
The Wald test of H
0
:
ϕ
= 0 for a one-dimensional parameter
ϕ
is based on the statistic
V =
b
ϕ
se(
ˆ
ϕ
)
(10.2)
where
b
ϕ
is the maximum likelihood estimate of
ϕ
under the alternative hypothesis H
1
, and se(
ˆ
ϕ
) is
the plug-in estimate of standard error of
b
ϕ
. The asymptotic null distribution of V is standard normal.
The likelihood ratio test is asymptotically equivalent to the Wald te st, under regularity conditions.
For a loglinear Poisson point process model fitted by ppm, the Wald test for each coefficient is
performed as part of the print metho d. It can be recovered ...