Analysing spatial point patterns in R - CSIRO

15.4 Fitted models 103
effectfun(fit, "slope")
lambda
0.005 0.010 0.015 0.020
0.00 0.05 0.10 0.15 0.20 0.25 0.30
slope
15.4.2 Model selection
Analysis of deviance for nested Poisson point process models is implemented in spatstat as
anova.ppm. The first model should be a sub-model of the second.
> fit fitnull anova(fitnull, fit, test = "Chi")
Analysis of Deviance Table
Model 1: .mpl.Y ~ 1
Model 2: .mpl.Y ~ slope
Resid. Df Resid. Dev Df Deviance P(>|Chi|)
1 20507 18728
2 20506 18346 1 382.25 < 2.2e-16 ***
---
Signif. codes: 0 *** 0.001 ** 0.01 * 0.05 . 0.1 1
This effectively performs the likelihood ratio test of the null hypothesis of a homogeneous
Poisson process (CSR) against the alternative of an inhomogeneous Poisson process with intensity
that is a loglinear function of the slope covariate (6). The p-value is extremely small,
indicating rejection of CSR in favour of the alternative. (Please ignore the columns Resid.Df
and Resid.Dev which are artefacts of the discretisation. Only the deviance difference and the
difference in degrees of freedom are valid.)
Note that standard Analysis of Deviance requires the null hypothesis to be a sub-model of the
alternative. Unfortunately the model (8), in which intensity is proportional to slope, does not
include the homogeneous Poisson process as a special case, so we cannot use analysis of deviance
to test the null hypothesis of homogeneous Poisson against the alternative of an inhomogeneous
Poisson with intensity (8).
One possibility here is to use the Akaike Information Criterion AIC for model selection.
> fitprop fitnull AIC(fitprop)
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