Analysing spatial point patterns in R - CSIRO

4.7 Models 25
E
K(r)
0 500 1000 1500 2000
obs
theo
hi
lo
0 5 10 15 20
r (one unit = 0.1 metres)
4.7 Models
The main strength of spatstat is that it supports statistical models of point patterns. Models
can be fitted to point pattern data; the fitted models can be used to summarise the data or
make predictions; the fitted models can be simulated (i.e. a random pattern can be generated
according to the model); and there are facilities for model selection, for testing whether a term in
the model is required (like analysis of variance), and for model criticism (like residuals, regression
diagnostics, and goodness-of-fit tests).
Participants in this workshop often say “I’m not interested in modelling my data; I only
want to analyse it.” However, any kind of data analysis or data manipulation is equivalent to
imposing assumptions. We can’t say something is ‘statistically significant’ unless we assume a
model, because the p-value is the probability according to a model. The purpose of statistical
modelling is to make these assumptions or hypotheses explicit. By doing so, we are able to
determine the best and most powerful way to analyse data, we can subject the assumptions
to criticism, and we are more aware of the potential pitfalls of analysis. In statistical usage, a
model is always tentative; it is assumed for the sake of argument; we might even want it to be
wrong. In the famous words of George Box: “All models are wrong, but some are useful.” If you
only want to do data analysis without statistical models, your results will be less informative
and more vulnerable to critique.
A statistical model for a point pattern is technically termed a point process model. Think of
a point process as a black box that generates a random spatial point pattern according to some
rules. To fit a point process model to a point pattern dataset in spatstat, use the function ppm
(point process model). This is analogous to the standard functions in R for fitting linear models
(lm), generalized linear models (glm) and so on.
> data(swedishpines)
> X fit fit
Stationary Strauss process
First order term:
beta
0.04378316
CopyrightCSIRO 2010