| quadrat.test {spatstat} | R Documentation |
Performs a chi-squared test of Complete Spatial Randomness for a given point pattern, based on quadrat counts. Alternatively performs a chi-squared goodness-of-fit test of a fitted inhomogeneous Poisson model.
quadrat.test(X, ...) ## S3 method for class 'ppp': quadrat.test(X, nx=5, ny=nx, xbreaks=NULL, ybreaks=NULL, ...) ## S3 method for class 'ppm': quadrat.test(X, nx=5, ny=nx, xbreaks=NULL, ybreaks=NULL, ...)
X |
A point pattern (object of class "ppp")
to be subjected to the goodness-of-fit test.
Alternatively a fitted point process model (object of class
"ppm") to be tested.
|
nx,ny |
Numbers of quadrats in the x and y directions.
Incompatible with xbreaks and ybreaks.
|
xbreaks |
Optional. Numeric vector giving the x coordinates of the
boundaries of the quadrats. Incompatible with nx.
|
ybreaks |
Optional. Numeric vector giving the y coordinates of the
boundaries of the quadrats. Incompatible with ny.
|
... |
Ignored. |
These functions perform chi^2 tests of goodness-of-fit for a point process model, based on quadrat counts.
The function quadrat.test is generic, with methods for
point patterns (class "ppp") and point process models
(class "ppm").
X is a point pattern, we test the null hypothesis
that the data pattern is a realisation of Complete Spatial
Randomness (the uniform Poisson point process).
X is a fitted point process model, then it should be
a Poisson point process model. The
data to which this model was fitted are extracted from the model
object, and are treated as the data point pattern for the test.
We test the null hypothesis
that the data pattern is a realisation of the (inhomogeneous) Poisson point
process specified by X.
In both cases, the window of observation is divided
into rectangular tiles, and the number of data points in each tile is
counted, as described in quadratcount.
The expected number of points in each quadrat is also calculated,
as determined by CSR (in the first case) or by the fitted model
(in the second case). Then we perform the
chi^2 test of goodness-of-fit to the quadrat counts.
The return value is an object of class "htest".
Printing the object gives comprehensible output
about the outcome of the test.
The return value also belongs to
the special class "quadrat.test". Plotting the object
will display the quadrats, annotated by their observed and expected
counts and the Pearson residuals. See the examples.
An object of class "htest". See chisq.test
for explanation.
The return value is also an object of the special class
"quadrat.test", and there is a plot method for this class.
See the examples.
Adrian Baddeley adrian@maths.uwa.edu.au http://www.maths.uwa.edu.au/~adrian/ and Rolf Turner rolf@math.unb.ca http://www.math.unb.ca/~rolf
quadratcount,
chisq.test,
ks.test.ppm.
To test a Poisson point process model against a specific alternative,
use anova.ppm.
data(simdat)
quadrat.test(simdat)
quadrat.test(simdat, 4)
# fitted model: inhomogeneous Poisson
fitx <- ppm(simdat, ~x, Poisson())
quadrat.test(fitx)
te <- quadrat.test(simdat, 4)
residuals(te) # Pearson residuals
plot(te)
plot(simdat, pch="+", col="green", cex=1.2, lwd=2)
plot(te, add=TRUE, col="red", cex=1.5, lty=2, lwd=3)
sublab <- eval(substitute(expression(p[chi^2]==z),
list(z=signif(te$p.value,3))))
title(sub=sublab, cex.sub=3)