quadrat.test
Chi-Squared Dispersion Test for Spatial Point Pattern Based on Quadrat Counts
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.
Usage
quadrat.test(X, nx = 5, ny = nx, xbreaks = NULL, ybreaks = NULL, fit)
Arguments
- 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
andybreaks
. - 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
. - fit
- Optional. A fitted point process model (object of class
"ppm"
). The point patternX
will be subjected to a test of goodness-of-fit to the modelfit
.
Details
This function performs a $\chi^2$ test of goodness-of-fit
to the Poisson point process (including
If X
is a point pattern, it is taken as the data point pattern
for the test. If X
is a fitted point process model, then 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.
The window of observation is divided into rectangular tiles
and the number of data points in each tile is counted,
as described in quadratcount
.
If fit
is absent, then we test the null hypothesis
that the data pattern is a realisation of Complete Spatial
Randomness (the uniform Poisson point process) by applying the
$\chi^2$ test of goodness-of-fit to the quadrat counts.
If fit
is present, then it should be a point process model
(object of class "ppm"
) and it should be a Poisson point
process. Then we test the null hypothesis
that the data pattern is a realisation of the (inhomogeneous) Poisson point
process specified by fit
. Again this is a
$\chi^2$ 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.
To test the Poisson point process against a specific alternative
point process model, use anova.ppm
.
Value
- An object of class
"htest"
. Seechisq.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.
See Also
Examples
data(simdat)
quadrat.test(simdat)
quadrat.test(simdat, 4)
# fitted model: inhomogeneous Poisson
fitx <- ppm(simdat, ~x, Poisson())
# equivalent:
quadrat.test(simdat, fit=fitx)
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)