Quadrat counting for a point pattern
Divides window into quadrats and counts the numbers of points in each quadrat.
quadratcount(X, ...)
## S3 method for class 'ppp'
quadratcount(X, nx=5, ny=nx, ...,
xbreaks=NULL, ybreaks=NULL, tess=NULL)
## S3 method for class 'splitppp'
quadratcount(X, ...)X |
A point pattern (object of class |
nx,ny |
Numbers of rectangular quadrats in the x and y directions.
Incompatible with |
... |
Additional arguments passed to |
xbreaks |
Numeric vector giving the x coordinates of the
boundaries of the rectangular quadrats. Incompatible with |
ybreaks |
Numeric vector giving the y coordinates of the
boundaries of the rectangular quadrats. Incompatible with |
tess |
Tessellation (object of class |
Quadrat counting is an elementary technique for analysing spatial point patterns. See Diggle (2003).
If X is a point pattern, then
by default, the window containing the point pattern X is divided into
an nx * ny grid of rectangular tiles or ‘quadrats’.
(If the window is not a rectangle, then these tiles are intersected
with the window.)
The number of points of X falling in each quadrat is
counted. These numbers are returned as a contingency table.
If xbreaks is given, it should be a numeric vector
giving the x coordinates of the quadrat boundaries.
If it is not given, it defaults to a
sequence of nx+1 values equally spaced
over the range of x coordinates in the window Window(X).
Similarly if ybreaks is given, it should be a numeric
vector giving the y coordinates of the quadrat boundaries.
It defaults to a vector of ny+1 values
equally spaced over the range of y coordinates in the window.
The lengths of xbreaks and ybreaks may be different.
Alternatively, quadrats of any shape may be used.
The argument tess can be a tessellation (object of class
"tess") whose tiles will serve as the quadrats.
The algorithm counts the number of points of X
falling in each quadrat, and returns these counts as a
contingency table.
The return value is a table which can be printed neatly.
The return value is also a member of the special class
"quadratcount". Plotting the object will display the
quadrats, annotated by their counts. See the examples.
To perform a chi-squared test based on the quadrat counts,
use quadrat.test.
To calculate an estimate of intensity based on the quadrat counts,
use intensity.quadratcount.
To extract the quadrats used in a quadratcount object,
use as.tess.
If X is a split point pattern (object of class
"splitppp" then quadrat counting will be performed on
each of the components point patterns, and the resulting
contingency tables will be returned in a list. This list can be
printed or plotted.
Marks attached to the points are ignored by quadratcount.ppp.
To obtain a separate contingency table for each type of point
in a multitype point pattern,
first separate the different points using split.ppp,
then apply quadratcount.splitppp. See the Examples.
The value of quadratcount.ppp is a
contingency table containing the number of points in each
quadrat. The table is also an object of the
special class "quadratcount"
and there is a plot method for this class.
The value of quadratcount.splitppp is a list of such
contingency tables, each containing the quadrat counts for one of the
component point patterns in X.
This list also has the class "solist" which has
print and plot methods.
If Q is the result of quadratcount
using rectangular tiles, then as.numeric(Q)
extracts the counts in the wrong order.
To obtain the quadrat counts in the same order as the
tiles of the corresponding tessellation would be listed,
use as.vector(t(Q)), which works in all cases.
To perform a chi-squared test based on the quadrat counts,
use quadrat.test.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
and Rolf Turner r.turner@auckland.ac.nz
Diggle, P.J. Statistical analysis of spatial point patterns. Academic Press, 2003.
Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point fields: methods of geometrical statistics. John Wiley and Sons.
X <- runifrect(50) quadratcount(X) quadratcount(X, 4, 5) quadratcount(X, xbreaks=c(0, 0.3, 1), ybreaks=c(0, 0.4, 0.8, 1)) qX <- quadratcount(X, 4, 5) # plotting: plot(X, pch="+") plot(qX, add=TRUE, col="red", cex=1.5, lty=2) # irregular window data(humberside) plot(humberside) qH <- quadratcount(humberside, 2, 3) plot(qH, add=TRUE, col="blue", cex=1.5, lwd=2) # multitype - split plot(quadratcount(split(humberside), 2, 3)) # quadrats determined by tessellation: B <- dirichlet(runifrect(6)) qX <- quadratcount(X, tess=B) plot(X, pch="+") plot(qX, add=TRUE, col="red", cex=1.5, lty=2)
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