quadratcount | R Documentation |
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 |
... |
Additional arguments passed to |
xbreaks |
Numeric vector giving the |
ybreaks |
Numeric vector giving the |
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 a quadratcount
object,
the ordering of entries in the table Q
may be different from the ordering of quadrats (tiles
in the tessellation as.tess(Q)
).
To obtain the entries of the table in the same order
as the quadrats, use
counts <- as.numeric(t(Q))
or counts <- marks(as.tess(Q))
.
To perform a chi-squared test based on the quadrat counts,
use quadrat.test
.
and \rolf
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.
plot.quadratcount
,
intensity.quadratcount
,
quadrats
,
quadrat.test
,
tess
,
hextess
,
quadratresample
,
miplot
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
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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