quadratcount
Quadrat counting for a point pattern
Divides window into quadrats and counts the numbers of points in each quadrat.
Usage
quadratcount(X, nx=5, ny=nx, xbreaks, ybreaks)
Arguments
- X
- A point pattern
(object of class
"ppp"
). - nx,ny
- Numbers of quadrats in the $x$ and $y$ directions.
Incompatible with
xbreaks
andybreaks
. - xbreaks
- Numeric vector giving the $x$ coordinates of the
boundaries of the quadrats. Incompatible with
nx
. - ybreaks
- Numeric vector giving the $y$ coordinates of the
boundaries of the quadrats. Incompatible with
ny
.
Details
Quadrat counting is an elementary technique for analysing spatial
point patterns. See Diggle (2003).
The window containing the point pattern X
is divided into
an nx * ny
grid of rectangular tiles or `quadrats'.
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 X$window
.
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.
The algorithm counts the number of points of X
falling in each quadrat, and returns these counts as a
contingency table. The [i,j]
entry in the contingency table
is the point count for the quadrat with coordinates
(xbreaks[i],xbreaks[i+1])
by (ybreaks[i], ybreaks[i+1])
.
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
.
Value
- 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.
References
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.
See Also
Examples
X <- runifpoint(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)