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
xbreaksandybreaks. - 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)