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Percentile

##### Quadrat counting for a point pattern

Divides window into quadrats and counts the numbers of points in each quadrat.

Keywords
spatial, math
##### Usage
quadratcount(X, …)  # S3 method for ppp
quadratcount(X, nx=5, ny=nx, …,
xbreaks=NULL, ybreaks=NULL, tess=NULL)  # S3 method for splitppp
quadratcount(X, …)
##### Arguments
X

A point pattern (object of class "ppp") or a split point pattern (object of class "splitppp").

nx,ny

Numbers of rectangular quadrats in the $x$ and $y$ directions. Incompatible with xbreaks and ybreaks.

Additional arguments passed to quadratcount.ppp.

xbreaks

Numeric vector giving the $x$ coordinates of the boundaries of the rectangular quadrats. Incompatible with nx.

ybreaks

Numeric vector giving the $y$ coordinates of the boundaries of the rectangular quadrats. Incompatible with ny.

tess

Tessellation (object of class "tess" or something acceptable to as.tess) determining the quadrats. Incompatible with nx,ny,xbreaks,ybreaks.

##### Details

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.

##### Value

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.

##### Note

To perform a chi-squared test based on the quadrat counts, use quadrat.test.

##### Warning

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.

##### 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.

plot.quadratcount, intensity.quadratcount, quadrats, quadrat.test, tess, hextess, quadratresample, miplot

##### Examples
# NOT RUN {
X <- runifpoint(50)
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
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