miplot
Morishita Index Plot
Displays the Morishita Index Plot of a spatial point pattern.
- Keywords
- spatial, nonparametric
Usage
miplot(X, ...)Arguments
- X
- A point pattern (object of class
"ppp") or something acceptable toas.ppp. - ...
- Optional arguments to control the appearance of the plot.
Details
Morishita (1959) defined an index of spatial aggregation for a spatial
point pattern based on quadrat counts. The spatial domain of the point
pattern is first divided into $Q$ subsets (quadrats) of equal size and
shape. The numbers of points falling in each quadrat are counted.
Then the Morishita Index is computed as
$$\mbox{MI} = Q \frac{\sum_{i=1}^Q n_i (n_i - 1)}{N(N-1)}$$
where $n_i$ is the number of points falling in the $i$-th
quadrat, and $N$ is the total number of points.
If the pattern is completely random, MI should be approximately
equal to 1. Values of MI greater than 1 suggest clustering.
The Morishita Index plot is a plot of the Morishita Index
MI against the linear dimension of the quadrats.
The point pattern dataset is divided into $2 \times 2$
quadrats, then $3 \times 3$ quadrats, etc, and the
Morishita Index is computed each time. This plot is an attempt to
discern different scales of dependence in the point pattern data.
Value
- None.
References
M. Morishita (1959) Measuring of the dispersion of individuals and analysis of the distributional patterns. Memoir of the Faculty of Science, Series E2, Kyushu University. Pages 215--235.
See Also
Examples
data(longleaf)
miplot(longleaf)
opa <- par(mfrow=c(2,3))
data(cells)
data(japanesepines)
data(redwood)
plot(cells)
plot(japanesepines)
plot(redwood)
miplot(cells)
miplot(japanesepines)
miplot(redwood)
par(opa)