# 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 to`as.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)
```

*Documentation reproduced from package spatstat, version 1.19-1, License: GPL (>= 2)*