R: Progress Plot of Test of Spatial Pattern

dclf.progress {spatstat.core} | R Documentation

## Progress Plot of Test of Spatial Pattern

### Description

Generates a progress plot (envelope representation) of the Diggle-Cressie-Loosmore-Ford test or the Maximum Absolute Deviation test for a spatial point pattern.

### Usage

    dclf.progress(X, ...)
    mad.progress(X, ...)
    mctest.progress(X, fun = Lest, ...,
                    exponent = 1, nrank = 1,
                    interpolate = FALSE, alpha, rmin=0)

### Arguments

`X` | Either a point pattern (object of class `"ppp"`, `"lpp"` or other class), a fitted point process model (object of class `"ppm"`, `"kppm"` or other class) or an envelope object (class `"envelope"`).
`...` | Arguments passed to `mctest.progress` or to `envelope`. Useful arguments include `fun` to determine the summary function, `nsim` to specify the number of Monte Carlo simulations, `alternative` to specify one-sided or two-sided envelopes, and `verbose=FALSE` to turn off the messages.
`fun` | Function that computes the desired summary statistic for a point pattern.
`exponent` | Positive number. The exponent of the L^p distance. See Details.
`nrank` | Integer. The rank of the critical value of the Monte Carlo test, amongst the `nsim` simulated values. A rank of 1 means that the minimum and maximum simulated values will become the critical values for the test.
`interpolate` | Logical value indicating how to compute the critical value. If `interpolate=FALSE` (the default), a standard Monte Carlo test is performed, and the critical value is the largest simulated value of the test statistic (if `nrank=1`) or the `nrank`-th largest (if `nrank` is another number). If `interpolate=TRUE`, kernel density estimation is applied to the simulated values, and the critical value is the upper `alpha` quantile of this estimated distribution.
`alpha` | Optional. The significance level of the test. Equivalent to `nrank/(nsim+1)` where `nsim` is the number of simulations.
`rmin` | Optional. Left endpoint for the interval of r values on which the test statistic is calculated.

### Details

The Diggle-Cressie-Loosmore-Ford test and the Maximum Absolute Deviation test for a spatial point pattern are described in `dclf.test`. These tests depend on the choice of an interval of distance values (the argument `rinterval`). A progress plot or envelope representation of the test (Baddeley et al, 2014) is a plot of the test statistic (and the corresponding critical value) against the length of the interval `rinterval`.

The command `dclf.progress` performs `dclf.test` on `X` using all possible intervals of the form [0,R], and returns the resulting values of the test statistic, and the corresponding critical values of the test, as a function of R.

Similarly `mad.progress` performs `mad.test` using all possible intervals and returns the test statistic and critical value.

More generally, `mctest.progress` performs a test based on the L^p discrepancy between the curves. The deviation between two curves is measured by the pth root of the integral of the pth power of the absolute value of the difference between the two curves. The exponent p is given by the argument `exponent`. The case `exponent=2` is the Cressie-Loosmore-Ford test, while `exponent=Inf` is the MAD test.

If the argument `rmin` is given, it specifies the left endpoint of the interval defining the test statistic: the tests are performed using intervals [rmin,R] where R ≥ rmin.

The result of each command is an object of class `"fv"` that can be plotted to obtain the progress plot. The display shows the test statistic (solid black line) and the Monte Carlo acceptance region (grey shading).

The significance level for the Monte Carlo test is `nrank/(nsim+1)`. Note that `nsim` defaults to 99, so if the values of `nrank` and `nsim` are not given, the default is a test with significance level 0.01.

If `X` is an envelope object, then some of the data stored in `X` may be re-used:

- If `X` is an envelope object containing simulated functions, and `fun=NULL`, then the code will re-use the simulated functions stored in `X`.

- If `X` is an envelope object containing simulated point patterns, then `fun` will be applied to the stored point patterns to obtain the simulated functions. If `fun` is not specified, it defaults to `Lest`.

- Otherwise, new simulations will be performed, and `fun` defaults to `Lest`.

### Value

An object of class `"fv"` that can be plotted to obtain the progress plot.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

, Andrew Hardegen, Tom Lawrence, Gopal Nair and Robin Milne.

### References

Baddeley, A., Diggle, P., Hardegen, A., Lawrence, T., Milne, R. and Nair, G. (2014) On tests of spatial pattern based on simulation envelopes. Ecological Monographs 84 (3) 477–489.

### See Also

`dclf.test` and `mad.test` for the tests.

See `plot.fv` for information on plotting objects of class `"fv"`.

### Examples

      plot(dclf.progress(cells, nsim=19))

[Package spatstat.core version 2.4-4 Index]