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

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

An object of class `"fv"`

that can be plotted to
obtain the progress plot.

- 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.

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

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

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 \(p\)th root of the integral of
the \(p\)th 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 \([r_{\mbox{\scriptsize min}},R]\)
where \(R \ge r_{\mbox{\scriptsize min}}\).

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`

.

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.

`dclf.test`

and
`mad.test`

for the tests.

See `plot.fv`

for information on plotting
objects of class `"fv"`

.

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

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