Generates a progress plot (envelope representation) of the Dao-Genton test for a spatial point pattern.

```
dg.progress(X, fun = Lest, ...,
exponent = 2, nsim = 19, nsimsub = nsim - 1,
nrank = 1, alpha, leaveout=1, interpolate = FALSE, rmin=0,
savefuns = FALSE, savepatterns = FALSE, verbose=TRUE)
```

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"`

).- fun
Function that computes the desired summary statistic for a point pattern.

- ...
Arguments passed to

`envelope`

. Useful arguments include`alternative`

to specify one-sided or two-sided envelopes.- exponent
Positive number. The exponent of the \(L^p\) distance. See Details.

- nsim
Number of repetitions of the basic test.

- nsimsub
Number of simulations in each basic test. There will be

`nsim`

repetitions of the basic test, each involving`nsimsub`

simulated realisations, so there will be a total of`nsim * (nsimsub + 1)`

simulations.- 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.- alpha
Optional. The significance level of the test. Equivalent to

`nrank/(nsim+1)`

where`nsim`

is the number of simulations.- leaveout
Optional integer 0, 1 or 2 indicating how to calculate the deviation between the observed summary function and the nominal reference value, when the reference value must be estimated by simulation. See Details.

- 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.- rmin
Optional. Left endpoint for the interval of \(r\) values on which the test statistic is calculated.

- savefuns
Logical value indicating whether to save the simulated function values (from the first stage).

- savepatterns
Logical value indicating whether to save the simulated point patterns (from the first stage).

- verbose
Logical value indicating whether to print progress reports.

Adrian Baddeley, Andrew Hardegen, Tom Lawrence, Robin Milne, Gopalan Nair and Suman Rakshit. Implemented by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner r.turner@auckland.ac.nz and Ege Rubak rubak@math.aau.dk.

The Dao and Genton (2014) test for a spatial point pattern
is described in `dg.test`

.
This test depends 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, 2015; Baddeley, Rubak and Turner, 2015) is a plot of the
test statistic (and the corresponding critical value) against the length of
the interval `rinterval`

.

The command `dg.progress`

effectively performs
`dg.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 \(R\).

The result 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 test
acceptance region (grey shading).
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`

.

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 argument `leaveout`

specifies how to calculate the
discrepancy between the summary function for the data and the
nominal reference value, when the reference value must be estimated
by simulation. The values `leaveout=0`

and
`leaveout=1`

are both algebraically equivalent (Baddeley et al, 2014,
Appendix) to computing the difference `observed - reference`

where the `reference`

is the mean of simulated values.
The value `leaveout=2`

gives the leave-two-out discrepancy
proposed by Dao and Genton (2014).

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.

Baddeley, A., Hardegen, A., Lawrence, L., Milne, R.K., Nair, G.M. and Rakshit, S. (2015) Pushing the envelope: extensions of graphical Monte Carlo tests. Unpublished manuscript.

Baddeley, A., Rubak, E. and Turner, R. (2015) *Spatial Point Patterns: Methodology and Applications with R*. Chapman and Hall/CRC Press.

Dao, N.A. and Genton, M. (2014)
A Monte Carlo adjusted goodness-of-fit test for
parametric models describing spatial point patterns.
*Journal of Graphical and Computational Statistics*
**23**, 497--517.

`dg.test`

,
`dclf.progress`

```
ns <- if(interactive()) 19 else 5
plot(dg.progress(cells, nsim=ns))
```

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