# dg.sigtrace

##### Significance Trace of Dao-Genton Test

Generates a Significance Trace of the Dao and Genton (2014) test for a spatial point pattern.

##### Usage

```
dg.sigtrace(X, fun = Lest, …,
exponent = 2, nsim = 19, nsimsub = nsim - 1,
alternative = c("two.sided", "less", "greater"),
rmin=0, leaveout=1,
interpolate = FALSE, confint = TRUE, alpha = 0.05,
savefuns=FALSE, savepatterns=FALSE, verbose=FALSE)
```

##### 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"`

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

- …
Arguments passed to

`envelope`

.- exponent
Positive number. Exponent used in the test statistic. Use

`exponent=2`

for the Diggle-Cressie-Loosmore-Ford test, and`exponent=Inf`

for the Maximum Absolute Deviation test. 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.- alternative
Character string specifying the alternative hypothesis. The default (

`alternative="two.sided"`

) is that the true value of the summary function is not equal to the theoretical value postulated under the null hypothesis. If`alternative="less"`

the alternative hypothesis is that the true value of the summary function is lower than the theoretical value.- rmin
Optional. Left endpoint for the interval of \(r\) values on which the test statistic is calculated.

- 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 whether to interpolate the distribution of the test statistic by kernel smoothing, as described in Dao and Genton (2014, Section 5).

- confint
Logical value indicating whether to compute a confidence interval for the ‘true’ \(p\)-value.

- alpha
Significance level to be plotted (this has no effect on the calculation but is simply plotted as a reference value).

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

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

- verbose
Logical flag indicating whether to print progress reports.

##### Details

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 *significance trace* (Bowman and Azzalini, 1997;
Baddeley et al, 2014, 2015)
of the test is a plot of the \(p\)-value
obtained from the test against the length of
the interval `rinterval`

.

The command `dg.sigtrace`

effectively performs
`dg.test`

on `X`

using all possible intervals
of the form \([0,R]\), and returns the resulting \(p\)-values
as a function of \(R\).

The result is an object of class `"fv"`

that can be plotted to
obtain the significance trace. The plot shows the
Dao-Genton adjusted
\(p\)-value (solid black line),
the critical value `0.05`

(dashed red line),
and a pointwise 95% confidence band (grey shading)
for the ‘true’ (Neyman-Pearson) \(p\)-value.
The confidence band is based on the Agresti-Coull (1998)
confidence interval for a binomial proportion.

If `X`

is an envelope object and `fun=NULL`

then
the code will re-use the simulated functions stored in `X`

.

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).

##### Value

An object of class `"fv"`

that can be plotted to
obtain the significance trace.

##### References

Agresti, A. and Coull, B.A. (1998)
Approximate is better than “Exact” for interval
estimation of binomial proportions.
*American Statistician* **52**, 119--126.

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. Submitted for publication.

Bowman, A.W. and Azzalini, A. (1997)
*Applied smoothing techniques for data analysis:
the kernel approach with S-Plus illustrations*.
Oxford University Press, Oxford.

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.

##### See Also

`dg.test`

for the Dao-Genton test,
`dclf.sigtrace`

for significance traces of other tests.

##### Examples

```
# NOT RUN {
ns <- if(interactive()) 19 else 5
plot(dg.sigtrace(cells, nsim=ns))
# }
```

*Documentation reproduced from package spatstat, version 1.55-1, License: GPL (>= 2)*