# bits.envelope

##### Global Envelopes for Balanced Independent Two-Stage Test

Computes the global envelopes corresponding to the balanced independent two-stage Monte Carlo test of goodness-of-fit.

##### Usage

```
bits.envelope(X, …,
nsim = 19, nrank = 1,
alternative=c("two.sided", "less", "greater"),
leaveout=1, interpolate = FALSE,
savefuns=FALSE, savepatterns=FALSE,
verbose = TRUE)
```

##### Arguments

- X
Either a point pattern dataset (object of class

`"ppp"`

,`"lpp"`

or`"pp3"`

) or a fitted point process model (object of class`"ppm"`

,`"kppm"`

or`"slrm"`

).- …
Arguments passed to

`mad.test`

or`envelope`

to control the conduct of the test. Useful arguments include`fun`

to determine the summary function,`rinterval`

to determine the range of \(r\) values used in the test, and`verbose=FALSE`

to turn off the messages.- nsim
Number of simulated patterns to be generated in each stage. Number of simulations in each basic test. There will be

`nsim`

repetitions of the basic test, each involving`nsim`

simulated realisations, together with one independent set of`nsim`

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

simulations.- nrank
Integer. Rank of the envelope value amongst the

`nsim`

simulated values. A rank of 1 means that the minimum and maximum simulated values will be used.- alternative
Character string determining whether the envelope corresponds to a two-sided test (

`alternative="two.sided"`

, the default) or a one-sided test with a lower critical boundary (`alternative="less"`

) or a one-sided test with an upper critical boundary (`alternative="greater"`

).- 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).

- 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 value determining whether to print progress reports.

##### Details

Computes global simulation envelopes corresponding to the balanced independent two-stage Monte Carlo test of goodness-of-fit described by Baddeley et al (2017). The envelopes are described in Baddeley et al (2019).

If `X`

is a point pattern, the null hypothesis is CSR.

If `X`

is a fitted model, the null hypothesis is that model.

This command is similar to `dg.envelope`

which corresponds
to the Dao-Genton test of goodness-of-fit.
It was shown in Baddeley et al (2017) that
the Dao-Genton test is biased when the significance level is very small
(small \(p\)-values are not reliable) and
we recommend `bits.envelope`

in this case.

##### Value

An object of class `"fv"`

.

##### References

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.

Baddeley, A., Hardegen, A., Lawrence, T.,
Milne, R.K., Nair, G. and Rakshit, S. (2017)
On two-stage Monte Carlo tests of composite
hypotheses. *Computational Statistics and Data Analysis*
**114**, 75--87.

Baddeley, A., Hardegen, A., Lawrence, L., Milne, R.K., Nair, G.M. and Rakshit, S. (2019) Pushing the envelope: extensions of graphical Monte Carlo tests. In preparation.

##### See Also

##### Examples

```
# NOT RUN {
ns <- if(interactive()) 19 else 4
E <- bits.envelope(swedishpines, Lest, nsim=ns)
E
plot(E)
Eo <- bits.envelope(swedishpines, Lest, alternative="less", nsim=ns)
Ei <- bits.envelope(swedishpines, Lest, interpolate=TRUE, nsim=ns)
# }
```

*Documentation reproduced from package spatstat, version 1.61-0, License: GPL (>= 2)*