R: Global Envelopes for Balanced Independent Two-Stage Test

bits.envelope {spatstat.core} | R Documentation

## Global Envelopes for Balanced Independent Two-Stage Test

### Description

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"`.

### Author(s)

Adrian Baddeley, Andrew Hardegen, Tom Lawrence, Robin Milne, Gopalan Nair and Suman Rakshit. Implemented by Adrian Baddeley Adrian.Baddeley@curtin.edu.au.

### 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

`dg.envelope`, `bits.test`, `mad.test`, `envelope`

### Examples

      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)

[Package spatstat.core version 2.4-4 Index]