spatstat (version 1.60-1)

bits.envelope: 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.

Value

An object of class "fv".

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.

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

# 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)
# }