bits.test: Balanced Independent Two-Stage Monte Carlo Test

Description

Performs a Balanced Independent Two-Stage Monte Carlo test of goodness-of-fit for spatial pattern.

Usage

bits.test(X, ...,
        exponent = 2, nsim=19, 
        alternative=c("two.sided", "less", "greater"),
        leaveout=1, interpolate = FALSE,
        savefuns=FALSE, savepatterns=FALSE,
        verbose = TRUE)

Value

A hypothesis test (object of class "htest"

which can be printed to show the outcome of the test.

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", "lppm" or "slrm").
...: Arguments passed to dclf.test or 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 use.theory described under Details.
exponent: 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.
nsim: Number of replicates in each stage of the test. A total of nsim * (nsim + 1) simulated point patterns will be generated, and the \(p\)-value will be a multiple of 1/(nsim+1).
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.
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 indicating whether to print progress reports.

Author

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.

Details

Performs the Balanced Independent Two-Stage Monte Carlo test proposed by Baddeley et al (2017), an improvement of the Dao-Genton (2014) test.

If X is a point pattern, the null hypothesis is CSR.

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

The argument use.theory passed to envelope determines whether to compare the summary function for the data to its theoretical value for CSR (use.theory=TRUE) or to the sample mean of simulations from CSR (use.theory=FALSE).

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).

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., Diggle, P.J., Hardegen, A., Lawrence, T., Milne, R.K. 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. (2017) On two-stage Monte Carlo tests of composite hypotheses. Computational Statistics and Data Analysis, in press.

Examples

Run this code

 ns <- if(interactive()) 19 else 4
 bits.test(cells, nsim=ns)
 bits.test(cells, alternative="less", nsim=ns)
 bits.test(cells, nsim=ns, interpolate=TRUE)

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