rank_envelope {GET}

The rank envelope test

Description

The rank envelope test, p-values and global envelopes. The test corresponds to the global envelope test that can be carriet out by global_envelope_test by specifying the type for which the options "rank", "erl", "cont" and "area" are available. The last three are modifications of the first one to treat the ties in the extreme rank ordering used in "rank". This function is kept for historical reasons.

Usage

rank_envelope(curve_set, type = "rank", ...)

Arguments

curve_set

A curve_set object, or an envelope object of spatstat. If an envelope object is given, it must contain the summary functions from the simulated patterns which can be achieved by setting savefuns = TRUE when calling the function of spatstat.

type

The type of the global envelope with current options for "rank", "erl", "cont" and "area". If "rank", the global rank envelope accompanied by the p-interval is given (Myllymäki et al., 2017). If "erl", the global rank envelope based on extreme rank lengths accompanied by the extreme rank length p-value is given (Myllymäki et al., 2017, Mrkvička et al., 2018). See details and additional sections thereafter.

...

Additional parameters to be passed to global_envelope_test.

Details

The "rank" envelope test is a completely non-parametric test, which provides the 100(1-alpha)% global envelope for the chosen test function T(r) on the chosen interval of distances and associated p-values. The other three types are solutions to break the ties in the extreme ranks on which the "rank" envelope test is based on.

Note: The method to break ties for the global type = "rank" envelope (Myllymäki et al., 2017) can be done by the argument ties with default to ties = "erl" corresponding to the extreme rank length breaking of ties. In this case the global envelope corresponds to the extreme rank measure. If instead choosing type to be "erl", "cont" or "area", then the global envelope corresponds to these measures.

Value

An object of class global_envelope of combined_global_envelope which can be printed and plotted directly. See global_envelope_test for more details.

Number of simulations

The global "erl", "cont", "area" envelope tests allow in principle a lower number of simulations to be used than the global "rank" test based on extreme ranks. However, if feasible, we recommend some thousands of simulations in any case to achieve a good power and repeatability of the test. For the global "rank" envelope test, Myllymäki et al. (2017) recommended to use at least 2500 simulations for testing at the significance level alpha = 0.05 for single function tests, experimented with summary functions for point processes.

References

Myllymäki, M., Mrkvička, T., Grabarnik, P., Seijo, H. and Hahn, U. (2017). Global envelope tests for spatial point patterns. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 79: 381–404. doi: 10.1111/rssb.12172

Mrkvička, T., Myllymäki, M. and Hahn, U. (2017). Multiple Monte Carlo testing, with applications in spatial point processes. Statistics & Computing 27 (5): 1239-1255. doi: 10.1007/s11222-016-9683-9

Mrkvička, T., Myllymäki, M., Jilek, M. and Hahn, U. (2020) A one-way ANOVA test for functional data with graphical interpretation. Kybernetika 56 (3), 432-458. doi: 10.14736/kyb-2020-3-0432

See Also

global_envelope_test

Examples

# See ?global_envelope_test for more examples

## Testing complete spatial randomness (CSR)
#-------------------------------------------
if(require("spatstat.explore", quietly=TRUE)) {
  X <- unmark(spruces)
  nsim <- 2499 # Number of simulations
  
  # Generate nsim simulations under CSR, calculate centred L-function for the data and simulations
  env <- envelope(X, fun="Lest", nsim=nsim, savefuns=TRUE,
                  correction="translate", transform=expression(.-r),
                  simulate=expression(runifpoint(ex=X)))
  # The rank envelope test
  res <- rank_envelope(env)
  # Plot the result.
  plot(res)

  ## Advanced use:
  # Choose the interval of distances [r_min, r_max] (at the same time create a curve_set from 'env')
  curve_set <- crop_curves(env, r_min=1, r_max=7)
  # Do the rank envelope test
  res <- rank_envelope(curve_set); plot(res)
}