GET (version 1.0-5)

qdir_envelope: Global scaled maximum absolute difference (MAD) envelope tests

Description

Performs the global scaled MAD envelope tests, either directional quantile or studentised, or the unscaled MAD envelope test. These tests correspond to calling the function global_envelope_test with type="qdir", type = "st" and type="unscaled", respectively. The functions qdir_envelope, st_envelope and unscaled_envelope have been kept for historical reasons; preferably use global_envelope_test with the suitable type argument.

Usage

qdir_envelope(curve_set, ...)
st_envelope(curve_set, ...)
unscaled_envelope(curve_set, ...)

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.

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.

...

Additional parameters to be passed to global_envelope_test.

Details

The directional quantile envelope test (Myllymäki et al., 2015, 2017) takes into account the unequal variances of the test function T(r) for different distances r and is also protected against asymmetry of T(r).

The studentised envelope test (Myllymäki et al., 2015, 2017) takes into account the unequal variances of the test function T(r) for different distances r.

The unscaled envelope test (Ripley, 1981) corresponds to the classical maximum deviation test without scaling, and leads to envelopes with constant width over the distances r. Thus, it suffers from unequal variance of T(r) over the distances r and from the asymmetry of distribution of T(r). We recommend to use the other global envelope tests available, see global_envelope_test for full list of alternatives.

References

Myllymäki, M., Grabarnik, P., Seijo, H. and Stoyan. D. (2015). Deviation test construction and power comparison for marked spatial point patterns. Spatial Statistics 11: 19-34. doi: 10.1016/j.spasta.2014.11.004

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

Ripley, B.D. (1981). Spatial statistics. Wiley, New Jersey.

See Also

global_envelope_test

Examples

# See more examples in ?global_envelope_test
## Testing complete spatial randomness (CSR)
#-------------------------------------------
if(require("spatstat.explore", quietly=TRUE)) {
  X <- spruces
  nsim <- 999 # Number of simulations
  nsim <- 19 # Number of simulations for testing
  ## Test for complete spatial randomness (CSR)
  # 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)))
  res_qdir <- qdir_envelope(env) # The directional quantile envelope test
  plot(res_qdir)

  ## Advanced use:
  # Create a curve set, choosing the interval of distances [r_min, r_max]
  curve_set <- crop_curves(env, r_min=1, r_max=8)
  # The directional quantile envelope test
  res_qdir <- qdir_envelope(curve_set); plot(res_qdir)
  # The studentised envelope test
  res_st <- st_envelope(curve_set); plot(res_st)
  # The unscaled envelope test
  res_unscaled <- unscaled_envelope(curve_set); plot(res_unscaled)
}