deviation_test {GET}R Documentation

Deviation test

Description

Crop the curve set to the interval of distances [r_min, r_max], calculate residuals, scale the residuals and perform a deviation test with a chosen deviation measure. The deviation tests are well known in spatial statistics; in GET they are provided for comparative purposes. Some (maximum type) of the deviation test have their corresponding envelope tests available, see Myllymäki et al., 2017 (and 'unscaled', 'st' and 'qdir' in global_envelope_test).

Usage

deviation_test(
  curve_set,
  r_min = NULL,
  r_max = NULL,
  use_theo = TRUE,
  scaling = "qdir",
  measure = "max",
  savedevs = FALSE
)

Arguments

curve_set

A residual curve_set object. Can be obtained by using residual().

r_min

The minimum radius to include.

r_max

The maximum radius to include.

use_theo

Whether to use the theoretical summary function or the mean of the functions in the curve_set.

scaling

The name of the scaling to use. Options include 'none', 'q', 'qdir' and 'st'. 'qdir' is default.

measure

The deviation measure to use. Default is 'max'. Must be one of the following: 'max', 'int' or 'int2'.

savedevs

Logical. Should the global rank values k_i, i=1,...,nsim+1 be returned? Default: FALSE.

Details

The deviation test is based on a test function T(r) and it works as follows:

1) The test function estimated for the data, T_1(r), and for nsim simulations from the null model, T_2(r), ...., T_{nsim+1}(r), must be saved in 'curve_set' and given to the deviation_test function.

2) The deviation_test function then

Currently, there is no special way to take care of the same values of T_i(r) occuring possibly for small distances. Thus, it is preferable to exclude from the test the very small distances r for which ties occur.

Value

If 'savedevs=FALSE' (default), the p-value is returned. If 'savedevs=TRUE', then a list containing the p-value and calculated deviation measures u_i, i=1,...,nsim+1 (where u_1 corresponds to the data pattern) is returned.

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

Examples

## Testing complete spatial randomness (CSR)
#-------------------------------------------
if(require("spatstat.explore", quietly=TRUE)) {
  pp <- unmark(spruces)
  nsim <- 999
  
  # Generate nsim simulations under CSR, calculate L-function for the data and simulations
  env <- envelope(pp, fun="Lest", nsim=nsim, savefuns=TRUE, correction="translate")
  # The deviation test using the integral deviation measure
  res <- deviation_test(env, measure='int')
  res
  # or
  res <- deviation_test(env, r_min=0, r_max=7, measure='int2')
}


[Package GET version 1.0-2 Index]