envsig {variosig}

Determine Significance of Spatial Dependence Using Pointwise Variogram Envelope

Description

Determine the significance of spatial dependence at different scales using pointwise variogram envelope based on permutation test.

Usage

envsig(envlist, index = NULL, method = c("eb", "fisher", "min"))

Arguments

envlist

output from envelope function.

index

integer. Indicating the index which the permutation test for spatial dependence is performed up to. For example, index = 2 indicates only the first two variogram estimates are considered in the hypothesis test, i.e. null hypothesis is there is no spatial dependence at small scales. If NULL, all variogram estimates are considered, which corresponds to the null hypothesis of no overall spatial dependence.

method

string. One of p-value combination methods.

Details

The default and preferred method for computing overall p-value is "eb" (empirical Brown's method), which has good power and close to nominal type I error rate. "fisher" (Fisher's method assumes independent pointwise p-values and requires higher sample size to achieve good power. "min" has the highest power but also much higher type I error rate.

Value

A list contains:

p.pointwise

Adjusted pointwise p-values.

p.overall

Overall p-value of the permutation test.

Author(s)

Craig Wang

References

Walker, D. D., J. C. Loftis, and J. P. W. Mielke (1997). Permutation methods for determining the significance of spatial dependence. Mathematical Geology 29(8), 1011–1024.

Fisher R. A. (1932). Statistical methods for research workers, 4th ed. Oliver & Boyd.

Poole, W., D. L. Gibbs, I. Shmulevich, B. Bernard, and T. A. Knijnenburg (2016). Combining dependent P-values with an empirical adaptation of Brown’s method. Bioinformatics 32(17), 430–436.

Wang, C., Furrer, R. (2018) Monte Carlo Permutation Tests for Assessing Spatial Dependence at Difference Scales. Nonparametric Statistics. (Submitted)

See Also

envelope to use Monte Carlo permutations for generating variogram envelope.

Examples

## Not run: 
library(sp)
data(meuse)
coordinates(meuse) = ~x+y
vario0 <- gstat::variogram(log(zinc)~1, meuse)
varioEnv <- envelope(vario0, data = meuse, formula = log(zinc)~1,
  nsim = 500, cluster = TRUE, n.cluster = 10)
envplot(varioEnv)
envsig(varioEnv, index = 2, method = "eb")

## End(Not run)