# qdir_envelope: Directional quantile envelope test In myllym/GET: Global Envelope Tests

## Description

The directional quantile envelope test, which 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).

## Usage

 1 qdir_envelope(curve_set, ...) 

## Arguments

 curve_set A curve_set (see create_curve_set) or an envelope object. 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 envelope. ... Additional parameters to be passed to global_envelope_test.

## Value

An object of class "global_envelope", "envelope" and "fv" (see fv.object), which can be printed and plotted directly.

Essentially a data frame containing columns

• r = the vector of values of the argument r at which the test was made

• obs = values of the test function for the data point pattern

• lo = the lower envelope based on the simulated functions

• hi = the upper envelope based on the simulated functions

• central = If the curve_set (or envelope object) contains a component 'theo', then this function is used as the central curve and returned in this component. Otherwise, the central curve is the mean of the test functions T_i(r), i=2, ..., s+1. Used for visualization only.

Additionally, the return value has attributes

• method = The name of the envelope test ("Directional quantile envelope test" for the directional quantile envelope test)

• alternative = "two-sided

• p = A point estimate for the p-value (default is the mid-rank p-value).

• u_alpha = The value of u corresponding to the 100(1-alpha)% global envelope.

• u = Deviation values (u[1] is the value for the data pattern).

• call = The call of the function.

and a punch of attributes for the "fv" object type.

## 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

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 ## Testing complete spatial randomness (CSR) #------------------------------------------- require(spatstat) pp <- spruces ## Test for complete spatial randomness (CSR) # Generate nsim simulations under CSR, calculate L-function for the data and simulations env <- envelope(pp, fun="Lest", nsim=999, savefuns=TRUE, correction="translate", simulate=expression(runifpoint(pp$n, win=pp$window))) # The directional quantile envelope test res <- qdir_envelope(env) plot(res) # or (requires R library ggplot2) plot(res, plot_style="ggplot2") ## 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) # For better visualisation, take the L(r)-r function curve_set <- residual(curve_set, use_theo = TRUE) # The directional quantile envelope test res <- qdir_envelope(curve_set); plot(res, plot_style="ggplot2") ## Random labeling test #---------------------- # requires library 'marksummary' mpp <- spruces # Use the test function T(r) = \hat{L}_m(r), an estimator of the L_m(r) function curve_set <- random_labelling(mpp, mtf_name = 'm', nsim=2499, r_min=1.5, r_max=9.5) res <- qdir_envelope(curve_set) plot(res, plot_style="ggplot2", ylab=expression(italic(L[m](r)-L(r)))) 

myllym/GET documentation built on Sept. 30, 2018, 5:49 a.m.