# unscaled_envelope: Unscaled envelope test In myllym/GET: Global Envelope Tests

## Description

The unscaled envelope test, which leads to envelopes with constant width over the distances r. It corresponds to the classical maximum deviation test without scaling.

## Usage

 1 unscaled_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.

## Details

This test 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 rank_envelope (if number of simulations close to 5000 can be afforded) or st_envelope/qdir_envelope (if large number of simulations cannot be afforded) instead.

## 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 ("Studentised envelope test" for the studentised 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

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

## 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 studentised envelope test res <- unscaled_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 studentised envelope test res <- unscaled_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 <- unscaled_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.