unscaled_envelope: Unscaled envelope test
In myllym/spptest: Spatial point process testing

Description Usage Arguments Details Value References Examples

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.

1	unscaled_envelope(curve_set, alpha = 0.05, savedevs = FALSE, ...)

`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().
`alpha`	The significance level. The 100(1-alpha)% global envelope will be calculated.
`savedevs`	Logical. Should the deviation values u_i, i=1,...,nsim+1 be returned? Default: FALSE.
`...`	Additional parameters passed to `estimate_p_value` to obtain a point estimate for the p-value. The default point estimate is the mid-rank p-value. The choice should not affect the result, since no ties are expected to occur.

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.

An "envelope_test" object containing the following fields:

r = Distances for which the test was made.
method = The name of the envelope test.
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). Returned only if savedevs = TRUE.
central_curve = 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.
data_curve = The test function for the data.
lower = The lower envelope.
upper = The upper envelope.
call = The call of the function.

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

## 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")
# The studentised envelope test
res <- unscaled_envelope(env)
plot(res)
# or (requires R library ggplot2)
plot(res, use_ggplot2=TRUE)

## 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, use_ggplot2=TRUE)

## 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, use_ggplot2=TRUE, ylab=expression(italic(L[m](r)-L(r))))