dg.progress {spatstat.explore}

Progress Plot of Dao-Genton Test of Spatial Pattern

Description

Generates a progress plot (envelope representation) of the Dao-Genton test for a spatial point pattern.

Usage

dg.progress(X, fun = Lest, ...,
            exponent = 2, nsim = 19, nsimsub = nsim - 1,
            nrank = 1, alpha, leaveout=1, interpolate = FALSE, rmin=0,
            savefuns = FALSE, savepatterns = FALSE, verbose=TRUE)

Arguments

X

Either a point pattern (object of class "ppp", "lpp" or other class), a fitted point process model (object of class "ppm", "kppm" or other class) or an envelope object (class "envelope").

fun

Function that computes the desired summary statistic for a point pattern.

...

Arguments passed to envelope. Useful arguments include alternative to specify one-sided or two-sided envelopes.

exponent

Positive number. The exponent of the L^p distance. See Details.

nsim

Number of repetitions of the basic test.

nsimsub

Number of simulations in each basic test. There will be nsim repetitions of the basic test, each involving nsimsub simulated realisations, so there will be a total of nsim * (nsimsub + 1) simulations.

nrank

Integer. The rank of the critical value of the Monte Carlo test, amongst the nsim simulated values. A rank of 1 means that the minimum and maximum simulated values will become the critical values for the test.

alpha

Optional. The significance level of the test. Equivalent to nrank/(nsim+1) where nsim is the number of simulations.

leaveout

Optional integer 0, 1 or 2 indicating how to calculate the deviation between the observed summary function and the nominal reference value, when the reference value must be estimated by simulation. See Details.

interpolate

Logical value indicating how to compute the critical value. If interpolate=FALSE (the default), a standard Monte Carlo test is performed, and the critical value is the largest simulated value of the test statistic (if nrank=1) or the nrank-th largest (if nrank is another number). If interpolate=TRUE, kernel density estimation is applied to the simulated values, and the critical value is the upper alpha quantile of this estimated distribution.

rmin

Optional. Left endpoint for the interval of r values on which the test statistic is calculated.

savefuns

Logical value indicating whether to save the simulated function values (from the first stage).

savepatterns

Logical value indicating whether to save the simulated point patterns (from the first stage).

verbose

Logical value indicating whether to print progress reports.

Details

The Dao and Genton (2014) test for a spatial point pattern is described in dg.test. This test depends on the choice of an interval of distance values (the argument rinterval). A progress plot or envelope representation of the test (Baddeley et al, 2014, 2015; Baddeley, Rubak and Turner, 2015) is a plot of the test statistic (and the corresponding critical value) against the length of the interval rinterval.

The command dg.progress effectively performs dg.test on X using all possible intervals of the form [0,R], and returns the resulting values of the test statistic, and the corresponding critical values of the test, as a function of R.

The result is an object of class "fv" that can be plotted to obtain the progress plot. The display shows the test statistic (solid black line) and the test acceptance region (grey shading). If X is an envelope object, then some of the data stored in X may be re-used:

• If X is an envelope object containing simulated functions, and fun=NULL, then the code will re-use the simulated functions stored in X.

• If X is an envelope object containing simulated point patterns, then fun will be applied to the stored point patterns to obtain the simulated functions. If fun is not specified, it defaults to Lest.

• Otherwise, new simulations will be performed, and fun defaults to Lest.

If the argument rmin is given, it specifies the left endpoint of the interval defining the test statistic: the tests are performed using intervals [r_{\mbox{\scriptsize min}},R] where R \ge r_{\mbox{\scriptsize min}}.

The argument leaveout specifies how to calculate the discrepancy between the summary function for the data and the nominal reference value, when the reference value must be estimated by simulation. The values leaveout=0 and leaveout=1 are both algebraically equivalent (Baddeley et al, 2014, Appendix) to computing the difference observed - reference where the reference is the mean of simulated values. The value leaveout=2 gives the leave-two-out discrepancy proposed by Dao and Genton (2014).

Value

An object of class "fv" that can be plotted to obtain the progress plot.

Author(s)

Adrian Baddeley, Andrew Hardegen, Tom Lawrence, Robin Milne, Gopalan Nair and Suman Rakshit. Implemented by Adrian Baddeley [e-mail], Rolf Turner [e-mail] and Ege Rubak [e-mail].

References

Baddeley, A., Diggle, P., Hardegen, A., Lawrence, T., Milne, R. and Nair, G. (2014) On tests of spatial pattern based on simulation envelopes. Ecological Monographs 84 (3) 477–489.

Baddeley, A., Hardegen, A., Lawrence, L., Milne, R.K., Nair, G.M. and Rakshit, S. (2015) Pushing the envelope: extensions of graphical Monte Carlo tests. Unpublished manuscript.

Baddeley, A., Rubak, E. and Turner, R. (2015) Spatial Point Patterns: Methodology and Applications with R. Chapman and Hall/CRC Press.

Dao, N.A. and Genton, M. (2014) A Monte Carlo adjusted goodness-of-fit test for parametric models describing spatial point patterns. Journal of Graphical and Computational Statistics 23, 497–517.

See Also

dg.test, dclf.progress

Examples

   ns <- if(interactive()) 19 else 5
   plot(dg.progress(cells, nsim=ns))