Generates a progress plot (envelope representation) of the Dao-Genton test for a spatial point pattern.
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)An object of class "fv" that can be plotted to
obtain the progress plot.
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").
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.
Positive number. The exponent of the \(L^p\) distance. See Details.
Number of repetitions of the basic test.
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.
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.
Optional. The significance level of the test.
Equivalent to nrank/(nsim+1) where nsim is the
number of simulations.
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.
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.
Optional. Left endpoint for the interval of \(r\) values on which the test statistic is calculated.
Logical value indicating whether to save the simulated function values (from the first stage).
Logical value indicating whether to save the simulated point patterns (from the first stage).
Logical value indicating whether to print progress reports.
Adrian Baddeley, Andrew Hardegen, Tom Lawrence, Robin Milne, Gopalan Nair and Suman Rakshit. Implemented by Adrian Baddeley Adrian.Baddeley@curtin.edu.au, Rolf Turner rolfturner@posteo.net and Ege Rubak rubak@math.aau.dk.
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).
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.
dg.test,
dclf.progress
ns <- if(interactive()) 19 else 5
plot(dg.progress(cells, nsim=ns))
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