Generates a Significance Trace of the Dao and Genton (2014) test for a spatial point pattern.
dg.sigtrace(X, fun = Lest, ...,
exponent = 2, nsim = 19, nsimsub = nsim - 1,
alternative = c("two.sided", "less", "greater"),
rmin=0, leaveout=1,
interpolate = FALSE, confint = TRUE, alpha = 0.05,
savefuns=FALSE, savepatterns=FALSE, verbose=FALSE)An object of class "fv" that can be plotted to
obtain the significance trace.
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.
Positive number. Exponent used in the test statistic. Use exponent=2
for the Diggle-Cressie-Loosmore-Ford test, and exponent=Inf
for the Maximum Absolute Deviation test.
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.
Character string specifying the alternative hypothesis.
The default (alternative="two.sided") is that the
true value of the summary function is not equal to the theoretical
value postulated under the null hypothesis.
If alternative="less" the alternative hypothesis is that the
true value of the summary function is lower than the theoretical value.
Optional. Left endpoint for the interval of \(r\) values on which the test statistic is calculated.
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 whether to interpolate the distribution of the test statistic by kernel smoothing, as described in Dao and Genton (2014, Section 5).
Logical value indicating whether to compute a confidence interval for the ‘true’ \(p\)-value.
Significance level to be plotted (this has no effect on the calculation but is simply plotted as a reference value).
Logical flag indicating whether to save the simulated function values (from the first stage).
Logical flag indicating whether to save the simulated point patterns (from the first stage).
Logical flag 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 r.turner@auckland.ac.nz 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 significance trace (Bowman and Azzalini, 1997;
Baddeley et al, 2014, 2015; Baddeley, Rubak and Turner, 2015)
of the test is a plot of the \(p\)-value
obtained from the test against the length of
the interval rinterval.
The command dg.sigtrace effectively performs
dg.test on X using all possible intervals
of the form \([0,R]\), and returns the resulting \(p\)-values
as a function of \(R\).
The result is an object of class "fv" that can be plotted to
obtain the significance trace. The plot shows the
Dao-Genton adjusted
\(p\)-value (solid black line),
the critical value 0.05 (dashed red line),
and a pointwise 95% confidence band (grey shading)
for the ‘true’ (Neyman-Pearson) \(p\)-value.
The confidence band is based on the Agresti-Coull (1998)
confidence interval for a binomial proportion.
If X is an envelope object and fun=NULL then
the code will re-use the simulated functions stored in X.
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).
Agresti, A. and Coull, B.A. (1998) Approximate is better than “Exact” for interval estimation of binomial proportions. American Statistician 52, 119--126.
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.
Bowman, A.W. and Azzalini, A. (1997) Applied smoothing techniques for data analysis: the kernel approach with S-Plus illustrations. Oxford University Press, Oxford.
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 for the Dao-Genton test,
dclf.sigtrace for significance traces of other tests.
ns <- if(interactive()) 19 else 5
plot(dg.sigtrace(cells, nsim=ns))
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