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)"ppp", "lpp"
or other class), a fitted point process model (object of class "ppm",
"kppm" or other class) or an envelope object (class
"envelope").
envelope.
exponent=2
for the Diggle-Cressie-Loosmore-Ford test, and exponent=Inf
for the Maximum Absolute Deviation test.
See Details.
nsim
repetitions of the basic test, each involving nsimsub simulated
realisations, so there will be a total
of nsim * (nsimsub + 1) simulations.
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.
"fv" that can be plotted to
obtain the significance trace.
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)
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 $[rmin,R]$
where $R \ge rmin$.
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. Submitted for publication.
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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