Generates a Significance Trace of the Diggle(1986)/ Cressie (1991)/ Loosmore and Ford (2006) test or the Maximum Absolute Deviation test for a spatial point pattern.
dclf.sigtrace(X, …)
mad.sigtrace(X, …)
mctest.sigtrace(X, fun=Lest, …,
exponent=1, interpolate=FALSE, alpha=0.05,
confint=TRUE, rmin=0)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").
Arguments passed to envelope
or mctest.progress.
Useful arguments include fun to determine the summary
function, nsim to specify the number of Monte Carlo
simulations, alternative to specify a one-sided test,
and verbose=FALSE to turn off the messages.
Function that computes the desired summary statistic for a point pattern.
Positive number. The exponent of the \(L^p\) distance. See Details.
Logical value specifying whether to calculate the \(p\)-value
by interpolation.
If interpolate=FALSE (the default), a standard Monte Carlo test
is performed, yielding a \(p\)-value of the form \((k+1)/(n+1)\)
where \(n\) is the number of simulations and \(k\) is the number
of simulated values which are more extreme than the observed value.
If interpolate=TRUE, the \(p\)-value is calculated by
applying kernel density estimation to the simulated values, and
computing the tail probability for this estimated distribution.
Significance level to be plotted (this has no effect on the calculation but is simply plotted as a reference value).
Logical value indicating whether to compute a confidence interval for the ‘true’ \(p\)-value.
Optional. Left endpoint for the interval of \(r\) values on which the test statistic is calculated.
An object of class "fv" that can be plotted to
obtain the significance trace.
The Diggle (1986)/ Cressie (1991)/Loosmore and Ford (2006) test and the
Maximum Absolute Deviation test for a spatial point pattern
are described in dclf.test.
These tests depend 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 dclf.sigtrace performs
dclf.test on X using all possible intervals
of the form \([0,R]\), and returns the resulting \(p\)-values
as a function of \(R\).
Similarly mad.sigtrace performs
mad.test using all possible intervals
and returns the \(p\)-values.
More generally, mctest.sigtrace performs a test based on the
\(L^p\) discrepancy between the curves. The deviation between two
curves is measured by the \(p\)th root of the integral of
the \(p\)th power of the absolute value of the difference
between the two curves. The exponent \(p\) is
given by the argument exponent. The case exponent=2
is the Cressie-Loosmore-Ford test, while exponent=Inf is the
MAD test.
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 result of each command
is an object of class "fv" that can be plotted to
obtain the significance trace. The plot shows the Monte Carlo
\(p\)-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 (when
interpolate=FALSE) or the delta method
and normal approximation (when interpolate=TRUE).
If X is an envelope object and fun=NULL then
the code will re-use the simulated functions stored in X.
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. 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.
dclf.test for the tests;
dclf.progress for progress plots.
See plot.fv for information on plotting
objects of class "fv".
See also dg.sigtrace.
# NOT RUN {
plot(dclf.sigtrace(cells, Lest, nsim=19))
# }
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