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.
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Either a point pattern (object of class
Arguments passed to
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
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.
The Diggle (1986)/ Cressie (1991)/Loosmore and Ford (2006) test and the
Maximum Absolute Deviation test for a spatial point pattern
are described in
These tests depend on the choice of an interval of
distance values (the argument
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
X using all possible intervals
of the form [0,R], and returns the resulting p-values
as a function of R.
mad.test using all possible intervals
and returns the p-values.
mctest.sigtrace performs a test based on the
L^p discrepancy between the curves. The deviation between two
curves is measured by the pth root of the integral of
the pth power of the absolute value of the difference
between the two curves. The exponent p is
given by the argument
exponent. The case
is the Cressie-Loosmore-Ford test, while
exponent=Inf is the
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 ≥ rmin.
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
X is an envelope object and
the code will re-use the simulated functions stored in
An object of class
"fv" that can be plotted to
obtain the significance trace.
, Andrew Hardegen, Tom Lawrence, Robin Milne, Gopalan Nair and Suman Rakshit. Implemented by \adrian\rolf
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.