dclf.sigtrace(X, ...)
mad.sigtrace(X, ...)
mctest.sigtrace(X, fun=Lest, ...,
exponent=1, interpolate=FALSE, alpha=0.05,
confint=TRUE, rmin=0)
"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
or mctest.progress
.
Useful arguments include fun
to determine the summary
function, nsim
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"fv"
that can be plotted to
obtain the significance trace.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 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
.
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
.
plot(dclf.sigtrace(cells, Lest, nsim=19))
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