Generates a progress plot (envelope representation) of the Diggle-Cressie-Loosmore-Ford test or the Maximum Absolute Deviation test for a spatial point pattern.
dclf.progress(X, ...)
mad.progress(X, ...)
mctest.progress(X, fun = Lest, ...,
exponent = 1, nrank = 1,
interpolate = FALSE, alpha, rmin=0)An object of class "fv" that can be plotted to
obtain the progress plot.
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 mctest.progress or to envelope.
Useful arguments include fun to determine the summary
function, nsim to specify the number of Monte Carlo
simulations, alternative to specify one-sided or two-sided
envelopes, 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.
Integer. The rank of the critical value of the Monte Carlo test,
amongst the nsim simulated values.
A rank of 1 means that the minimum and maximum
simulated values will become the critical values for the test.
Logical value indicating how to compute the critical value.
If interpolate=FALSE (the default), a standard Monte Carlo test
is performed, and the critical value is the largest
simulated value of the test statistic (if nrank=1)
or the nrank-th largest (if nrank is another number).
If interpolate=TRUE, kernel density estimation
is applied to the simulated values, and the critical value is
the upper alpha quantile of this estimated distribution.
Optional. The significance level of the test.
Equivalent to nrank/(nsim+1) where nsim is the
number of simulations.
Optional. Left endpoint for the interval of \(r\) values on which the test statistic is calculated.
Adrian Baddeley Adrian.Baddeley@curtin.edu.au
, Andrew Hardegen, Tom Lawrence, Gopal Nair and Robin Milne.
The Diggle-Cressie-Loosmore-Ford 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 progress plot or envelope representation
of the test (Baddeley et al, 2014) is a plot of the
test statistic (and the corresponding critical value) against the length of
the interval rinterval.
The command dclf.progress performs
dclf.test on X using all possible intervals
of the form \([0,R]\), and returns the resulting values of the test
statistic, and the corresponding critical values of the test,
as a function of \(R\).
Similarly mad.progress performs
mad.test using all possible intervals
and returns the test statistic and critical value.
More generally, mctest.progress 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 progress plot. The display shows
the test statistic (solid black line) and the Monte Carlo
acceptance region (grey shading).
The significance level for the Monte Carlo test is
nrank/(nsim+1). Note that nsim defaults to 99,
so if the values of nrank and nsim are not given,
the default is a test with significance level 0.01.
If X is an envelope object, then some of the data stored
in X may be re-used:
If X is an envelope object containing simulated functions,
and fun=NULL, then
the code will re-use the simulated functions stored in X.
If X is an envelope object containing
simulated point patterns,
then fun will be applied to the stored point patterns
to obtain the simulated functions.
If fun is not specified, it defaults to Lest.
Otherwise, new simulations will be performed,
and fun defaults to Lest.
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.
dclf.test and
mad.test for the tests.
See plot.fv for information on plotting
objects of class "fv".
plot(dclf.progress(cells, nsim=19))
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