Progress Plot of Test of Spatial Pattern
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, ..., nrank = 1) mad.progress(X, ..., nrank = 1) mctest.progress(X, fun = Lest, ..., expo = 1, nrank = 1)
- Either a point pattern (object of class
"lpp"or other class), a fitted point process model (object of class
"kppm"or other class) or an envelope object (class
- Arguments passed to
envelope. Useful arguments include
funto determine the summary function,
nsimto specify the number of Monte Carlo simulations, and
- Integer. The rank of the critical value of the Monte Carlo test,
nsimsimulated values. A rank of 1 means that the minimum and maximum simulated values will become the critical values for the test.
- Function that computes the desired summary statistic for a point pattern.
- Positive number. The exponent of the $L^p$ distance. See Details.
The Diggle-Cressie-Loosmore-Ford 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 progress plot or envelope representation
of the test (Baddeley et al, 2013) is a plot of the
test statistic (and the corresponding critical value) against the length of
X using all possible intervals
of the form $c(0,r)$, and returns the resulting values of the test
statistic, and the corresponding critical values of the test,
as a function of $r$.
mad.test using all possible intervals
and returns the test statistic and critical value.
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
expo. The case
is the Cressie-Loosmore-Ford test, while
expo=Inf is the
The result of each command is an object of class
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
nsim are not given,
the default is a test with significance level 0.01.
X is an envelope object, then some of the data stored
X may be re-used:
Xis an envelope object containing simulated functions, and
fun=NULL, then the code will re-use the simulated functions stored in
Xis an envelope object containing simulated point patterns, then
funwill be applied to the stored point patterns to obtain the simulated functions. If
funis not specified, it defaults to
- Otherwise, new simulations will be performed,
- An object of class
"fv"that can be plotted to obtain the progress plot.
Baddeley, A., Diggle, P., Hardegen, A., Lawrence, T., Milne, R. and Nair, G. (2013) On tests of spatial pattern based on simulation envelopes. Submitted for publication.