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.

htest, spatial
dclf.progress(X, ..., nrank = 1)
mad.progress(X, ..., nrank = 1)
mctest.progress(X, fun = Lest, ..., exponent = 1, nrank = 1)
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. Useful arguments include fun to determine the summary function, nsim to specify the number of Monte Carlo simulations, and verbose=
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.
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 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 $c(0,r)$, and returns the resulting values of the test statistic, and the corresponding critical values of the test, as a function of $r$.

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.

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:

  • IfXis an envelope object containing simulated functions, andfun=NULL, then the code will re-use the simulated functions stored inX.
  • IfXis an envelope object containing simulated point patterns, thenfunwill be applied to the stored point patterns to obtain the simulated functions. Iffunis not specified, it defaults toLest.
  • Otherwise, new simulations will be performed, andfundefaults toLest.


  • 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. (2014) On tests of spatial pattern based on simulation envelopes. Ecological Monographs 84 (3) 477--489.

See Also

dclf.test and mad.test for the tests. See plot.fv for information on plotting objects of class "fv".

  • dclf.progress
  • mad.progress
  • mctest.progress
plot(dclf.progress(cells, nsim=19))
Documentation reproduced from package spatstat, version 1.42-2, License: GPL (>= 2)

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