dclf.test(X, ..., rinterval = NULL, use.theo=FALSE)
mad.test(X, ..., rinterval = NULL, use.theo=FALSE)"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.
Useful arguments include fun to determine the summary
function, nsim to specify the number of Monte Carlo
simulations, and verbose=r
over which the maximum absolute deviation, or the integral,
will be computed for the test. A numeric vector of length 2.use.theo=TRUE)
or to the sample mean of simulations from CSR (use.theo=FALSE)."htest".
Printing this object gives a report on the result of the test.
The $p$-value is contained in the component p.value. dclf.test performs the test advocated by Loosmore and Ford (2006)
which is also described in Diggle (1986), Cressie (1991, page 667, equation
(8.5.42)) and Diggle (2003, page 14).
mad.test performs the
The type of test depends on the type of argument X.
Xis some kind of point pattern, then a test of Complete
Spatial Randomness (CSR) will be performed. That is,
the null hypothesis is that the point pattern is completely random.Xis a fitted point process model, then a test of
goodness-of-fit for the fitted model will be performed. The model object
contains the data point pattern to which it was originally fitted.
The null hypothesis is that the data point pattern is a realisation
of the model.Xis an envelope object generated byenvelope,
then it should have been generated withsavefuns=TRUEorsavepatterns=TRUEso that it contains simulation results.
These simulations will be treated as realisations from the null
hypothesis.envelope to
generate or extract the simulated summary functions.
The number of simulations that will be generated or extracted,
is determined by the argument nsim, and defaults to 99.
The summary function that will be computed is determined by the
argument fun (or the first unnamed argument in the list
...) and defaults to Kest (except when
X is an envelope object generated with savefuns=TRUE,
when these functions will be taken). The choice of summary function fun affects the power of the
test. It is normally recommended to apply a variance-stabilising
transformation (Ripley, 1981). If you are using the $K$ function,
the normal practice is to replace this by the $L$ function
(Besag, 1977) computed by Lest. If you are using
the $F$ or $G$ functions, the recommended practice is to apply
Fisher's variance-stabilising transformation
$\sin^{-1}\sqrt x$ using the argument
transform. See the Examples.
Diggle, P. J. (1986). Displaced amacrine cells in the retina of a rabbit : analysis of a bivariate spatial point pattern. J. Neuroscience Methods 18, 115--125. Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.
Loosmore, N.B. and Ford, E.D. (2006) Statistical inference using the G or K point pattern spatial statistics. Ecology 87, 1925--1931.
Ripley, B.D. (1977) Modelling spatial patterns (with discussion). Journal of the Royal Statistical Society, Series B, 39, 172 -- 212.
Ripley, B.D. (1981) Spatial statistics. John Wiley and Sons.
envelopedclf.test(cells, Lest, nsim=39)
m <- mad.test(cells, Lest, verbose=FALSE, rinterval=c(0, 0.1), nsim=19)
m
# extract the p-value
m$p.value
# variance stabilised G function
dclf.test(cells, Gest, transform=expression(asin(sqrt(.))),
verbose=FALSE, nsim=19)Run the code above in your browser using DataLab