dclf.sigtrace.Rd
\name{dclf.sigtrace}
\alias{dclf.sigtrace}
\alias{mad.sigtrace}
\alias{mctest.sigtrace}
\title{
Significance Trace of Cressie-Loosmore-Ford or Maximum Absolute
Deviation Test
}
\description{
Generates a Significance Trace of the
Diggle(1986)/ Cressie (1991)/ Loosmore and Ford (2006) test or the
Maximum Absolute Deviation test for a spatial point pattern.
}
\usage{
dclf.sigtrace(X, \dots)
mad.sigtrace(X, \dots)
mctest.sigtrace(X, fun=Lest, \dots,
exponent=1, interpolate=FALSE, alpha=0.05,
confint=TRUE, rmin=0)
}
\arguments{
\item{X}{
Either a point pattern (object of class \code{"ppp"}, \code{"lpp"}
or other class), a fitted point process model (object of class \code{"ppm"},
\code{"kppm"} or other class) or an envelope object (class
\code{"envelope"}).
}
\item{\dots}{
Arguments passed to \code{\link{envelope}}
or \code{\link{mctest.progress}}.
Useful arguments include \code{fun} to determine the summary
function, \code{nsim} to specify the number of Monte Carlo
simulations, \code{alternative} to specify a one-sided test,
and \code{verbose=FALSE} to turn off the messages.
}
\item{fun}{
Function that computes the desired summary statistic
for a point pattern.
}
\item{exponent}{
Positive number. The exponent of the \eqn{L^p} distance.
See Details.
}
\item{interpolate}{
Logical value specifying whether to calculate the \eqn{p}-value
by interpolation.
If \code{interpolate=FALSE} (the default), a standard Monte Carlo test
is performed, yielding a \eqn{p}-value of the form \eqn{(k+1)/(n+1)}
where \eqn{n} is the number of simulations and \eqn{k} is the number
of simulated values which are more extreme than the observed value.
If \code{interpolate=TRUE}, the \eqn{p}-value is calculated by
applying kernel density estimation to the simulated values, and
computing the tail probability for this estimated distribution.
}
\item{alpha}{
Significance level to be plotted (this has no effect on the calculation
but is simply plotted as a reference value).
}
\item{confint}{
Logical value indicating whether to compute a confidence interval
for the \sQuote{true} \eqn{p}-value.
}
\item{rmin}{
Optional. Left endpoint for the interval of \eqn{r} values
on which the test statistic is calculated.
}
}
\details{
The Diggle (1986)/ Cressie (1991)/Loosmore and Ford (2006) test and the
Maximum Absolute Deviation test for a spatial point pattern
are described in \code{\link{dclf.test}}.
These tests depend on the choice of an interval of
distance values (the argument \code{rinterval}).
A \emph{significance trace} (Bowman and Azzalini, 1997;
Baddeley et al, 2014, 2015)
of the test is a plot of the \eqn{p}-value
obtained from the test against the length of
the interval \code{rinterval}.
The command \code{dclf.sigtrace} performs
\code{\link{dclf.test}} on \code{X} using all possible intervals
of the form \eqn{[0,R]}, and returns the resulting \eqn{p}-values
as a function of \eqn{R}.
Similarly \code{mad.sigtrace} performs
\code{\link{mad.test}} using all possible intervals
and returns the \eqn{p}-values.
More generally, \code{mctest.sigtrace} performs a test based on the
\eqn{L^p} discrepancy between the curves. The deviation between two
curves is measured by the \eqn{p}th root of the integral of
the \eqn{p}th power of the absolute value of the difference
between the two curves. The exponent \eqn{p} is
given by the argument \code{exponent}. The case \code{exponent=2}
is the Cressie-Loosmore-Ford test, while \code{exponent=Inf} is the
MAD test.
If the argument \code{rmin} is given, it specifies the left endpoint
of the interval defining the test statistic: the tests are
performed using intervals \eqn{[r_{\mbox{\scriptsize min}},R]}{[rmin,R]}
where \eqn{R \ge r_{\mbox{\scriptsize min}}}{R \ge rmin}.
The result of each command
is an object of class \code{"fv"} that can be plotted to
obtain the significance trace. The plot shows the Monte Carlo
\eqn{p}-value (solid black line),
the critical value \code{0.05} (dashed red line),
and a pointwise 95\% confidence band (grey shading)
for the \sQuote{true} (Neyman-Pearson) \eqn{p}-value.
The confidence band is based on the Agresti-Coull (1998)
confidence interval for a binomial proportion (when
\code{interpolate=FALSE}) or the delta method
and normal approximation (when \code{interpolate=TRUE}).
If \code{X} is an envelope object and \code{fun=NULL} then
the code will re-use the simulated functions stored in \code{X}.
}
\value{
An object of class \code{"fv"} that can be plotted to
obtain the significance trace.
}
\references{
Agresti, A. and Coull, B.A. (1998)
Approximate is better than \dQuote{Exact} for interval
estimation of binomial proportions.
\emph{American Statistician} \bold{52}, 119--126.
Baddeley, A., Diggle, P., Hardegen, A., Lawrence, T.,
Milne, R. and Nair, G. (2014)
On tests of spatial pattern based on simulation envelopes.
\emph{Ecological Monographs} \bold{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)
\emph{Applied smoothing techniques for data analysis:
the kernel approach with S-Plus illustrations}.
Oxford University Press, Oxford.
}
\author{
\adrian, Andrew Hardegen, Tom Lawrence,
Robin Milne, Gopalan Nair and Suman Rakshit.
Implemented by
\adrian
\rolf
and \ege
}
\seealso{
\code{\link{dclf.test}} for the tests;
\code{\link{dclf.progress}} for progress plots.
See \code{\link{plot.fv}} for information on plotting
objects of class \code{"fv"}.
See also \code{\link{dg.sigtrace}}.
}
\examples{
plot(dclf.sigtrace(cells, Lest, nsim=19))
}
\keyword{spatial}
\keyword{htest}