scanLRTS(X, r, ...,
method = c("poisson", "binomial"),
baseline = NULL, case = 2,
alternative = c("greater", "less", "two.sided"),
saveopt = FALSE,
Xmask = NULL)"ppp").as.mask to determine the
spatial resolution of the computations."poisson" or "binomial"
specifying the type of likelihood.method="poisson".
A pixel image or a function.method="binomial".
Integer or character string."greater" if the alternative
postulates that the mean number of points inside the circle
will be greater than expected under the null.r
at each location."im") whose pixel values
are the values of the (profile) Likelihood Ratio Test Statistic at each
spatial location.scanLRTS is a pixel image
on a larger window than the original window of X.
The expanded window contains the centre of any circle
of radius r
that has nonempty intersection with the original window.u,
the Likelihood Ratio Test Statistic $\Lambda(u)$
for a test of homogeneity at the location $u$, as described
below. The result is a pixel image giving the values of
$\Lambda(u)$ at each pixel. The maximum value of $\Lambda(u)$ over all locations
$u$ is the scan statistic, which is the basis of
the scan test performed by scan.test.
method="poisson"then the test statistic is based on Poisson
likelihood.
The datasetXis treated as an unmarked point pattern.
By default (ifbaselineis not specified)
the null hypothesis is complete spatial randomness CSR
(i.e. a uniform Poisson process).
At the spatial location$u$,
the alternative hypothesis is a Poisson process with
one intensity$\beta_1$inside the circle of radiusrcentred at$u$,
and another intensity$\beta_0$outside the
circle.
Ifbaselineis given, then it should be a pixel image
or afunction(x,y). The null hypothesis is
an inhomogeneous Poisson process with intensity proportional
tobaseline. The alternative hypothesis is an inhomogeneous
Poisson process with intensitybeta1 * baselineinside the circle,
andbeta0 * baselineoutside the circle.method="binomial"then the test statistic is based on
binomial likelihood.
The datasetXmust be a bivariate point pattern,
i.e. a multitype point pattern with two types.
The null hypothesis is that all permutations of the type labels are
equally likely.
The alternative hypothesis is that the circle of radiusrcentred at$u$has a higher proportion of points of the second type,
than expected under the null hypothesis. If r is a vector of more than one value for the radius,
then the calculations described above are performed for
every value of r. Then the maximum over r is taken
for each spatial location $u$.
The resulting pixel value of scanLRTS at a location
$u$ is the profile maximum of the Likelihood Ratio Test Statistic,
that is, the maximum of the
Likelihood Ratio Test Statistic for circles of all radii,
centred at the same location $u$.
If you have already performed a scan test using
scan.test, the Likelihood Ratio Test Statistic
can be extracted from the test result using the
function as.im.scan.test.
scan.test,
as.im.scan.testplot(scanLRTS(redwood, 0.1, method="poisson"))
sc <- scanLRTS(chorley, 1, method="binomial", case="larynx")
plot(sc)
scanstatchorley <- max(sc)Run the code above in your browser using DataLab