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 dataset X is treated as an unmarked point pattern.
By default (if baseline is 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 $beta1$ inside the circle of radius
r centred at $u$,
and another intensity $beta0$ outside the
circle.
If baseline is given, then it should be a pixel image
or a function(x,y). The null hypothesis is
an inhomogeneous Poisson process with intensity proportional
to baseline. The alternative hypothesis is an inhomogeneous
Poisson process with intensity
beta1 * baseline inside the circle,
and beta0 * baseline outside the circle.
method="binomial" then the test statistic is based on
binomial likelihood.
The dataset X must 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 radius
r centred 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.test
plot(scanLRTS(redwood, 0.1, method="poisson"))
sc <- scanLRTS(chorley, 1, method="binomial", case="larynx")
plot(sc)
scanstatchorley <- max(sc)
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