relrisk
Nonparametric Estimate of Spatially-Varying Relative Risk
Given a multitype point pattern, this function estimates the spatially-varying probability of each type of point, using kernel smoothing. The default smoothing bandwidth is selected by cross-validation.
Usage
relrisk(X, sigma = NULL, ..., varcov = NULL, at = "pixels", casecontrol=TRUE)
Arguments
- X
- A multitype point pattern (object of class
"ppp"
which has factor valued marks). - sigma
- Optional. Standard deviation of isotropic Gaussian smoothing kernel.
- ...
- Arguments passed to
bw.relrisk
to select the bandwidth, or passed todensity.ppp
to control the pixel resolution. - varcov
- Optional. Variance-covariance matrix of anisotopic Gaussian
smoothing kernel. Incompatible with
sigma
. - at
- String specifying whether to compute the probability values
at a grid of pixel locations (
at="pixels"
) or only at the points ofX
(at="points"
). - casecontrol
- Logical. Whether to treat a bivariate point pattern as consisting of cases and controls. See Details.
Details
If X
is a bivariate point pattern
(a multitype point pattern consisting of two types of points)
then by default,
the points of the first type (the first level of marks(X)
)
are treated as controls or non-events, and points of the second type
are treated as cases or events. Then this command computes
the spatially-varying risk of an event,
i.e. the probability $p(u)$
that a point at spatial location $u$
will be a case.
If X
is a multitype point pattern with $m > 2$ types,
or if X
is a bivariate point pattern
and casecontrol=FALSE
,
then this command computes, for each type $j$,
a nonparametric estimate of
the spatially-varying risk of an event of type $j$.
This is the probability $p_j(u)$
that a point at spatial location $u$
will belong to type $j$.
If at = "pixels"
the calculation is performed for
every spatial location $u$ on a fine pixel grid, and the result
is a pixel image representing the function $p(u)$
or a list of pixel images representing the functions
$p_j(u)$ for $j = 1,\ldots,m$.
If at = "points"
the calculation is performed
only at the data points $x_i$. The result is a vector of values
$p(x_i)$ giving the estimated probability of a case
at each data point, or a matrix of values
$p_j(x_i)$ giving the estimated probability of
each possible type $j$ at each data point.
Estimation is performed by a simple Nadaraja-Watson type kernel
smoother (Diggle, 2003). If sigma
and varcov
are both missing or null, then the smoothing bandwidth sigma
is selected by cross-validation using bw.relrisk
.
Value
- If
X
consists of only two types of points, the result is a pixel image (ifat="pixels"
) or a vector of probabilities (ifat="points"
).If
X
consists of more than two types of points, the result is:- (if
at="pixels"
) a list of pixel images, with one image for each possible type of point. The result also belongs to the class"listof"
so that it can be printed and plotted. - (if
at="points"
) a matrix of probabilities, with rows corresponding to data points$x_i$, and columns corresponding to types$j$.
- (if
References
Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.
See Also
Examples
data(urkiola)
p <- relrisk(urkiola, 20)
if(interactive()) {
plot(p, main="proportion of oak")
plot(eval.im(p > 0.3), main="More than 30 percent oak")
data(lansing)
z <- relrisk(lansing)
plot(z, main="Lansing Woods")
plot(which.max.im(z), main="Most common species")
}