# relrisk

0th

Percentile

##### 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 cross-validated kernel smoothing.

Keywords
methods, smooth, spatial
##### Usage
relrisk(X, sigma = NULL, ..., varcov = NULL, at = "pixels")
##### 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 to density.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 of X (at="points").
##### Details

If X is a multitype point pattern with $m > 2$ types, 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 X consists of only two types of points, then 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 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 (if at="pixels") or a vector of probabilities (if at="points").

If X consists of more than two types of points, the result is:

• (ifat="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.
• (ifat="points") a matrix of probabilities, with rows corresponding to data points$x_i$, and columns corresponding to types$j$.

##### References

Diggle, P.J. (2003) Statistical analysis of spatial point patterns, Second edition. Arnold.

bw.relrisk, density.ppp, smooth.ppp

• relrisk
##### Examples
data(urkiola)
p <- relrisk(urkiola, 20)
plot(p, main="proportion of oak")
Documentation reproduced from package spatstat, version 1.21-0, License: GPL (>= 2)

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