spatstat (version 1.21-0)

bw.relrisk: Cross Validated Bandwidth Selection for Relative Risk Estimation

Description

Uses cross-validation to select a smoothing bandwidth for the estimation of relative risk.

Usage

bw.relrisk(X, method = "likelihood", nh = 32)

Arguments

X

A multitype point pattern (object of class "ppp" which has factor valued marks).

method

Character string determining the cross-validation method. Current options are "likelihood", "leastsquares" or "weightedleastsquares".

nh

Number of trial values of smoothing bandwith sigma to consider.

Value

• A numerical value giving the selected bandwidth. The result also belongs to the class "bw.relrisk".

Details

This function selects an appropriate bandwidth for the nonparametric estimation of relative risk using relrisk. Consider the indicators $y_{ij}$ which equal $1$ when data point $x_i$ belongs to type $j$, and equal $0$ otherwise. For a particular value of smoothing bandwidth, let $\hat p_j(u)$ be the estimated probabilities that a point at location $u$ will belong to type $j$. Then the bandwidth is chosen to minimise either the likelihood, the squared error, or the approximately standardised squared error, of the indicators $y_{ij}$ relative to the fitted values $\hat p_j(x_i)$. See Diggle (2003).

The result is a numerical value giving the selected bandwidth sigma. The result also belongs to the class "bw.relrisk" allowing it to be printed and plotted. The plot shows the cross-validation criterion as a function of bandwidth.

References

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

See Also

relrisk

Examples

data(urkiola)
  b <- bw.relrisk(urkiola)
  b
  plot(b)