smacpod (version 2.6)

kdest: Difference of estimated K functions

Description

kdest computes the difference in estimated K functions for a set of cases and controls, with KD(r) = K_case(r) - K_control(r) denoting the estimated difference at distance r. If nsim > 0, then pointwise tolerance envelopes for KD(r) are constructed under the random labeling hypothesis for each distance r. The summary function can be used to determine the distances for which KD(r) is above or below the tolerance envelopes. The plot function will plot KD(r) versus r, along with the tolerance envelopes, the min/max envelopes of KD(r) simulated under the random labeling hypothesis, and the average KD(r) under the random labeling hypothesis.

Usage

kdest(
  x,
  case = 2,
  nsim = 0,
  level = 0.95,
  r = NULL,
  rmax = NULL,
  breaks = NULL,
  correction = c("border", "isotropic", "Ripley", "translate"),
  nlarge = 3000,
  domain = NULL,
  var.approx = FALSE,
  ratio = FALSE
)

Value

Returns a kdenv object. See documentation for Kest.

Arguments

x

A ppp object package with marks for the case and control groups. x$marks is assumed to be a factor. Automatic conversion is attempted if it is not.

case

The name of the desired "case" group in levels(x$marks). Alternatively, the position of the name of the "case" group in levels(x$marks). Since we don't know the group names, the default is 2, the second position of levels(x$marks). x$marks is assumed to be a factor. Automatic conversion is attempted if it is not.

nsim

The number of simulated data sets from which to construct tolerance envelopes under the random labeling hypothesis. The default is 0 (i.e., no envelopes).

level

The level of the tolerance envelopes.

r

Optional. Vector of values for the argument \(r\) at which \(K(r)\) should be evaluated. Users are advised not to specify this argument; there is a sensible default. If necessary, specify rmax.

rmax

Optional. Maximum desired value of the argument \(r\).

breaks

This argument is for internal use only.

correction

Optional. A character vector containing any selection of the options "none", "border", "bord.modif", "isotropic", "Ripley", "translate", "translation", "rigid", "none", "periodic", "good" or "best". It specifies the edge correction(s) to be applied. Alternatively correction="all" selects all options.

nlarge

Optional. Efficiency threshold. If the number of points exceeds nlarge, then only the border correction will be computed (by default), using a fast algorithm.

domain

Optional. Calculations will be restricted to this subset of the window. See Details.

var.approx

Logical. If TRUE, the approximate variance of \(\hat K(r)\) under CSR will also be computed.

ratio

Logical. If TRUE, the numerator and denominator of each edge-corrected estimate will also be saved, for use in analysing replicated point patterns.

Author

Joshua French

Details

This function relies internally on the Kest and eval.fv functions. The arguments are essentially the same as the Kest function, and the user is referred there for more details about the various arguments.

References

Waller, L.A. and Gotway, C.A. (2005). Applied Spatial Statistics for Public Health Data. Hoboken, NJ: Wiley.

See Also

Kest, eval.fv

Examples

data(grave)
# estimate and plot KD(r)
kd1 = kdest(grave, case = "affected")
plot(kd1, iso ~ r, ylab = "difference", legend = FALSE, main = "")
kd2 = kdest(grave, case = 2, nsim = 9, level = 0.8)
kd2 # print object
summary(kd2) # summarize distances KD(r) outside envelopes
plot(kd2)
# manually add legend
legend("bottomright", legend = c("obs", "avg", "max/min env", "95% env"),
       lty = c(1, 2, 1, 2), col = c("black", "red", "darkgrey", "lightgrey"),
       lwd = c(1, 1, 10, 10))