R: Modified envelope of K12hat from random toroidal shifts of...

Kenv.tor1 {splancs} | R Documentation

## Modified envelope of K12hat from random toroidal shifts of two point patterns

### Description

Modification of `Kenv.tor()` to allow the assignment of a p value to the goodness of fit, following the method outlined in Peter Diggle's 1986 paper (J Neurosci methods 18:115-125) and in his 2002 book.

### Usage

    Kenv.tor1(pts1, pts2, poly, nsim, s, quiet = FALSE)

### Arguments

`pts1` | First point data set
`pts2` | Second point data set
`poly` | Polygon containing the points
`nsim` | Number of random toroidal shifts to do
`s` | Vector of distances at which to calculate the envelope
`quiet` | If FALSE, print a message after every simulation for progress monitoring. If TRUE, print no messages

### Value

A list with components: `$upper`, `$lower`, `real`, `u`, `ksim`, and `rank`. The first three components are vectors like `s`, the next two contain results passed back from the simulations, and the final is a one-element vector with the rank of the observed data set.

### Author(s)

Stephen Eglen <stephen@inf.ed.ac.uk>

### See Also

`Kenv.tor`

### Examples

    data(amacrines)
    ama.a <- rbind(amacrines.on, amacrines.off)
    ama.bb <- bboxx(bbox(as.points(ama.a)))
    ama.t <- seq(from = 0.002, to=.250, by=0.002)
    nsim=999
    plot(amacrines.on, asp=1, pch=19,
     main="Data set, match figure 1.4 of Diggle(2002)?")
    points(amacrines.off, pch=1)
    #
    k12 <- k12hat(amacrines.on, amacrines.off, ama.bb, ama.t)
    #
    k11 <- khat(amacrines.on, ama.bb, ama.t)
    k22 <- khat(amacrines.off, ama.bb, ama.t)
    k00 <- khat(ama.a, ama.bb, ama.t)
    theor <- pi * (ama.t^2)
    #
    plot(ama.t, k12-theor, ylim=c(min( c(k12, k11, k22, k00) - theor),
     max( c(k12, k11, k22, k00) - theor)),
     main="2nd order properties, match figure 4.8 of Diggle (2002)", type="l")
    lines(ama.t, -theor)
    lines(ama.t, k11-theor, lty=2)
    lines(ama.t, k22-theor, lty=3)
    lines(ama.t, k00-theor, lty=5)
    #
    k12.tor <- Kenv.tor(amacrines.on, amacrines.off, ama.bb,
     nsim, ama.t, quiet=TRUE)
    plot(ama.t, k12-theor, type="l", main="Output from Kenv.tor")
    lines(ama.t, k12.tor$upper-theor, type="l", col="red")
    lines(ama.t, k12.tor$lower-theor, type="l", col="red")
    #
    k12.sims <- Kenv.tor1(amacrines.on, amacrines.off, ama.bb,
     nsim, ama.t, quiet=TRUE)
    plot(ama.t, sqrt(k12.sims$real/pi), type="l", asp=1, bty="n",
     main=paste("K12 versus toroidal sims; rank ", k12.sims$rank, "of",
     length(k12.sims$u)))
    lines(ama.t, sqrt(k12.sims$upper/pi), col="red")
    lines(ama.t, sqrt(k12.sims$lower/pi), col="red")

[Package splancs version 2.01-40 Index]