# Modified envelope of K12hat from random toroidal shifts of two point patterns 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. ```r 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 ## Returns 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 ## See Also `Kenv.tor` ## Examples ```r 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") ```

Kenv.tor1 function