pairwise_overlap: Feasibility of all Pairwise Ellipse Overlaps

Description

Determin if pairs of ellipses intersect non-emptily..

Usage

pairwise_overlap(ell, ...)

Arguments

ell

a list of at least two (non degenerate) ellipses; see wrangle_ellipse.

...

additional arguments to be passed to the low level funcitons.

Value

The pairwise_overlap function returns an object of class "pairwise_overlap" with the following components:

intersection

a data.frame where the two first columns specify the two ellipses intersected and the last coloumn indicate if they have a non-empty intersection.

call

the matched call.

Details

The pairwise_overlap functions goes through all pairs of ellipses from ell and checks if their intersection is non-empty.

Note that if all pairs of ellipses intersect this does not mean that the intersection of all the ellipses is non-empty. The example below is constructed to illustrate this.

Examples

Run this code

# NOT RUN {
## three different two dimensional ellipses
e1 <- list(c = c(0, 0.7), P = matrix(c(0.2, 0, 0, 3), ncol = 2), r = 0.5)
e2 <- list(c = c(0, 1), P = matrix(c(3, -1.5, -1.5, 1), ncol = 2), r = 1)
e3 <- list(c = c(1.5, 1), P = matrix(c(3, 1.2, 1.2, 1), ncol = 2), r = 1.2)
# Note: These ellipses have been chosen so all pairs intersect,
#       but the intersection of all three is empty.

# test pairwise overlaps
pairwise_overlap(list(e1, e2, e3))

## regression example
# generate data
n <- 100
E <- rbinom(n, 2, 0.5)
X <- rnorm(n, 3 * E, 1)
Y <- rnorm(n, 2 + 1.5 * E, 1)
m0 <- lm(Y ~ X, data = data.frame(Y,X), subset = (E == 0))
m1 <- lm(Y ~ X, data = data.frame(Y,X), subset = (E == 1))
m2 <- lm(Y ~ X, data = data.frame(Y,X), subset = (E == 2))

# create 95% confidence ellipses and check pairwise intersection
q <- qchisq(0.95, 2) # df = 2, as there are two covariates (1, X)
E0 <- list(c = coefficients(m0), S = vcov(m0), r = q)
E1 <- list(c = coefficients(m1), S = vcov(m1), r = q)
E2 <- list(c = coefficients(m2), S = vcov(m2), r = q)
pairwise_overlap(list("model 0" = E0, "model 1" = E1, "model 2" = E2))

# }