marginal_overlap: Feasibility of all Marginal Ellipse Overlaps
In fellov: Feasible Ellipse Overlap

Description Usage Arguments Details Value See Also Examples

View source: R/marginal_overlap.R

Determin if the projections of ellipses onto each margin overlap.

1	marginal_overlap(ell, margins = "all")

`ell`	a list of at least two (non degenerate) ellipses; see `wrangle_ellipse`.
`margins`	either "all" or a vector indicating the margins to project the ellipses onto and take intersections.

The ellipses are projected onto the specified margins. For each margin the intersection of the projected ellipses is found. The Lower and Upper endpoints of the intersection interval is reported. If the intersection along a margin is empty then Lower and Upper is reported as NA.

Note that if the ellipses overlap when projected onto each margin this does not imply that the ellipses themselves intersect non-emptily. The example below is constructed to illustrate this.

marginal_overlap returns an object of class "marginal_overlap" which contains a data.frame where the coloumns descibe the following

`Margin`	Intputted `margins`.
`Overlap`	Whether the ellipses overlap when projected onto corresponding margin.
`Lower`	Lower endpoint of intersection interval. `NA` if the intersection is empty.
`Upper`	Upper endpoint of intersection interval. `NA` if the intersection is empty.

wrangle_ellipse for detailed on ellipse parameterization.

## two dimensional ellipses
e1 <- list(c = c(0.1, 0), P = matrix(c(3, 0, 0, 1), ncol = 2), r = 1)
e2 <- list(c = c(1, 1), P = matrix(c(3, 1.2, 1.2, 1), ncol = 2), r = 0.8)
e3 <- list(c = c(2, 1.5), P = matrix(c(1, 0.6, 0.6, 1), ncol = 2), r = 0.4)
# Note: These three ellipses have been chosen so (some of) the marginal
#       projections intersect, but the actual ellipses do not intersect.

# Ellipses e1 and e2 overlap when projected onto margin 1 and 2 respectivly.
marginal_overlap(list(e1, e2))

# Adding ellipse e3:
# Then there is no overlap when projecting onto margin 1
marginal_overlap(list(e1, e2, e3), margins = c(1))


## regression example
n <- 100
E <- rbinom(n, 1, 0.5)
X <- rnorm(n, E * 3, 1)
Y <- rnorm(n, 2 + X, 1)
lm_E0 <- lm(Y ~ X, data = data.frame(Y, X), subset = (E == 0))
lm_E1 <- lm(Y ~ X, data = data.frame(Y, X), subset = (E == 1))

# create 95% confidence ellipses and check marginal overlap
q <- qchisq(0.95, 2) # df = 2, as there are two covariates (1, X)
ell0 <- list(c = coefficients(lm_E0), S = vcov(lm_E0), r = q)
ell1 <- list(c = coefficients(lm_E1), S = vcov(lm_E1), r = q)
marginal_overlap(list(ell0, ell1))