Ellipsoids are a generalization of ellipses to higher dimensions. Herein, confidence ellipsoids refers as a three-dimensional graphical representations, plotted in the space defined by three variables in a trivariate dataset.
data(glass, package = "ConfidenceEllipse")Coordinate points
The confidence_ellipsoid function accepts
x, y and z input variables and
computes the coordinate points of the ellipsoid at the specified
confidence level conf_level.
ellipsoid <- glass %>%
confidence_ellipsoid(x = SiO2, y = Na2O, z = Fe2O3, conf_level = 0.95)
ellipsoid %>% glimpse()
#> Rows: 2,500
#> Columns: 3
#> $ x <dbl> 66.54472, 66.54472, 66.54472, 66.54472, 66.54472, 66.54472, 66.54472…
#> $ y <dbl> 12.55263, 12.55263, 12.55263, 12.55263, 12.55263, 12.55263, 12.55263…
#> $ z <dbl> 0.6815153, 0.6815153, 0.6815153, 0.6815153, 0.6815153, 0.6815153, 0.…
rgl::setupKnitr(autoprint = TRUE)
rgl::plot3d(
x = ellipsoid$x,
y = ellipsoid$y,
z = ellipsoid$z,
xlab = "SiO2 (wt.%)",
ylab = "Na2O (wt.%)",
zlab = "Fe2O3 (wt.%)",
type = "l",
radius = .05,
col = "darkgrey"
)
rgl::points3d(
x = glass$SiO2,
y = glass$Na2O,
z = glass$Fe2O3,
col = "darkred",
size = 5
)
rgl::view3d(zoom = .8)
Grouping
For grouping trivariate data, the .group_by argument can
be used if the data contains an unique grouping variable
(.group_by = NULL by default). When a grouping variable is
provided, the function will compute the ellipsoid separately for each
level of the factor. It’s important to note that the grouping variable
should be appropriately coded as a factor before passing it to the
.group_by argument.
ellipsoid_grp <- glass %>%
confidence_ellipsoid(x = SiO2, y = Na2O, z = Fe2O3, .group_by = glassType, conf_level = 0.95)
ellipsoid_grp %>% glimpse()
#> Rows: 10,000
#> Columns: 4
#> $ x <dbl> 67.31799, 67.31799, 67.31799, 67.31799, 67.31799, 67.31799, …
#> $ y <dbl> 14.51513, 14.51513, 14.51513, 14.51513, 14.51513, 14.51513, …
#> $ z <dbl> 0.1425195, 0.1425195, 0.1425195, 0.1425195, 0.1425195, 0.142…
#> $ glassType <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
rgl::setupKnitr(autoprint = TRUE)
rgl::plot3d(
x = ellipsoid_grp$x,
y = ellipsoid_grp$y,
z = ellipsoid_grp$z,
xlab = "SiO2 (wt.%)",
ylab = "Na2O (wt.%)",
zlab = "Fe2O3 (wt.%)",
type = "s",
radius = .03,
col = as.numeric(ellipsoid_grp$glassType)
)
rgl::points3d(
x = glass$SiO2,
y = glass$Na2O,
z = glass$Fe2O3,
col = as.numeric(glass$glassType),
size = 5
)
rgl::view3d(zoom = .8)