Lorenz and funnel plots

Two plots for results that are plain data frames rather than classed objects. plot_lorenz() draws the Lorenz curve of a vector (or of lorenz's output) with the Gini coefficient in the title. plot_funnel() draws every area's ratio of observed to expected against its expected count, inside the control limits of funnel_limits, the standard small-area funnel plot. Use the Lorenz plot to show how concentrated a total is across units, and the funnel plot to judge which areas' rates differ from the target by more than chance would allow given their size.

Usage

plot_lorenz(x, ..., main = NULL, col = NULL, palette = NULL)

plot_funnel(
  observed,
  expected,
  area = NULL,
  levels = c(0.95, 0.998),
  target = 1,
  ...,
  main = NULL,
  col = NULL,
  palette = NULL
)

Arguments

x

For plot_lorenz(), a numeric vector of non-negative values (one per unit), or the data frame lorenz() returns (columns population and value).

main, col, palette, ...

As in plot-methods: the title, colours overriding the palette, a bricklayer_palette name, and arguments passed to plot().

observed, expected

Numeric vectors of observed and expected counts per area, the same length; observed non-negative, expected positive.

area

Optional vector of labels, one per area, drawn for the areas outside the limits. Default NULL.

levels

Numeric vector of control-limit levels strictly between 0 and 1, as in funnel_limits; default c(0.95, 0.998) (about two and three standard deviations).

target

Numeric scalar, the ratio the limits are drawn around; default 1 (observed equals expected).

Value

The data drawn, invisibly. plot_lorenz(): a data frame with population and value, starting at the origin. plot_funnel(): a data frame with area, observed, expected, ratio and outside (logical, outside the widest limits).

Details

plot_lorenz(): from a numeric vector the curve is computed by lorenz and the title carries gini; a data frame is used as given (sorted, with the origin added when missing) and the title has no Gini. The dashed diagonal is perfect equality.

plot_funnel(): each area's ratio observed / expected is drawn against its expected count. The limits are exact Poisson quantiles around target, computed by funnel_limits at the expected counts present: the widest level is drawn solid, the others dashed. A point outside the widest limits is coloured and, with area, labelled.

Errors: plot_lorenz() given a data frame whose columns are not cumulative shares in \([0, 1]\) that never decrease, or invalid values for lorenz; plot_funnel() given negative or non-finite counts, an expected count of zero or less, observed and expected of different lengths, area of another length, levels outside (0, 1), or a target that is not one positive number. Both draw on the current device.

Examples

plot_lorenz(c(1, 1, 2, 3, 5, 8, 13))

plot_funnel(observed = c(4, 20, 50, 9), expected = c(5, 22, 40, 20),
            area = c("a", "b", "c", "d"))


# a funnel with one area well above expectation, around a target of 1
set.seed(4)
e <- c(5, 10, 20, 40, 80, 160)
o <- rpois(6, e)
o[5] <- 130
fd <- plot_funnel(o, e, area = LETTERS[1:6], levels = 0.95)

fd[fd$outside, ]
#>   area observed expected ratio outside
#> 5    E      130       80 1.625    TRUE

# a curve from lorenz(), styled
plot_lorenz(lorenz(c(rep(1, 50), rep(10, 5), 200)), col = "darkred",
            main = "Placements per person")


# a hand-made frame must be cumulative shares
try(plot_lorenz(data.frame(population = c(0, 0.5, 1), value = c(0, 0.8, 0.5))))
#> Error : `x` must be a Lorenz frame: cumulative population and value shares in [0, 1], both non-decreasing