Lorenz and funnel plots

Two plots for results that are plain data frames rather than classed objects. plotlrnz() draws the Lorenz curve of a vector (or of lorenzc's output) with the Gini coefficient in the title. plotfnl() draws every area's ratio of observed to expected against its expected count, inside the control limits of fnllim, 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

plotlrnz(x, ..., main = NULL, col = NULL, pal = NULL)

plotfnl(
  obs,
  expd,
  area = NULL,
  lvls = c(0.95, 0.998),
  target = 1,
  ...,
  main = NULL,
  col = NULL,
  pal = NULL
)

Arguments

x

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

main, col, pal, ...

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

obs, expd

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.

lvls

Numeric vector of control-limit levels strictly between 0 and 1, as in fnllim; 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. plotlrnz(): a data frame with population and value, starting at the origin. plotfnl(): a data frame with area, observed, expected, ratio and outside (logical, outside the widest limits).

Details

plotlrnz(): from a numeric vector the curve is computed with lorenzc, and the title carries ginicoef; 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.

plotfnl(): each area's ratio observed / expected is drawn against its expected count. The limits are exact Poisson quantiles around target, computed by fnllim 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: plotlrnz() given a data frame whose columns are not cumulative shares in \([0, 1]\) that never decrease, or invalid values for lorenzc; plotfnl() 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

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

plotfnl(obs = c(4, 20, 50, 9), expd = 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 <- plotfnl(o, e, area = LETTERS[1:6], lvls = 0.95)

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

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


# a hand-made frame must be cumulative shares
try(plotlrnz(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