Polarisation index

Computes the Wolfson bipolarisation index, which measures the extent to which a distribution is bimodal (clustering at the tails) rather than unimodal. Higher values indicate more polarisation.

Usage

iq_polarisation(
  x,
  weights = NULL,
  na.rm = FALSE,
  ci = FALSE,
  R = 1000L,
  level = 0.95,
  negatives = c("error", "keep")
)

Arguments

x

Numeric vector of incomes.

weights

Optional numeric vector of survey weights.

na.rm

Logical. Remove NA values? Default FALSE.

ci

Logical. Compute bootstrap confidence intervals? Default FALSE.

R

Integer. Number of bootstrap replicates. Default 1000.

level

Numeric. Confidence level. Default 0.95.

negatives

Character. "error" (default) aborts on negatives; "keep" permits them.

Value

An S3 object of class "iq_polarisation" with elements:

wolfson

Numeric. The Wolfson polarisation index.

gini

Numeric. The Gini coefficient.

median

Numeric. The weighted median income.

mean

Numeric. The weighted mean income.

n

Integer. Number of observations.

se, ci_lower, ci_upper, level

Bootstrap CI fields, NULL unless ci = TRUE.

References

Wolfson, M. C. (1994). "When Inequalities Diverge." American Economic Review, 84(2), 353–358.

Foster, J. E. and Wolfson, M. C. (2010). "Polarization and the Decline of the Middle Class: Canada and the US." Journal of Economic Inequality, 8(2), 247–273.

Examples

d <- iq_sample_data("income")
iq_polarisation(d$income)
#> 
#> ── Polarisation ────────────────────────────────────────────────────────────────
#> • Wolfson index: 0.1988
#> • Gini: 0.43
#> • Median income: 35934.96
#> • Mean income: 49190.12
#> • Observations: 1000

# With bootstrap CIs
iq_polarisation(d$income, ci = TRUE, R = 200)
#> 
#> ── Polarisation ────────────────────────────────────────────────────────────────
#> • Wolfson index: 0.1988
#> • Gini: 0.43
#> • Median income: 35934.96
#> • Mean income: 49190.12
#> • Observations: 1000
#> • Bootstrap 95% CI: [0.1862, 0.2174]