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Inequality Measurement in DCEA

Overview

dceasimR provides five inequality measures commonly used in DCEA: SII, RII, concentration index, Atkinson index, and Gini coefficient.

df <- tibble::tibble(
  group      = 1:5,
  mean_hale  = c(52.1, 56.3, 59.8, 63.2, 66.8),
  pop_share  = rep(0.2, 5)
)

Slope Index of Inequality (SII)

The SII estimates the absolute health difference from the most to the least deprived using a weighted regression on ridit scores.

calc_sii(df, "mean_hale", "group", "pop_share")
#> $sii
#> [1] 18.15
#> 
#> $rii
#> [1] 0.304326
#> 
#> $se_sii
#> [1] 0.4112988
#> 
#> $p_value
#> [1] 2.561597e-05
#> 
#> $model
#> 
#> Call:
#> stats::lm(formula = h ~ ridit, weights = w)
#> 
#> Coefficients:
#> (Intercept)        ridit  
#>       50.57        18.15

A positive SII means better health in more advantaged groups.

Relative Index of Inequality (RII)

The RII expresses the SII relative to mean health, facilitating comparisons across populations and time.

calc_rii(df, "mean_hale", "group", "pop_share")
#> $sii
#> [1] 18.15
#> 
#> $rii
#> [1] 0.304326
#> 
#> $se_sii
#> [1] 0.4112988
#> 
#> $p_value
#> [1] 2.561597e-05
#> 
#> $model
#> 
#> Call:
#> stats::lm(formula = h ~ ridit, weights = w)
#> 
#> Coefficients:
#> (Intercept)        ridit  
#>       50.57        18.15  
#> 
#> 
#> $se_rii
#> [1] 0.006896357

Concentration Index

calc_concentration_index(df, "mean_hale", "group", "pop_share",
                          type = "standard")
#> $ci
#> [1] 0.04869215
#> 
#> $se
#> [1] NA
#> 
#> $type
#> [1] "standard"

Atkinson Index

calc_atkinson_index(df$mean_hale, df$pop_share, epsilon = 1)
#> [1] 0.003744955

Gini Coefficient

calc_gini(df$mean_hale, df$pop_share)
#> [1] 0.04869215

All indices at once

calc_all_inequality_indices(df, "mean_hale", "group", "pop_share",
                             epsilon_values = c(0.5, 1, 2))
#> # A tibble: 7 × 3
#>   index                   value description                   
#>   <chr>                   <dbl> <chr>                         
#> 1 sii                  18.1     Slope Index of Inequality     
#> 2 rii                   0.304   Relative Index of Inequality  
#> 3 concentration_index   0.0487  Concentration Index (standard)
#> 4 gini                  0.0487  Gini coefficient              
#> 5 atkinson_epsilon_0.5  0.00187 Atkinson index (epsilon = 0.5)
#> 6 atkinson_epsilon_1    0.00374 Atkinson index (epsilon = 1)  
#> 7 atkinson_epsilon_2    0.00751 Atkinson index (epsilon = 2)

Lorenz curves

ld <- compute_lorenz_data(df$mean_hale, df$pop_share, "England 2019")
library(ggplot2)
ggplot(ld, aes(cum_pop, cum_health)) +
  geom_line(colour = "steelblue", linewidth = 1) +
  geom_abline(linetype = "dashed") +
  labs(x = "Cumulative population", y = "Cumulative health",
       title = "Lorenz Curve") +
  theme_minimal()

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.