The Theil index (TI) is a relative measure of inequality that considers all population subgroups. Subgroups are weighted according to their population share.
Arguments
- est
The subgroup estimate. Estimates must be available for at least 85% of subgroups.
- se
The standard error of the subgroup estimate. If this is missing, 95% confidence intervals cannot be calculated.
- pop
The number of people within each subgroup.Population size must be available for all subgroups.
- conf.level
Confidence level of the interval. Default is 0.95 (95%).
- force
TRUE/FALSE statement to force calculation when more than 85% of subgroup estimates are missing.
- ...
Further arguments passed to or from other methods.
Value
The estimated TI value, corresponding estimated standard error,
and confidence interval as a data.frame.
Details
TI measures the extent to which the shares of the population and shares of the health indicator differ across subgroups, weighted by shares of the health indicator. TI is calculated as the sum of products of the natural logarithm of the share of the indicator of each subgroup, the share of the indicator of each subgroup and the population share of each subgroup. TI may be easily interpreted when multiplied by 1000. For more information on this inequality measure see Schlotheuber (2022) below.
Interpretation: TI is 0 if there is no inequality. Greater absolute values indicate higher levels of inequality. TI is more sensitive to differences further from the setting average (by the use of the logarithm). TI has no unit.
Type of summary measure: Complex; relative; weighted
Applicability: Non-ordered dimensions of inequality with more than two subgroups
Warning: The confidence intervals are approximate and might be biased. See Ahn (2018) below for further information on the standard error formula.
References
Schlotheuber, A, Hosseinpoor, AR. Summary measures of health inequality: A review of existing measures and their application. Int J Environ Res Public Health. 2022;19(6):3697. doi:10.3390/ijerph19063697.
Ahn J, Harper S, Yu M, Feuer EJ, Liu B, Luta G. Variance estimation and confidence intervals for 11 commonly used health disparity measures. JCO Clin Cancer Inform. 2018;2:1-19. doi:10.1200/CCI.18.00031.
Examples
# example code
data(NonorderedSample)
head(NonorderedSample)
#> indicator dimension
#> 1 Births attended by skilled health personnel (%) Subnational region
#> 2 Births attended by skilled health personnel (%) Subnational region
#> 3 Births attended by skilled health personnel (%) Subnational region
#> 4 Births attended by skilled health personnel (%) Subnational region
#> 5 Births attended by skilled health personnel (%) Subnational region
#> 6 Births attended by skilled health personnel (%) Subnational region
#> subgroup estimate se population setting_average
#> 1 aceh 95.11784 1.5384434 230.20508 91.59669
#> 2 bali 100.00000 0.0000000 149.46272 91.59669
#> 3 bangka balitung 97.41001 1.2676437 55.66533 91.59669
#> 4 banten 80.35694 3.5440531 451.26550 91.59669
#> 5 bengkulu 94.25756 2.7740061 70.17540 91.59669
#> 6 central java 98.56168 0.6476116 1221.94446 91.59669
#> favourable_indicator ordered_dimension indicator_scale reference_subgroup
#> 1 1 0 100 1
#> 2 1 0 100 0
#> 3 1 0 100 0
#> 4 1 0 100 0
#> 5 1 0 100 0
#> 6 1 0 100 0
with(NonorderedSample,
ti(est = estimate,
se = se,
pop = population))
#> measure estimate se lowerci upperci
#> 1 ti 3.143872 0.000623933 3.142649 3.145095