The relative index of inequality (RII) is a relative measure of inequality that represents the ratio of predicted values of an indicator between the most advantaged and most disadvantaged subgroups, obtained by fitting a regression model.
Usage
rii(
est,
subgroup_order,
pop = NULL,
weight = NULL,
psu = NULL,
strata = NULL,
fpc = NULL,
conf.level = 0.95,
linear = FALSE,
force = FALSE,
...
)Arguments
- est
The indicator estimate. Estimates must be available for all subgroups/individuals (unless force=TRUE).
- subgroup_order
The order of subgroups/individuals in an increasing sequence.
- pop
For disaggregated data, the number of people within each subgroup. This must be available for all subgroups.
- weight
The individual sampling weight, for individual-level data from a survey. This must be available for all individuals.
- psu
Primary sampling unit, for individual-level data from a survey.
- strata
Strata, for individual-level data from a survey.
- fpc
Finite population correction, for individual-level data from a survey where sample size is large relative to population size.
- conf.level
Confidence level of the interval. Default is 0.95 (95%).
- linear
TRUE/FALSE statement to specify the use of a linear regression model (default is logistic regression).
- force
TRUE/FALSE statement to force calculation with missing indicator estimate values.
- ...
Further arguments passed to or from other methods.
Value
The estimated RII value, corresponding estimated standard error,
and confidence interval as a data.frame.
Details
RII can be calculated using disaggregated data and individual-level data. Subgroups in disaggregated data are weighted according to their population share, while individuals are weighted by sample weight in the case of data from surveys.
To calculate RII, a weighted sample of the whole population is ranked from the most disadvantaged subgroup (at rank 0) to the most advantaged subgroup (at rank 1). This ranking is weighted, accounting for the proportional distribution of the population within each subgroup. The indicator of interest is then regressed against this relative rank using an appropriate regression model, and the predicted values of the indicator are calculated for the two extremes (rank 1 and rank 0). RII is calculated as the ratio between the predicted values at rank 1 and rank 0 (covering the entire distribution). For more information on this inequality measure see Schlotheuber (2022) below.
The default regression model used is a generalized linear model with logit link. In logistic regression, the relationship between the indicator and the subgroup rank is not assumed to be linear and, due to the logit link, the predicted values from the regression model will be bounded between 0 and 1 (which is ideal for indicators measured as percentages). Specify Linear=TRUE to use a linear regression model, which may be more appropriate for indicators without a 0-1 or 0-100% scale.
Interpretation: RII takes only positive values. RII has the value of 1 if there is no inequality. Values larger than 1 indicate the level of the indicator is higher among advantaged subgroups, and values lower than 1 indicate the level of the indicator is higher among disadvantaged subgroups. Note that this results in different interpretations for favourable and adverse indicators. RII is a multiplicative measure and therefore results should be displayed on a logarithmic scale. Values larger than 1 are equivalent in magnitude to their reciprocal values smaller than 1 (e.g. a value of 2 is equivalent in magnitude to a value of 0.5).
Type of summary measure: Complex; relative; weighted
Applicability: Ordered dimension of inequality with more than two subgroups
Warning: The confidence intervals are approximate and might be biased.
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.
Examples
# example code 1
data(IndividualSample)
head(IndividualSample)
#> id psu strata weight subgroup subgroup_order sba dtp3
#> 1 1 88 1 0.351672 Quintile 3 3 1 NA
#> 2 2 1337 38 0.431545 Quintile 1 (poorest) 1 1 1
#> 3 3 450 18 0.482483 Quintile 2 2 1 NA
#> 4 4 1692 56 0.407390 Quintile 1 (poorest) 1 0 NA
#> 5 5 752 23 1.547062 Quintile 5 (richest) 5 1 NA
#> 6 6 1033 30 2.429523 Quintile 5 (richest) 5 1 NA
#> favourable_indicator indicator_scale
#> 1 1 100
#> 2 1 100
#> 3 1 100
#> 4 1 100
#> 5 1 100
#> 6 1 100
with(IndividualSample,
rii(est = sba,
subgroup_order = subgroup_order,
weight = weight,
psu = psu,
strata = strata))
#> measure estimate se lowerci upperci
#> 1 rii 2.038107 0.03503773 1.902842 2.182987
# example code 2
data(OrderedSample)
head(OrderedSample)
#> indicator
#> 1 Births attended by skilled health personnel (%)
#> 2 Births attended by skilled health personnel (%)
#> 3 Births attended by skilled health personnel (%)
#> 4 Births attended by skilled health personnel (%)
#> 5 Births attended by skilled health personnel (%)
#> dimension subgroup subgroup_order
#> 1 Economic status (wealth quintile) Quintile 1 (poorest) 1
#> 2 Economic status (wealth quintile) Quintile 2 2
#> 3 Economic status (wealth quintile) Quintile 3 3
#> 4 Economic status (wealth quintile) Quintile 4 4
#> 5 Economic status (wealth quintile) Quintile 5 (richest) 5
#> estimate se population setting_average favourable_indicator
#> 1 75.60530 1.5996131 2072.436 91.59669 1
#> 2 91.01997 1.1351504 2112.204 91.59669 1
#> 3 96.03959 0.6461946 1983.059 91.59669 1
#> 4 97.04223 0.5676206 2052.124 91.59669 1
#> 5 99.22405 0.2237683 1884.510 91.59669 1
#> ordered_dimension indicator_scale
#> 1 1 100
#> 2 1 100
#> 3 1 100
#> 4 1 100
#> 5 1 100
with(OrderedSample,
rii(est = estimate,
subgroup_order = subgroup_order,
pop = population))
#> measure estimate se lowerci upperci
#> 1 rii 1.466089 0.04372912 1.345669 1.597286