The relative index of inequality (RII) is a relative measure of inequality that represents the ratio of estimated indicator values between the most-advantaged and most-disadvantaged, while taking into consideration the situation in all other subgroups/individuals – using an appropriate regression model. 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.
Usage
rii(
est,
subgroup_order,
pop = NULL,
scaleval = NULL,
weight = NULL,
psu = NULL,
fpc = NULL,
strata = 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
The number of people within each subgroup (for disaggregated data). Population size must be available for all subgroups.
- scaleval
The scale of the indicator. For example, the scale of an indicator measured as a percentage is 100. The scale of an indicator measured as a rate per 1000 population is 1000.
- weight
Individual sampling weight (required if data come from a survey)
- psu
Primary sampling unit (required if data come from a survey)
- fpc
Finite population correction (if data come from a survey and sample size is large relative to population size).
- strata
Strata (required if data come from a survey)
- 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 for RII estimation (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
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 population of each subgroup is then considered in terms of its range in the cumulative population distribution, and the midpoint of this range. The indicator of interest is then regressed against this midpoint value using an appropriate regression model (e.g., a generalized linear model with logit link), and the predicted values of the indicator are calculated for the two extremes (rank 1 and rank 0). The ratio between the estimated values at rank 1 and rank 0 (covering the entire distribution) generates the RII value. For more information on this inequality measure see Schlotheuber, A., & Hosseinpoor, A. R. (2022) below.
Interpretation: RII has the value of one if there is no inequality. RII has only positive values. Greater absolute values indicate higher levels of inequality. The further the value of RII from one, the higher the level of inequality. For favourable indicators, values larger than one indicate a concentration of the indicator among the advantaged and values smaller than one indicate a concentration of the indicator among the disadvantaged. For adverse indicators, values larger than one indicate a concentration of the indicator among the disadvantaged and values smaller than one indicate a concentration of the indicator among the advantaged. RII is a multiplicative measure and has to be displayed on a logarithmic scale (values larger than one are equivalent in magnitude to their reciprocal values smaller than one, 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; more than two subgroups
Warning: The confidence intervals are approximate and might be biased.
References
Schlotheuber, A., & Hosseinpoor, A. R. (2022). Summary measures of health inequality: A review of existing measures and their application. International journal of environmental research and public health, 19 (6), 3697.
Examples
# example code
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