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CPS1866 Milica Maricic et al.
as suggested by De Bin and associates (2016), and for the number of bootstrap
iterations we choose 500. The second step is to choose weight bounds. Herein,
we chose minimum and maximum bootstrap CIDI weight. Finally, the
optimization problem is solved using the enhanced Scatter Search
metaheuristics (Egea et al., 2009). For more details regarding the eSS-CIDI
please consult Maricic (2018).
The eSS-CIDI is therefore a data-driven approach for devising weights
which is based on acknowledged statistical and optimization methods. So far,
the eSS-CIDI was used to devise a weighting scheme of a novel composite
indicator. Maricic (2018) used the approach in the creation of a European Index
of Life Satisfaction (EILS). Herein we aim to extend the application of the
method to its use in dimension reduction.

4. Results
The dataset needed for the analysis contained all 21 indicator values for
154 countries for the year 2016. The dataset is available online on the official
website of the SSI (Sustainable Society Foundation, 2018). The dataset was
originally normalised, so the next step in our analysis was to inspect whether
all the indicators correlate positively with the I-distance. Namely, if some
indicators correlate negatively with the final value of the I-distance that
indicates that their direction should be changed and that reciprocated values
of the indicator should be used. In our case, five variables correlated
negatively: Energy Use (-0.671), Greenhouse Gasses (-0.616), Consumption (-
0.587), Renewable Energy (-0.460) and Public Debt (-0.028). Therefore, prior to
conducting the eSS-CIDI approach we computed the reciprocated values of
the above listed indicators.
The first step in the eSS-CIDI algorithm is the bootstrap CIDI. We
performed 500 bootstrap replications with the sample size of 97 as


154 0.632 97.328 97 . The obtained results are given in Table 2. The

bootstrap CIDI intervals suggest to give more importance to indicators
Sufficient Food, Sufficient to Drink, Safe Sanitation, Education, Healthy life,
Gender Equality, Population Growth, Good Governance, GDP. In cases of other
indicators, they suggest lower weights or the bootstrap interval covers the
official weight. It is of interest to observe that the lower bound of three
indicators is 0 - Renewable Water Resources, Employment and Public Debt.
This could indicate that these indicators might not be valuable for the ranking
process and in some bootstrap samples they were insignificant. In the final
step, the optimization model was solved using eSS.
The optimal weighting scheme suggested by the eSS-CIDI approach is
given in Table 2 and it provides interesting insights. Firstly, several indicators
have been awarded with visibly higher weights than the official ones (e.g.
Good Governance from 3.70% to 8.2%), while some were given visibly lower

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