The Effect of Public Health System Performance on Child Well-Being: An Analysis Through the Construction and Selection of Composite Indicators

Abstract

Interest in child health and well-being is growing, and both are multidimensional. Composite indicators (CIs) are useful tools for analyzing their relationships. This study examines the correlation between the CI of child well-being and that of public health system performance and proposes a weighting scheme for constructing CIs. Among schemes, entropy weighting yielded the strongest correlation. Uncertainty analysis revealed that country rankings with entropy weighting are the most stable, demonstrating robust CI. Strong explanatory power indicates that the CIs correlate with GDP, validating their compatibility with a key reference variable. High discriminant power confirms that CIs provide informational diversity, helping decision-makers distinguish between countries. The analysis shows that better health system performance is associated with higher child well-being, reinforcing the role of public health systems in promoting sustainable development and child well-being.

1. Introduction

The growing interest in the search for improvements in child well-being has stimulated several studies in recent decades, especially after the declaration of the Sustainable Development Goals (SDGs) by the United Nations [1]. In particular, Goal 3 of the SDGs, which seeks to ensure healthy lives and promote well-being for individuals of all ages [2], underscores the need to evaluate well-being alongside health system performance.

Child well-being reflects key factors such as health, safety, education, social inclusion, and affection—dimensions that evolve together [3]. This conceptual framework highlights not only the need for a positive childhood today but also the need for preparation for adulthood [4,5]. Building on this foundation, there has been a notable rise in global efforts to track children’s well-being, employing systematic measures such as indicators and indices [6]. Moreover, international comparisons are particularly valuable, enabling countries to assess their own conditions over time and benchmark their progress against nations with similar contexts [7,8]. Typically, comparing these indicators aims to pinpoint where countries excel or lag, an approach prevalent in global reports evaluating progress in securing children’s rights and welfare [3]. Ultimately, assessing child well-being requires a broad array of metrics considering both status and development, alongside influences from family, school, and society.

In turn, the past few decades have seen rising demands on health systems, further intensified by international goals like the UN Sustainable Development Goals (SDGs), compelling health providers to strive for improved outcomes and greater societal benefit [9]. Therefore, assessing health system performance is pivotal for guiding policy, enhancing service quality, and fostering equitable access [10]. In this context, performance indicators play a central role in monitoring, comparing, and refining health systems across different settings [11]. Composite indicators (CIs) aggregate multiple measures into a single indicator, making it easier to convey health system performance [9,10]. Indeed, these tools help summarize complex data, highlight intervention priorities, and inform policy decisions—yet they require careful methodology to ensure accuracy and value [12].

The interplay between child well-being and public health systems can be observed through impacts on critical well-being indicators, such as those measuring quality of life, economics, and social factors [13,14]. Nonetheless, relying solely on individual indicators limits understanding, as both well-being and health systems comprise multiple measures. For example, ref. [15] stands out by examining this relationship from a multidimensional perspective using data envelopment analysis, offering evidence of a positive correlation between public health and well-being, although it does not directly measure either domain. To fully capture the complexity, both well-being and health systems require the simultaneous analysis of their many factors—a challenge that requires significant cognitive effort [16]. CIs can mitigate this issue by integrating multiple domains for a broader assessment than approaches focused on single factors [17,18]. As a result, this multidimensional focus makes CIs especially useful for understanding the intricate nature of well-being and public health systems [19].

It should be noted, however, that the construction of CIs presents some points of attention. Among them is the choice of the weighting scheme and its repercussions on scores and on the quality and reliability of the CI [20]. The possibility of weighing the sub-indicators by different methods yields CIs with different scores [21], raising doubts about which CIs best represent the relationship between well-being and the health system and whether they have satisfactory quality and reliability.

In this sense, the method used to construct CIs can influence the ability to assign importance to sub-indicators [22]. Sampling errors can affect reliability by generating estimation errors of the CI [23]. The review and development of indicators can be affected by a lack of transparency and subjectivity in decisions about aggregation methods and sub-indicator selection [16].

To overcome these difficulties, this study aims to construct CIs for child well-being and the public health system’s performance using different weighting schemes. Specifically, to assess the connection between child well-being and the public health system in low- and middle-income countries, CI selection is based on the correlation between the CI child well-being and the CI performance of the public health system. The analysis of robustness and quality of the results is done through measures of uncertainty, explanatory power, and discriminant power.

This article thereby contributes to improving the construction, selection, and validation of CIs. The process of choosing the best weighting scheme and verifying the robustness of the results helps provide a better understanding of the relationship between child well-being and the performance of the public health system, providing valuable data for managers, politicians, and society.

The article is organized as follows. After this introduction, Section 2 presents the methodology for constructing and validating CIs. Subsequently, Section 3 analyzes the robustness and quality of the results. Section 4 then displays dimensions and sub-indicators, followed by Section 5, which discusses the results. Finally, Section 6 presents the conclusions.

2. Construction of CIs: Methods Adopted

Many different methodological approaches are used to construct composite indicators (CIs), which are summary measures that combine several individual indicators. The first step is data scaling, which standardizes data (puts different types on the same scale) to a dimensionless scale, allowing consistent comparison and analysis regardless of the original values. For example, the max/min method converts data to a [0, 1] range using the following equation:

$${Sb}_{j0}={\displaystyle \frac{x_{j0}-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_{j0}\right)}{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_{j0}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_{j0}\right)}}$$

(1)

or

$${Sb}_{j0}={\displaystyle \frac{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_{j0}\right)-x_{j0}}{\mathrm{m}\mathrm{a}\mathrm{x}\left(x_{j0}\right)-\mathrm{m}\mathrm{i}\mathrm{n}\left(x_{j0}\right)}}$$

(2)

where $x_{j0}$ is the value of the sub-indicator $j$ of the unit under review 0; $\mathrm{m}\mathrm{a}\mathrm{x}\left(x_{j0}\right)$ is the highest value of the sub-indicator $j$ among the units under review 0; $\mathrm{m}\mathrm{i}\mathrm{n}\left(x_{j0}\right)$ is the lowest value of the sub-indicator $j$ among the 0 units under review.

If the sub-indicator has positive polarity, the scale transformation shown in Equation (1), in which the higher value of $x_j$ provides ${Sb}_j$ equal to 1. In the case of negative polarity, the transformation presented in Equation (2), in which the higher value of $x_j$ provides ${Sb}_j$ equal to 0.

Among the weighting schemes addressed in this study, the Benefit of the doubt (BoD) method—a technique that assigns weights to maximize each unit’s performance score—does not require data normalization [24].

However, for simplicity, the data set was normalized, allowing the application of all methods, including the BoD, which does not require such standardization. The BoD model is, by nature, invariant to positive linear transformations of the data. This means that if normalization is linear (such as Min-Max normalization), the final ranking of Decision Making Units (DMUs) usually remains stable, although efficiency scores change [24].

The choice of weighting scheme (the way importance is assigned to indicators) is the next key decision. Methods can be objective, data-driven, or subjective. Some may use expert or stakeholder opinions [25].

2.1. Equal Weighting Scheme

The use of equal weights in constructing composite indices (CIs), meaning assigning the same importance to each component indicator, is a common practice in studies of quality of life and well-being. Equal weighting is often seen as a straightforward and neutral approach, but it does not always reflect the true importance of each component indicator [25]. After adjusting the scale of the sub-indicators using Equation (1) or Equation (2), and with all weights set equally, the composite index (CI, which summarizes multiple indicators into one number) can be calculated by the arithmetic mean using the following equation:

$$CI={\displaystyle \frac{{\displaystyle {\sum }_{j=1}^n}{w}_{j0}{Sb}_{j0}}{{\displaystyle {\sum }_{j=1}^n}{w}_{j0}}}$$

(3)

where $w_{j0}$ is the corresponding weight of the sub-indicator j of the unit under review 0 and ${Sb}_{j0}$ is the normalized sub-indicator.

The weights can also be defined using other objective approaches that yield more robust and informative results than the equal-weights method [26]. However, these weighting schemes are more difficult to communicate to a broader audience [27] and can introduce additional complexities [26].

2.2. Weighting Scheme by Factor Analysis

The weights in Equation (3) can be determined by factor analysis. This method combines data and describes correlated variables in a smaller, independent set of variables, with little loss of information [28].

The objective of factor analysis is to represent a set of variables with a smaller number of factors, emphasizing their relationships. To do this, it considers the relationship between the underlying factors and the observed responses, rather than the individual responses themselves [29]. The variance of the data can be decomposed into values estimated by common and single factors [27] through:

$$\begin{gathered} x_1={\alpha }_{11}{F}_1+{\alpha }_{12}{F}_2+\cdots +{\alpha }_{1m}{F}_m+e_1 \\ {x}_2={\alpha }_{21}{F}_1+{\alpha }_{22}{F}_2+\cdots +{\alpha }_{2m}{F}_m+e_2 \\ {x}_j={\alpha }_{j1}{F}_1+{\alpha }_{j2}{F}_2+\cdots +{\alpha }_{jm}{F}_m+e_j \end{gathered}$$

(4)

where $x_j$ (j = 1,…, n) are the original values of the standardized variables with zero mean and unit variance; the factor weights related to the variable $x_j$ are represented by ${\alpha }_{j1},{\alpha }_{j2},\dots ,{\alpha }_{jm}$. The common uncorrelated factors, each with a zero mean and unit variance, are represented by $F_1, F_2,\dots ,F_m$. Finally, $e_i$ represents the specific factors Q, which are assumed to be independent and identically distributed with mean zero.

There are several approaches to deal with the method presented in Equation (4) [27]. In this study, the classical eigenvalue/eigenvector extraction method (spectral decomposition) of PCA was used, applied to the correlation matrix (in most cases) [30].

CIs favor interpretability and informational power. The use of multiple factors compromises interpretability, as it requires simultaneous analysis of all of them. In turn, conceptually significant variables tend to correlate strongly with the first factor and show weak, negligible, or even inverse correlations with other factors, indicating their unsuitability for representing the multidimensional phenomenon [31].

The factor loadings are normalized to the range 0 to 1, with a sum equal to 1. Then, these weights are applied to the normalized sub-indicators. The estimated CI values are equal to the sum of the component scores multiplied by their respective weights [30].

2.3. Entropy Weighting Scheme

Shannon entropy is a measure of uncertainty or complexity in a system [32]. The Shannon Entropy weighting mechanism ensures that each variable is assigned an objective weight that reflects its data variability [33]. The lower the variable’s uncertainty, the greater its weight in the weighting.

In the entropy weighting scheme, $m$ Indicators and $n$ samples are defined in the evaluation, and the measured value of the $j$-th indicator at $0$-th sample is recorded as ${Sb}_{jk}$. After the normalization of the sub-indicators, the entropy calculation is performed through the following equation:

$$E_j=-{\displaystyle \frac{{\displaystyle {\sum }_{k=1}^n}{p}_{j0}.\ln p_{j0}}{\ln n}}$$

(5)

and,

$$p_{j0}={\displaystyle \frac{{Sb}_{j0}}{{\displaystyle {\sum }_{k=1}^n}{Sb}_{j0}}}$$

(6)

The degree of importance and weight of each variable are defined by Equations (7) and (8), respectively:

$$I_j=1-E_j$$

(7)

and,

$$w_j={\displaystyle \frac{I_j}{{\displaystyle {\sum }_{j=1}^m}{I}_j}}$$

(8)

where ${Sb}_{j0}$ are the sub-indicators j of the unit under review 0, after the scale transformation (see Equations (1) and (2)), n is the total number of sub-indicators, m is the total number of units under analysis, E is the entropy, I is the degree of importance, and w is the weights.

2.4. Benefit of the Doubt Weighting Scheme

Benefit of the Doubt (BoD) is a method of constructing CIs based on Data Envelopment Analysis [34]. The method was proposed by [35] to evaluate macroeconomic performance and is now applied to measure other multidimensional phenomena, such as the Human Development Index [36] and social exclusion and vulnerability [37].

The method uses sub-indicators as outputs and simulates an input of 1 for all units under analysis. The focus is exclusively on aggregating the various sub-performance indicators, without explicit reference to the inputs used [38]. It measures the relationship between a unit’s performance and its benchmark performance.

In the absence of true weights, the BoD assigns each sub-indicator a weight determined by the data to construct the composite score [39]. The weights are obtained based on the reference performance of each unit [25]. The individualized weighting process assigns low weights to the worst-performing sub-indicators and higher weights to the best-performing sub-indicators [40]. After transforming the scale of the sub-indicators (see Equations (1) and (2)), it is possible to construct the CI by BoD by applying the following equation:

$$CI={max}_{w_{j0}}{\displaystyle {\sum }_{j=1}^n}{w}_{j0}{Sb}_{j0}$$

(9)

with the following restrictions:

$${\displaystyle {\sum }_{\mathrm{j}=1}^n}{w}_{j0}{Sb}_{j0}\le 1\forall i\in \left\{\mathrm{1,2},\dots ,n\right\}$$

(10)

$$w_{j0}\ge 0\forall i\in \left\{1,\dots ,n\right\};\forall O\in \left\{\mathrm{1,2},\dots ,m\right\}$$

(11)

where $w_{jk}$ is the corresponding weight of the sub-indicator j of the unit under review k and ${Sb}_{j0}$ are the sub-indicators j of the unit under review 0.

The use of the BoD requires attention, as it is sensitive to extreme values, outliers, and measurement errors [25]. In addition, as it is an endogenous measure, generated internally to the model, it may not be compatible with the theoretical framework of the multidimensional phenomenon. In turn, the exogenous weightings of the sub-indicators, generated outside the model, disregard their relative importance, thereby compromising results when the dimensions have different numbers of sub-indicators [41].

3. Method Selection, Robustness, and Quality Analysis

The weighting scheme for the CIs of child well-being and health system performance was chosen based on Spearman’s correlation coefficients among the indicators. The objective is to identify the method that presents the greatest association in the classifications of each unit for both indices. The relevance of this association is supported by the literature [13,14,15]. Next, the robustness and quality measures of the results are shown.

To test the robustness and quality of the CIs generated by the selected method, the analyses of uncertainty, explanatory power, and discriminant power of the CIs constructed by the selected weighting scheme are performed.

3.1. Uncertainty Analysis

Uncertainty analysis offers a measure of CI stability [25]. It allows checking how much a country’s ranking varies with changes in the weighting scheme, in other words, the degree of uncertainty of the results. The robustness measure of the positions of the units under analysis in the CI ranking is operationalized by Equation (12):

$${\overline{U}}_{{CI}_j}={\displaystyle \frac{1}{m}}{\displaystyle {\sum }_{j=1}^m}\left|Rank\left({CI}_j\right)-Rank\left({CI}_j^f\right)\right|$$

(12)

where ${\overline{U}}_{{CI}_j}$ is the relative change in the position of all the countries of the CI$j$, m is the maximum possible variation for the system, Rank (CI_j) is the ranking of the j-th country not CI, e Rank (${CI}_j^f$) is the ranking of the j-th country of the f indicators constructed by the weighting obtained by different schemes.

3.2. Explanatory Power

A measure often adopted for indicator validation is the correlation between the CIs and a conceptually significant external reference variable [42]. The connection with the external variable indicates how well the CI aligns with the reference variable of the multidimensional phenomenon [43]. External validation is obtained by correlation with the external reference variable in Equation (13):

$$R={\displaystyle \frac{\sum \left({CI}_j-\overline{CI}\right)\left({Ext}_j-\overline{Ext}\right)}{\sqrt{\sum {\left({CI}_j-\overline{CI}\right)}^2\sum {{(Ext}_j-\overline{Ext})}^2}}}$$

(13)

where R is the correlation coefficient between the CI and the external variable Ext, CI_j is the score of the country’s CI j, $\overline{CI}$ is the average of the CI scores, Ext_j is the country’s external variable j e $\overline{Ext}$ is the average value of the external variable.

Based on the rule of thumb of [44], it is possible to indicate the explanatory power of the CI based on its correlation with the most conceptually significant variable of the multidimensional phenomenon: R > 0.90 very strong, 0.70 < R < 0.90 strong, 0.50 < R < 0.70 moderate, 0.30 < R < 0.50 weak, and R < 0.30 insignificant.

3.3. Discriminating Power

The dispersion of the CI scores indicates the indicator’s discriminant power across countries. The greater the degree of dispersion, the greater the degree of differentiation, and the more information can be derived [45]. It offers a measure of information diversity and signals the ease (or difficulty) of differentiating countries. The measure of the discriminant power of the CI used is the entropy index of [32]:

$$H^{\prime }=-{\displaystyle \frac{1}{\mathit{ln}\delta }}{\displaystyle {\sum }_{j=1}^{\delta }}{CI}_0\mathit{ln}{CI}_0$$

(14)

where H’ corresponds to the diversity of Shannon’s information, CI₀ is the value of the CI under analysis of country 0.

4. Data: Dimensions and Sub-Indicators

Data on the sub-indicators of child well-being and the performance of the public health system were extracted from the World Health Organization (WHO) database. Data from World Health Statistics 2022, available at https://www.who.int/data/gho/publications/world-health-statistics, accessed on 10 September 2025, were collected. The sample for analysis comprises data from 62 middle- and low-income countries with available data. The choice of countries analyzed was based on classification as a middle- or low-income country and on the availability of all data, to avoid missing data.

Studies on child well-being typically include key domains such as education, health, and material well-being. These domains are consistently identified as decisive in providing a comprehensive picture of child well-being [4]. Given the available data, this study uses eight sub-indicators to represent five dimensions, as shown in

Table 1. Child well-being dimensions and sub-indicators.

Dimensions	Code	Sub-Indicator
Demographic	Wb1	Life expectancy at birth (years)
	Wb2	Child dependency ratio
Child Health	Wb3	Under-five mortality rate
	Wb4	Prevalence of overweight (% of children under 5)
Education	Wb5	One year before the primary entry age, Male
	Wb6	One year before the primary entry age, Female
Maternal Health	Wb7	Service coverage subindex on reproductive, maternal, newborn, and child health
	Wb8	Stillbirth rate
External Variable	Ext	Gross Domestic Product (GDP) per capita (current US$) 2010–2019

Note: GDP per capita was used to define the normalization function of the sub-indicators as defined in Equations (1) and (2).

.

The public health system should be evaluated based on its health resources and structures, including health financing, governance, human resources for health, and healthcare programs [46]. However, this data is not always available, making accurate measurements and international comparisons difficult [47]. This limitation applies to this study, which adopts available information on five sub-indicators from three dimensions, as shown in

Table 2. Health System dimensions and sub-indicators.

Dimensions	Code	Sub-Indicators
Service	Sh1	Medical doctors per 10,000 population
	Sh2	Nursing and midwifery personnel per 10,000 population
	Sh3	Dentists per 10,000 population
Capabilities to respond to risks and emergencies	Sh4	Average of 13 International Health Regulations core capacity scores
Expenditure	Sh5	Domestic general government health expenditure (% of government expenditure)
External Variable	Ext	Gross Domestic Product (GDP) per capita (current US$) 2010–2019

Note: GDP per capita was used to define the normalization function of the sub-indicators as defined in Equations (1) and (2).

.

5. Results Analysis and Discussions

The sub-indicators used to construct the CIs of child well-being and health system performance were statistically analyzed. Figure 1 shows the boxplot for all sub-indicators. The results indicate higher values and greater dispersion for the child well-being sub-indicators, and no outliers were found in the sample.

Table 3. Spearman’s correlation between the external variable and child well-being sub-indicators.

Sub-Indicators	Ext	Wb1	Wb2	Wb3	Wb4	Wb5	Wb6	Wb7	Wb8
Ext	1
Wb1	0.721	1
Wb2	−0.785	−0.817	1
Wb3	−0.797	−0.906	0.840	1
Wb4	0.661	0.459	−0.504	−0.551	1
Wb5	−0.589	−0.541	0.576	0.598	−0.318	1
Wb6	−0.600	−0.548	0.588	0.608	−0.330	0.991	1
Wb7	0.807	0.848	−0.867	−0.904	0.573	−0.551	−0.574	1
Wb8	−0.734	−0.886	0.766	0.939	−0.498	0.568	0.580	−0.855	1

Note: significance level of 0.05.

shows Spearman’s correlation between the external variable and the sub-indicators of child well-being. The results confirm a moderate to strong correlation. It is important to note that most sub-indicators of child well-being have negative coefficients. This information is important for the data normalization stage of the composite indicator construction.

Spearman’s correlation between the external variable and the sub-indicators of health system performance confirms a moderate correlation.

Table 4. Spearman’s correlation between the external variable and public health system performance sub-indicators.

Sub-Indicators	Ext	Sh1	Sh2	Sh3	Sh4	Sh5
Ext	1
Sh1	0.79	1
Sh2	0.67	0.788	1
Sh3	0.72	0.885	0.684	1
Sh4	0.46	0.588	0.415	0.592	1
Sh5	0.68	0.578	0.487	0.551	0.288	1

Note: significance level of 0.05.

presents the correlation matrix of the health system sub-indicators.

The results of the correlation analysis between the external variable and the sub-indicators, together with the rationale from the literature, validate the choice of the sub-indicators.

Figure 2 demonstrates that the child well-being CIs obtained are higher than the Health System CIs, except for the Bod method. It can also be seen that the results for child well-being CIs are more dispersed than for Health System CIs. Despite the large dispersion identified by the interquartile ranges, no outliers were identified. This result indicates that the health systems of the countries analyzed have greater potential for targeted interventions.

The findings in Figure 3, Figure 4 and Figure 5 demonstrate a significant positive correlation between CIs of child well-being and health system performance, with the entropy weighting scheme showing the strongest relationship.

To solidify the choice of method, the results of the robustness analysis are presented in

Table 5. Robustness analysis of the CIs.

Well-Being	${\overline{\mathit{U}}}_{{\mathit{C}\mathit{I}}_{\mathit{j}}}$	Health System	${\overline{\mathit{U}}}_{{\mathit{C}\mathit{I}}_{\mathit{j}}}$
Equal weights	0.0012	Equal weights	0.0011
Factorial	0.0026	Factorial	0.0012
Entropy	0.0011	Entropy	0.0011
BoD	0.0013	BoD	0.0024

and indicate that the entropy method shows the least variation among the methods analyzed. The lower uncertainty obtained from entropy weighting corroborates the validity of the results generated by the selected weighting scheme.

However, the results of the correlation and robustness analysis should be considered with caution as a basis for choosing a method, since the values for each method are similar.

The quality analysis of results from CIs constructed using the entropy-weighted method demonstrates that indicators of child well-being and the performance of the public health system have strong explanatory power (Figure 6).

The analysis of the discriminant power, presented in Figure 7, shows that the CIs constructed with the entropy-weighted method exhibit a class distribution that allows clear differentiation of results by country; that is, they enable identification of differences between the evaluated units. The results presented in Figure 3 indicate that countries have more concentrated performances in child well-being around 0.75. Regarding the CIs of the health system, the countries under analysis obtained more differentiated CIs; that is, the CIs indicate that the countries have different levels of performance in the health system.

In practical terms, the discriminatory power result indicates that the countries analyzed differ in ways that can influence each country’s response to public policies. In this sense, individualized studies are needed to evaluate each country’s response to actions aimed at improving these indicators.

In summary, the data indicate that the entropy weighting scheme is more appropriate for constructing CIs when evaluating the influence of the health system’s performance on child well-being. The results show a positive relationship between the performance of the countries’ public health systems and child well-being indicators.

6. Conclusions

The growing interest in improving child well-being is accompanied by the challenge of synthesizing the multiple dimensions involved. In this sense, Goal 3 of the SDGs highlights the importance of jointly analyzing the health system’s well-being and performance.

Given the multidimensional nature of well-being and the public health system, CIs are a valuable tool for assessing the relationship between the two. Seeking robust and high-quality CIs, this study presents robustness analyses of four methods for selecting the best method for constructing the proposed indicators and a quality analysis of the results of the indicator built with the chosen method.

The correlation analysis between Child Well-being CIs and Health systems performance CIs supports existing literature, demonstrating that countries with more effective public health systems tend to achieve superior outcomes in child well-being indicators. These findings further substantiate the critical role of public health systems in advancing progress toward the Sustainable Development Goals (SDGs).

The analysis of the results obtained for the 62 middle- and low-income countries with available data in World Health Statistics 2022 indicates that these countries have, on average, low values for child well-being CI and health system CI. In addition, they yield different results, indicating distinct internal problems and distinct needs for public policy action. In this sense, the results reaffirm the need for further studies in this area.

Concerning selecting the weighting scheme, the entropy scheme showed the strongest correlation with the CIs and the best robustness. It should be noted that this result should be considered with caution, since the values obtained for each method are similar. In the analysis of the quality of the results, it was found that they have strong explanatory and discriminant power.

It should be noted that endogenously determined weight methods entail certain negative consequences. Weights derived solely from the data structure can clash with the normative framework of policy, generating strange “shadow prices” between dimensions (for example, how much one sub-indicator compensates for another) [42].

In this regard, future studies should expand the analysis to consider the importance of sub-indicator weights in selecting public policy actions. One way to overcome this issue is to combine expert/stakeholder preferences with statistical criteria (information, entropy, explained variance) to balance theoretical coherence and discriminatory capacity [42].

The results demonstrate the importance of developing studies that delve into the techniques for constructing and evaluating CIs. The construction of CIs, whose results are verified, is a valuable tool for developing actions that help countries promote improvements and overcome their difficulties more effectively.