Using Ranked Weights and Acceptability Analysis to Construct Composite Indicators: A Case Study of Regional Sustainable Society Index

A variety of published composite indicators, i.e., Energy Trilemma Index and Sustainable Society Index, are commonly aggregated with equal weights. However, this plausible scheme is criticized as eclecticism and ignores the discriminating power of the different indicators. Differing from the traditional methods that assign weights to each indicator for the purpose of aggregation, this paper proposes a new mechanism to construct composite indicators using ranked weights and stochastic multicriteria acceptability analysis. More specifically, this study comprehensively consider all possible preferences among the indicators. Under each preference, we develop a sophisticated mathematical transformation to calculate the least and most favorable scores of each entity, which formulates the lower and upper bounds of the intervals. Then an interval decision matrix, alternatively described as a stochastic decision problem, is formulated to construct the composite indicators. Holistic acceptability indices are generated and regarded as a new composite indicator, which is capable of providing a comprehensive and robust composite indicator with more discriminating power. We apply the proposed method to modify the regional sustainable society index and present the obtained results and comparisons.     

Application of Different Techniques of Factor Analysis to Develop Neighborhood Social Capital Rating Scale

Composite indicators are widely used to determine the ranking of countries, organizations or individuals in terms of overall performance on multiple criteria. Their calculation requires standardization of the individual statistical criteria and aggregation of the standardized indicators. These operations introduce a potential propagation effect of extreme values on the calculation of the composite indicator of all entities. In this paper, we propose robust composite indicators for which this propagation effect is limited. The approach uses winsorization based on a robust estimate of the distribution of the sub-indicators. It is designed such that the winsorization affects only the composite indicator rank but has no effect on the entities ranking in each sub-indicator. The simulation study documents the benefits of distribution-based winsorization in the presence of outliers. It leads to a ranking that is closer to the clean data ranking when compared to the ranking obtained using either no winsorization or the traditional winsorization based on empirical quantiles. In the empirical application, we illustrate the use of winsorization for ranking countries based on the United Nations Industrial Development Organization’s Competitive Industrial Performance index. We show that even though the sub-indicator ranking does not change, the robust winsorization approach has a material impact on the ranking of the composite indicator for countries with large discrepancies in the scores of the sub-indicators.

     

Application of the “Benefit-Of-the-Doubt” Approach for the Construction of a Digital Access Indicator: A Revaluation of the “Digital Access Index”

The use of composite indicators as a tool for ranking and making decisions is ever increasing in a world marked by the inequalities and competition in all domains. However, the dependence of countries ranking on the weighing scheme used to aggregate individual indices or sub-indicators, most of the time set by experts/stakeholders may weaken the credibility of composite indicators. One method which is able to overcome these limits is the “Data Envelopment Analysis” approach, particularly named “Benefit-Of-the-Doubt” in the context of composite indicators’ construction. We propose a revaluation of the Digital Access Index given that Information technology is the most important factor driving improvement in a wide array of areas critical for the quality of life for individuals as well as societies. We have shown that this method is more suitable for identifying trends and drawing attention to particular issues and also for setting policy priorities. In fact, the weights of the individual indices, used to compute the composite indicators are based on the data itself and are proper for the country under consideration. These weights contain adequate information in order to help policy-makers to better understand the nature of the new innovation economy and the types of public policies needed to drive innovation, productivity and broad-based prosperity for its citizens.     

The weighting of an international health status index

The major purpose of this paper is to suggest possible weights for a global index of health status. The indicators for the global index are taken from the World Health Organization's definition of health as physical, mental and social well-being. These indicators are combined with mortality indicators to arrive at a finalized index. Survey methodology is used to make initial estimates of the weighting of appropriate indicators, based upon a sample of international health scholars. Preliminary results indicate that mortality is weighted 40%, physical health (morbidity and disability) 25%, mental health 15%, and social health 20%. These results are intended as a starting point for future research.     

Measuring Well-Being Over Time: The Adjusted Mazziotta–Pareto Index Versus Other Non-compensatory Indices

Most of the socio-economic phenomena such as development, well-being, and quality of life have a multidimensional nature and require the definition of a set of individual indicators to be properly assessed. Often, individual indicators are summarized and a composite index is created. One of the main problems in constructing composite indices is the choice of a method which allows time comparisons. In this paper, we consider the Adjusted Mazziotta–Pareto Index, a non-compensatory composite index used by the Italian National Institute of Statistics for measuring “Equitable and Sustainable Well-being” in Italy. An empirical comparison with some traditional non-compensatory indices is presented and an Influence Analysis is, for the first time, performed in order to assess the robustness of the index.     

Modeling Local BES Indicators by Copula-Based Bayesian Networks

In Italy, the measure of the Equitable and Sustainable Well-being is provided by the Italian Institute of Statistics by means of a dashboard of basic and composite indicators. To investigate the dependence structure between the different domains of well-being, we propose the use of Non-Parametric Bayesian Networks based on the normal copula distribution, that allow to explore the conditional independence relationships between the composite indicators. The main advantage of the non-parametric models is that, as opposed to the parametric approach, they do not require any assumption on the marginal distributions of the variables. The proposed model is applied to the Equitable and Sustainable Well-being indicators measured at the provincial level and enriches the analysis of well-being by inspecting similarities and differences between Italian urban areas and territories.

     

Weighting and Aggregation in Composite Indicator Construction: a Multiplicative Optimization Approach

Composite indicators (CIs) have increasingly been accepted as a useful tool for benchmarking, performance comparisons, policy analysis and public communication in many different fields. Several recent studies show that as a data aggregation technique in CI construction the weighted product (WP) method has some desirable properties. However, a problem in the application of the WP method is the difficulty and subjectivity in determining the weights for sub-indicators. In this paper, we extend the WP method and propose a multiplicative optimization approach to constructing CIs. This approach requires no prior knowledge of the weights for sub-indicators. Instead, the weights are generated by solving a series of multiplicative data envelopment analysis type models that can be transformed into equivalent linear programs. Additional relevant information on the weights, if available, can be incorporated into the proposed models. We apply the proposed approach to the 2005 data of 27 economies in the Asia and the Pacific region in the United Nations’ Human Development Index study and present the results.     

An Introduction to ‘Benefit of the Doubt’ Composite Indicators

Despite their increasing use, composite indicators remain controversial. The undesirable dependence of countries’ rankings on the preliminary normalization stage, and the disagreement among experts/stakeholders on the specific weighting scheme used to aggregate sub-indicators, are often invoked to undermine the credibility of composite indicators. Data envelopment analysis may be instrumental in overcoming these limitations. One part of its appeal in the composite indicator context stems from its invariance to measurement units, which entails that a normalization stage can be skipped. Secondly, it fills the informational gap in the ‘right’ set of weights by generating flexible ‘benefit of the doubt’-weights for each evaluated country. The ease of interpretation is a third advantage of the specific model that is the main focus of this paper. In sum, the method may help to neutralize some recurring sources of criticism on composite indicators, allowing one to shift the focus to other, and perhaps more essential stages of their construction. An abridged version of this paper was presented at the Workshop on European Indicators and Scoreboards, organised by DG Education and the Joint Research Centre within the auspices of CRELL, in Brussels, October 24–25, 2005.     

Media Use and Satisfaction with Democracy: Testing the Role of Political Interest

An interesting measure for equitable and sustainable well-being has been proposed recently by the National Institute of Statistics in Italy and the National Council for Economy and Labour. It is called BES (from the Italian Benessere Equo e Sostenibile). A set of indicators, partitioned into several domains and themes, is used for measuring the BES. Taking into account prior knowledge of both the structure of this set of indicators and the relationships among them, the paper proposes a hierarchical composite model for measuring and modeling the BES of the Italian provinces. This hierarchical model allows us to synthesize individual indicators into single indexes in order to construct composite indicators at a global and a partial level. Moreover, we analyze the relationships among the different domains and themes as well as the effects of these on equitable and sustainable well-being, in order to search for strongly influential factors. In order to estimate the parameters of the model, we use both Partial Least Squares path modeling and a new method, called Quantile Composite-based path modeling. In particular, Partial Least Squares path modeling is used to estimate average effects in the network of relationships between variables, while with Quantile Composite-based path modeling we investigate whether the magnitude of these effects changes across different parts of the variable distributions, providing a more complete picture and uncovering specific local leveraging factors for improvement. A final ranking of the Italian provinces, according to the BES composite indicator, is also provided at the national level and for different geographic areas of Italy.     

A Non-radial DEA Index for Peruvian Regional Competitiveness

In this paper, we propose a method to measure competitiveness performance at the subnational level, with an application to Peruvian regions. For this, we propose a benefit-of-the-doubt composite index that summarizes the information of several indicators that characterize competitiveness. It is based on an optimization approach, using data enveloping analysis (DEA) techniques, so that each indicator is weighted in an endogenous way, and each unit is evaluated in the most favourable light. Our proposed index is a non-radial variant of the typical DEA scores, which avoids the traditional pitfalls of DEA-based composite indices, such as unreasonable weights. Additionally, we propose a meta-frontier approach in order to compare the competitiveness performances across different periods of evaluation. Our assessments of the Peruvian regions’ competitiveness performance improve on the results of traditional DEA methods, which award high marks to regions with very heterogeneous performance (i.e., regions with very high scores in some indicators, and very poor in others). Additionally, the comparison of the performance across time shows a general decrease in the average competitiveness between 2008 and 2014 of the Peruvian regions.     

Composite Indices of Development and Poverty: An Application to MDGs

The measurement of development or poverty as multidimensional phenomena is very difficult because there are several theoretical, methodological and empirical problems involved. The literature of composite indicators offers a wide variety of aggregation methods, all with their pros and cons. In this paper, we propose a new, alternative composite index denoted as MPI (Mazziotta-Pareto Index) which, starting from a linear aggregation, introduces penalties for the countries or geographical areas with ‘unbalanced’ values of the indicators. As an example of application of the MPI, we consider a set of indicators in order to measure the Millennium Development Goals (MDGs) and we present a comparison between HDI (Human Development Index) methodology, HPI (Human Poverty Index) methodology and MPI.     

Drivers of Youth Labour Market Integration Across European Regions

Territorial disparities and youth labour markets have been often considered as separated themes, due to challenges in data availability. Comparative regional or sub-regional research on youth labour market integration (YLMI) have been therefore scarce. In this article, we address this gap by presenting a composite measure of YLMI that covers a wide range of indicators and sheds light on the EU territorial divide of young peoples’ opportunities at regional level. In order to build the YLMI index, we use benefit-of-the-doubt-weighting, a seminal methodology on composite indicators (CI) that combines sequence with conditional weights based on the range of each sub-indicator. To proof the usefulness of YLMI, we analyze the evolution of regional YLMI in the EU before and after the economic crisis; and the trends of homogenization or differentiation across EU territories. Furthermore, we investigate to what extent employment conditions, skills supply and technological resources explain cross-regional variations in YLMI.

     

Composite Indicator of Social Inclusion for European Countries

Social inclusion is one of the key challenges of the European Union (EU) Sustainable Development Strategy. We use four indicators from EU policies to measure social inclusion for the 27 member countries of Europe. In particular, we aggregate the four indicators in a multiplicative composite indicator via a DEA-BoD approach with weights determined endogenously with proportion constraints. We obtain a score of social inclusion that allows us to grade the 27 EU countries from 2006 to 2010. In this way, we highlight the specific role played by the four indicators in determining improvements and deteriorations of social inclusion during the European phase of the financial and economic crisis.     

Measuring World Better Life Frontier: A Composite Indicator for OECD Better Life Index

The OECD Better Life initiative recently released a comprehensive set of 11 indicators of well-being covering a group of countries. Each individual indicator corresponds to a key topic that is essential to well-being. However, the problem of aggregating them is left to users of this dataset. Using these as individual indicators, we propose a composite indicator of overall well-being, which is intended to measure the performance of each country in terms of providing well-being to its people. The ‘benefit of the doubt’ approach (BOD), a well-known aggregation tool based on a weighed sum, assigns the most favourable weights for each entity under investigation. BOD may also be considered to evaluate the performance of each entity in terms of its efficiency. Regarding individual indicators as outputs, it constructs the benchmark production frontier from observed individual indicators. A composite indicator based on BOD equals the distance between each entity’s individual indicator and the production frontier, indicating its efficiency. It is widely considered that the well-being of a country’s people stems from its productive base, which is characterized by capital assets and social infrastructures. Thus, the productive base can be considered the input used to produce well-being, which is reflected by individual indicators. Therefore, when we apply BOD to aggregate individual well-being indicators across countries, we implicitly assume that all countries have the same productive base, as BOD addresses only the output and neglects the input. This inaccurate assumption leads to a distorted performance measure. Data envelopment analysis (DEA), in which BOD has its roots, is a tool to measure the efficiency of each entity by allowing for differences in inputs as well as outputs across entities. DEA also measures efficiency by using the distance to the production frontier; however, unlike BOD, DEA constructs the production frontier more accurately by utilizing the information of inputs as well as outputs, leading to a better performance measure. We apply DEA to aggregate 11 individual well-being indicators into a composite indicator using the World Bank’s estimates of each country’s productive base. The composite indicator based on BOD is distributed similarly to and is highly correlated with the existing Human Development Indicator (HDI). It is also positively correlated with GDP per capita. On the other hand, we show that the composite indicator based on DEA is negatively correlated with HDI as well as GDP per capita.     

Socio-economic Indexes in Surveys for Comparisons between Countries

The study of socio-economic inequalities from across-national perspective has been hampered by the lack of adequate common indices of socio-economic status that can be used in a self-report survey instrument. This paper examines the construction and the properties of global social indexes in general, and of the Family Affluence Scale (henceforth FAS) in particular. The paper proposes a new strategy for making comparisons of the global index with stratified data, building a revised FAS based on Adapted Canonical Variate Analysis (henceforth ACVA). This alternative strategy for constructing a global index is available in standard software, and the new proposal for stratified data only requires a simple program, which is justified, explained and provided in the text. Data come from the 1998 Health Behaviour in School-Aged Children (HBSC), a WHO Cross-National Study using cluster sampling of schoolchildren from five countries: Denmark, Latvia, Portugal, Scotland and the USA. The results reveal that in every country we would have had a completely different evaluation of the three indicators of Family Affluence if we had used either linear or nonlinear approaches to compute the global indexes. Moreover, Family Affluence comparisons among countries shows that the relative contribution of the three indicators to the overall FAS, changes from country to country. We conclude that separate indicators of Family Affluence are not equally relevant in each country and, as a consequence, do not contribute equally to the global index. For cross-cultural studies, the strategy for constructing an index should be country specific. The methodological developments presented in the paper open up opportunities to study socio-economic patterning of health among young people in the developed world, since self completed surveys can now employ a common measure of family material wealth. The findings show that the RFAS (Revised FAS) is a useful index of socio-economic status for use in national and cross-national surveys of adolescent health and health behaviour. The new strategy for weighting observed indicators in the index gives it enhanced power to detect in equalities.     

Rank-Optimal Weighting or “How to be Best in the OECD Better Life Index?”

We present a method of rank-optimal weighting which can be used to explore the best possible position of a subject in a ranking based on a composite indicator by means of a mathematical optimization problem. As an example, we explore the dataset of the OECD Better Life Index and compute for each country a weight vector which brings it as far up in the ranking as possible with the greatest advance of the immediate rivals. The method is able to answer the question “What is the best possible rank a country can achieve with a given set of weighted indicators?” Typically, weights in composite indicators are justified normatively and not empirically. Our approach helps to give bounds on what is achievable by such normative judgments from a purely output-oriented and strongly competitive perspective. The method can serve as a basis for exact bounds in sensitivity analysis focused on ranking positions. In the OECD Better Life Index data we find that 19 out the 36 countries in the OECD Better Life Index 2014 can be brought to the top of the ranking by specific weights. We give a table of weights for each country which brings it to its highest possible position. Many countries achieve their best rank by focusing on their strong dimensions and setting the weights of many others to zero. Although setting dimensions to zero is possible in the OECD’s online tool, this contradicts the idea of better life being multidimensional in essence. We discuss modifications of the optimization problem which could take this into account, e.g. by allowing only a minimal weight of one. Methods to find rank-optimal weights can be useful for various multidimensional datasets like the ones used to rank universities or employers.     

Measuring Progress and Well-Being: A Comparative Review of Indicators

We provide a new database sampling well-being and progress indicators implemented since the 1970s at all geographic scales. Starting from an empirical assessment, we describe and quantify trends in the institutional basis, methodology, and content of indicators which are intended to capture the broadest conceptions of human social progress. We pay special attention to the roles of sustainability and subjective well-being in these efforts, and find that certain types of indicators are more successful in terms of transparency, accountability, as well as longevity. Our taxonomy encompasses money-denominated accounts of “progress”, unaggregated collections of indicators, indices, and measures oriented around subjective well-being. We find that a most promising innovation is the indices whose weights are accountable to empirical data, in particular through models of subjective well-being. We conclude by amplifying others’ advocacy for the appropriate separation of current well-being from environmental indicators, and for the avoidance of aggregation except where it is meaningful.     

On the measurement of certain aspects of social development

An attempt has been made in this paper to measure social development. There has been some limited use of per capita national income as a measure of development. A number of social indicators from various societal areas may, alternatively, better represent social development of a region. A composite index of selected social indicators has been proposed as a measure of social development. Certain existing methods of construction of composite indexes have been examined and new methods proposed using the variance-covariance matrix and intercorrelation matrix of the indicators and the concept of (Euclidean) distance. Two examples of intertemporal and international comparisons have been presented to illustrate the proposed methods.The author is grateful to Prof. M. Mukherjee under whose supervision and guidance this work was carried out. However, the views expressed in this paper are those of the author and not of the institution to which he belongs.     

One Size Fits All? The Validity of a Composite Poverty Index Across Urban and Rural Households in South Africa

Composite indices have been prominently used in poverty research. However, validity of these indices remains subject to debate. This paper examines the validity of a common type of composite poverty indices using data from a cross-sectional survey of 2477 households in urban and rural KwaZulu-Natal, South Africa. Multiple-group comparisons in structural equation modelling were employed for testing differences in the measurement model across urban and rural groups. The analysis revealed substantial variations between urban and rural respondents both in the conceptualisation of poverty as well as in the weights and importance assigned to individual poverty indicators. The validity of a ‘one size fits all’ measurement model can therefore not be confirmed. In consequence, it becomes virtually impossible to determine a household’s poverty level relative to the full sample. Findings from our analysis have important practical implications in nuancing how we can sensitively use composite poverty indices to identify poor people.