Data aggregation in constructing composite indicators: A perspective of information loss

Composite indicators (CIs) have been widely accepted as a useful tool for performance comparisons, public communication and decision support in a wide spectrum of fields, e.g. economy, environment and knowledge/information/innovation. The quality and reliability of a CI depend heavily on the underlying construction scheme where data aggregation is a major step. This paper analyzes the data aggregation problem in CI construction from the point of view of information loss. Based on the ''minimum information loss'' principle, the distance-based and entropy-based aggregation models for constructing CIs are presented. The entropy-based aggregation model has also been extended to deal with qualitative data. It is shown that the proposed aggregation models have close relationships with several popular MCDA aggregation methods in CI construction, although our proposed models seem to be more flexible while more complex in application. Two case studies are presented to illustrate the use of the proposed aggregation models.

[1]  Giuseppe Munda,et al.  Noncompensatory/nonlinear composite indicators for ranking countries: a defensible setting , 2009 .

[2]  B. W. Ang,et al.  A mathematical programming approach to constructing composite indicators , 2007 .

[3]  P. Glavič,et al.  How to compare companies on relevant dimensions of sustainability , 2005 .

[4]  J. N. Kapur,et al.  Entropy optimization principles with applications , 1992 .

[5]  P. Murias,et al.  A Composite Indicator for University Quality Assesment: The Case of Spanish Higher Education System , 2008 .

[6]  Wei-Wen Wu,et al.  Choosing knowledge management strategies by using a combined ANP and DEMATEL approach , 2008, Expert Syst. Appl..

[7]  M. Paruccini,et al.  The aggregation of environmental data using multicriteria methods , 2007 .

[8]  Gwo-Hshiung Tzeng,et al.  Evaluating intertwined effects in e-learning programs: A novel hybrid MCDM model based on factor analysis and DEMATEL , 2007, Expert Syst. Appl..

[9]  Andrea Bettini.  Il Sole 24 Ore , 2009 .

[10]  S. Fang,et al.  Entropy Optimization and Mathematical Programming , 1997 .

[11]  Dimitris K. Despotis,et al.  Measuring human development via data envelopment analysis: the case of Asia and the Pacific , 2005 .

[12]  B. W. Ang,et al.  Comparing aggregating methods for constructing the composite environmental index: An objective measure , 2006 .

[13]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[14]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[15]  Stefano Tarantola,et al.  Handbook on Constructing Composite Indicators: Methodology and User Guide , 2005 .

[16]  Peng Zhou,et al.  A survey of data envelopment analysis in energy and environmental studies , 2008, Eur. J. Oper. Res..

[17]  J. Church.  Human Development Report , 2001 .

[18]  Sherman Robinson,et al.  Updating and Estimating a Social Accounting Matrix Using Cross Entropy Methods , 2001 .

[19]  G. Munda.  “Measuring Sustainability”: A Multi-Criterion Framework , 2005 .

[20]  Ching-Lai Hwang,et al.  Multiple attribute decision making : an introduction , 1995 .

[21]  Gwo-Hshiung Tzeng,et al.  Combined MCDM techniques for exploring stock selection based on Gordon model , 2009, Expert Syst. Appl..

[22]  Krishna B. Misra,et al.  Handbook of Performability Engineering , 2008 .

[23]  H. Welsch,et al.  Meaningful environmental indices: a social choice approach , 2004 .

[24]  Laurens Cherchye,et al.  An Introduction to ‘Benefit of the Doubt’ Composite Indicators , 2007 .

[25]  Leonidas Ntziachristos,et al.  Uncertainty and Sensitivity Analysis of COPERT 4 , 2010 .

[26]  F. Booysen.  An Overview and Evaluation of Composite Indices of Development , 2002 .

[27]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[28]  Evangelos Triantaphyllou,et al.  Multi-criteria Decision Making Methods: A Comparative Study , 2000 .

[29]  C. Lovell,et al.  One Market, One Number? A Composite Indicator Assessment of EU Internal Market Dynamics , 2005 .

[30]  Wei-Wen Wu,et al.  Selecting knowledge management strategies by using the analytic network process , 2007, Expert Syst. Appl..

[31]  Giuseppe Munda,et al.  Version November , 2003 On the Methodological Foundations of Composite Indicators Used for Ranking Countries , 2003 .

[32]  Douglas J. Miller,et al.  Maximum entropy econometrics: robust estimation with limited data , 1996 .

[33]  C. Romero,et al.  In search of a natural systems sustainability index , 2004 .

[34]  B. W. Ang,et al.  Comparing MCDA Aggregation Methods in Constructing Composite Indicators Using the Shannon-Spearman Measure , 2009 .

[35]  Chung-Hsing Yeh,et al.  Inter-company comparison using modified TOPSIS with objective weights , 2000, Comput. Oper. Res..

[36]  Milan Zeleny,et al.  Multiple Criteria Decision Making (MCDM) , 2004 .

[37]  B. W. Ang,et al.  Indicators for Assessing Sustainability Performance , 2008 .

[38]  Rajiv Khosla,et al.  Index evaluations and business strategies on communities of practice , 2009, Expert Syst. Appl..

[39]  U. Tappeiner,et al.  The Stability of Rankings Derived From Composite Indicators: Analysis of the “IL Sole 24 Ore” Quality of Life Report , 2006 .

[40]  Sherman Robinson,et al.  Recovering Information from Incomplete or Partial Multisectoral Economic Data , 1994 .

[41]  Laurens Cherchye,et al.  Creating composite indicators with DEA and robustness analysis: the case of the Technology Achievement Index , 2006, J. Oper. Res. Soc..

[42]  Stefano Tarantola,et al.  Uncertainty and sensitivity analysis techniques as tools for the quality assessment of composite indicators , 2005 .