Advances in Data Analysis and Classification

, Volume 11, Issue 1, pp 139–158 | Cite as

A generalized maximum entropy estimator to simple linear measurement error model with a composite indicator

  • Maurizio CarpitaEmail author
  • Enrico Ciavolino
Regular Article


We extend the simple linear measurement error model through the inclusion of a composite indicator by using the generalized maximum entropy estimator. A Monte Carlo simulation study is proposed for comparing the performances of the proposed estimator to his counterpart the ordinary least squares “Adjusted for attenuation”. The two estimators are compared in term of correlation with the true latent variable, standard error and root mean of squared error. Two illustrative case studies are reported in order to discuss the results obtained on the real data set, and relate them to the conclusions drawn via simulation study.


Simple linear measurement error model Generalized maximum entropy Composite indicator Global innovation index Manager performance 

Mathematics Subject Classification

97K70 97K80 47N30 94A17 91B82 

Supplementary material

11634_2016_237_MOESM1_ESM.pdf (23 kb)
Supplementary material 1 (pdf 23 KB)


  1. Al-Nasser AD (2005) Entropy type estimator to simple linear measurement error models. Aust J Stat 34(3):283–294MathSciNetGoogle Scholar
  2. Bollen K (1989) Structural equations with latent variables. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  3. Brentari E, Zuccolotto P (2011) The impact of chemical and sensorial characteristics on the market price of Italian red wines. Electron J Appl Stat Anal 4(2):265–276Google Scholar
  4. Buonaccorsi JP (2010) Measurement error models, methods and applications. Boca Raton: Chapman & Hall, CRC PressGoogle Scholar
  5. Carpita M, Manisera M (2012) Constructing indicators of unobservable variables from parallel measurements. Electron J Appl Stat Anal 5(3):320–326MathSciNetGoogle Scholar
  6. Carpita M, Ciavolino E (2014) MEM and SEM in the GME framework: statistical modelling of perception and satisfaction. Procedia Econ Financ 17:20–29CrossRefGoogle Scholar
  7. Carroll RJ, Ruppert D, Stefanski LA (1995) Measurement error in nonlinear models. Chapman & Hall, LondonCrossRefzbMATHGoogle Scholar
  8. Cheng C-L, Van Ness JW (2010) Statistical regression with measurement error. Wiley, New YorkzbMATHGoogle Scholar
  9. Ciavolino E, Al-Nasser AD (2009) Comparing generalized maximum entropy and partial least squares methods for structural equation models. J Nonparametr Stat 21(8):1017–1036MathSciNetCrossRefzbMATHGoogle Scholar
  10. Ciavolino E, Carpita M (2015) The GME estimator for the regression model with a composite indicator as explanatory variable. Qual Quant 49(3):955–965CrossRefGoogle Scholar
  11. Ciavolino E, Carpita M, Al-Nasser AD (2015) Modeling the quality of work in the Italian social co-operatives combining NPCA-RSM and SEM-GME approaches. J Appl Stat 42(1):161–179MathSciNetCrossRefGoogle Scholar
  12. Ciavolino E, Dahlgaard JJ (2009) Simultaneous equation model based on generalized maximum entropy for studying the effect of the management’s factors on the enterprise performances. J Appl Stat 36(7):801–815MathSciNetCrossRefzbMATHGoogle Scholar
  13. Decancq K, Lugo MA (2013) Weights in multidimensional indices of wellbeing: an overview. Econ Rev 32(1):7–34MathSciNetCrossRefGoogle Scholar
  14. Dutta S (2012) The global innovation index 2012: stronger innovation linkages for global growth. INSEAD, FranceGoogle Scholar
  15. Foster JE, McGillivray M, Suman S (2013) Composite indices: rank robustness, statistical association, and redundancy. Econ Rev 32(1):35–56MathSciNetCrossRefGoogle Scholar
  16. Fuller WA (1987) Measurement errors models. Wiley, New YorkCrossRefzbMATHGoogle Scholar
  17. Golan A (2006) Information and entropy econometrics. A review and synthesis, foundation and trends\(^{{\textregistered }}\) in Econometrics. 2(1–2), 1–145Google Scholar
  18. Golan A, Judge G, Miller D (1996) A maximum entropy econometrics: robust estimation with limited data. Wiley, New YorkzbMATHGoogle Scholar
  19. Madansky A (1959) The fighting of straight lines when both variables are subject to error. J Am Stat Assoc 55:173–205MathSciNetCrossRefzbMATHGoogle Scholar
  20. Nunnally JC, Bernstein IH (1994) Psychometric theory, 3rd edn. McGraw-Hill, New YorkGoogle Scholar
  21. Oberski DL, Satorra A (2013) Measurement error models with uncertainty about the error variance. Struct Equ Model 20:409–428MathSciNetCrossRefGoogle Scholar
  22. Organisation for Economic Co-operation and Development (2008) Handbook on constructing composite indicators: methodology and user guide. Organisation for Economic Co-operation and Development, ParisGoogle Scholar
  23. Pagani L, Zanarotti M (2015) Some considerations to carry out a composite indicator for ordinal data. Electron J Appl Stat Anal 8(3):384–397MathSciNetGoogle Scholar
  24. Paruolo P, Saisana M, Saltelli A (2013) Ratings and rankings: voodoo or science? J R Stat Soc Ser A 176(3):609–634MathSciNetCrossRefGoogle Scholar
  25. Pukelsheim F (1994) The three sigma rule. Am Stat 48(2):88–91MathSciNetGoogle Scholar
  26. Roeder K, Carroll RJ, Lindsay BG (1996) A semiparametric mixture approach to case–control studies with errors in covariables. J Am Stat Assoc 91:722–732MathSciNetCrossRefzbMATHGoogle Scholar
  27. Saltelli A (2007) Composite indicators between analysis and advocacy. Soc Indic Res 81:65–77CrossRefGoogle Scholar
  28. Schumacker R, Lomax R (2004) A beginner’s guide to structural equation modeling. Lawrence Erlbaum, MahwahzbMATHGoogle Scholar
  29. Shannon CE (1948) A mathematical theory of communication. Bell Syst Tech J 27:379–423MathSciNetCrossRefzbMATHGoogle Scholar
  30. Vezzoli M, Manisera M (2012) Assessing item contribution on unobservable variables’ measures with hierarchical data. Electron J Appl Stat Anal 5(3):314–319MathSciNetGoogle Scholar
  31. Wansbeek T, Maijer E (2000) Measurement error and latent variables in econometrics. Elsevier, AmsterdamzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of Economics and ManagementUniversity of BresciaBresciaItaly
  2. 2.Department of History, Society and Human StudiesUniversity of SalentoLecceItaly

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