IDEAS home Printed from https://ideas.repec.org/a/spr/soinre/v136y2018i3d10.1007_s11205-016-1500-5.html
   My bibliography  Save this article

Variable Weighting via Multidimensional IRT Models in Composite Indicators Construction

Author

Listed:
  • Michela Gnaldi

    (University of Perugia)

  • Simone Del Sarto

    (University of Perugia)

Abstract

One of the most controversial steps in Composite Indicators (CIs) construction is the selection of one (possibly) best weighting technique. In this paper, we introduce a new endogenous weighting methodology developed in an extended Item Response Theory (IRT) framework. As weighting is much more thorough when carried out by accounting for the dimensionality of a dataset rather than by ignoring it, we suggest to assign weights on the basis of the discrimination parameters estimated through a multidimensional two-parameter logistic IRT model. Specifically, the procedure is developed through two consecutive steps. The first applies a hierarchical clustering algorithm to ascertain the number of dimensions measured by the data. The second estimates the discrimination parameters under the multidimensional two-parameter logistic model selected at the first step. The discrimination parameters can then be used to compare and weight the items that refer to the same dimension. Besides, in order to make such discrimination indices comparable across dimensions, the distribution of the latent trait is standardised for each dimension. The potentialities of this novel weighting technique are illustrated through an application to educational data, which refer to a national standardised test developed and collected by the Italian National Institute for the Evaluation of the Education System.

Suggested Citation

  • Michela Gnaldi & Simone Del Sarto, 2018. "Variable Weighting via Multidimensional IRT Models in Composite Indicators Construction," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 136(3), pages 1139-1156, April.
    • Handle: RePEc:spr:soinre:v:136:y:2018:i:3:d:10.1007_s11205-016-1500-5
    DOI: 10.1007/s11205-016-1500-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11205-016-1500-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11205-016-1500-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alessio Fusco & Paul Dickes, 2008. "The Rasch Model and Multidimensional Poverty Measurement," Palgrave Macmillan Books, in: Nanak Kakwani & Jacques Silber (ed.), Quantitative Approaches to Multidimensional Poverty Measurement, chapter 3, pages 49-62, Palgrave Macmillan.
    2. P. Jenkins, Stephen & Cappellari, Lorenzo, 2006. "Summarizing multiple deprivation indicators," ISER Working Paper Series 2006-40, Institute for Social and Economic Research.
    3. Hussein Sayed & Ramadan Hamed & Mohamed Ramadan & Samaa Hosny, 2015. "Using Meta-goal Programming for a New Human Development Indicator with Distinguishable Country Ranks," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 123(1), pages 1-27, August.
    4. Amal Ray, 2008. "Measurement of social development: an international comparison," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 86(1), pages 1-46, March.
    5. Riccardo Natoli & Segu Zuhair, 2011. "Measuring Progress: A Comparison of the GDP, HDI, GS and the RIE," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 103(1), pages 33-56, August.
    6. Bartolucci, Francesco & Bacci, Silvia & Gnaldi, Michela, 2014. "MultiLCIRT: An R package for multidimensional latent class item response models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 971-985.
    7. Michela Gnaldi & M. Giovanna Ranalli, 2016. "Measuring University Performance by Means of Composite Indicators: A Robustness Analysis of the Composite Measure Used for the Benchmark of Italian Universities," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 129(2), pages 659-675, November.
    8. Francesco Bartolucci, 2007. "A class of multidimensional IRT models for testing unidimensionality and clustering items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 141-157, June.
    9. Nanak Kakwani & Jacques Silber (ed.), 2008. "Quantitative Approaches to Multidimensional Poverty Measurement," Palgrave Macmillan Books, Palgrave Macmillan, number 978-0-230-58235-4.
    10. Monica Szeles & Alessio Fusco, 2013. "Item response theory and the measurement of deprivation: evidence from Luxembourg data," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(3), pages 1545-1560, April.
    11. F. Bartolucci & G. Montanari & S. Pandolfi, 2012. "Dimensionality of the Latent Structure and Item Selection Via Latent Class Multidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 782-802, October.
    12. Milo Vandemoortele, 2014. "Measuring Household Wealth with Latent Trait Modelling: An Application to Malawian DHS Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 118(2), pages 877-891, September.
    13. Silvia Bacci & Michela Gnaldi, 2015. "A classification of university courses based on students’ satisfaction: an application of a two-level mixture item response model," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 927-940, May.
    14. Mishra, SK, 2008. "On construction of robust composite indices by linear aggregation," MPRA Paper 9232, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Marta Ewa Kuc-Czarnecka & Magdalena Olczyk & Marek Zinecker, 2021. "Improvements and Spatial Dependencies in Energy Transition Measures," Energies, MDPI, vol. 14(13), pages 1-22, June.
    2. Tianjiao Wang & Yelin Fu, 2020. "Constructing Composite Indicators with Individual Judgements and Best–Worst Method: An Illustration of Value Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(1), pages 1-14, May.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joseph Deutsch & Anne-Catherine Guio & Marco Pomati & Jacques Silber, 2015. "Material Deprivation in Europe: Which Expenditures are Curtailed First?," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 120(3), pages 723-740, February.
    2. Anne-Catherine Guio & David Gordon & Eric Marlier & Hector Najera & Marco Pomati, 2018. "Towards an EU measure of child deprivation," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 11(3), pages 835-860, June.
    3. Nick Bailey, 2020. "Measuring Poverty Efficiently Using Adaptive Deprivation Scales," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(3), pages 891-910, June.
    4. Silvia Bacci & Michela Gnaldi, 2015. "A classification of university courses based on students’ satisfaction: an application of a two-level mixture item response model," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 927-940, May.
    5. Tanveer Ahmed Naveed & David Gordon & Sami Ullah & Mary Zhang, 2021. "The Construction of an Asset Index at Household Level and Measurement of Economic Disparities in Punjab (Pakistan) by using MICS-Micro Data," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 155(1), pages 73-95, May.
    6. FAYE Ousmane & BASCHIERI Angela & FALKINGHAM Jane & MUINDI Kanyiva, 2010. "Hunger and Food Insecurity in Nairobi's Slums: An assessment using IRT models'," LISER Working Paper Series 2010-33, Luxembourg Institute of Socio-Economic Research (LISER).
    7. Fusco, Alessio, 2015. "The relationship between income and housing deprivation: A longitudinal analysis," Economic Modelling, Elsevier, vol. 49(C), pages 137-143.
    8. Raffaele Lagravinese & Paolo Liberati & Giuliano Resce, 2020. "Measuring Health Inequality in US: A Composite Index Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 147(3), pages 921-946, February.
    9. Deutsch, Joseph & Silber, Jacques & Wan, Guanghua & Zhao, Mengxue, 2020. "Asset indexes and the measurement of poverty, inequality and welfare in Southeast Asia," Journal of Asian Economics, Elsevier, vol. 70(C).
    10. RAILEANU SZELES Monica & FUSCO Alessio, 2009. "Item response theory and the measurement of deprivation: Evidence from PSELL-3," IRISS Working Paper Series 2009-05, IRISS at CEPS/INSTEAD.
    11. Monica Szeles & Alessio Fusco, 2013. "Item response theory and the measurement of deprivation: evidence from Luxembourg data," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(3), pages 1545-1560, April.
    12. Michael Brusco & Hans-Friedrich Köhn & Douglas Steinley, 2015. "An Exact Method for Partitioning Dichotomous Items Within the Framework of the Monotone Homogeneity Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 949-967, December.
    13. Joachim Merz & Tim Rathjen, 2011. "Intensity of Time and Income Interdependent Multidimensional Poverty: Well-Being and Minimum 2DGAP – German Evidence," FFB-Discussionpaper 92, Research Institute on Professions (Forschungsinstitut Freie Berufe (FFB)), LEUPHANA University Lüneburg.
    14. Gaetano Grilli & Antonella D’Agostino & Antoanneta Potsi, 2018. "Social Participation and Safety Deprivation of Children in Italy: PIIGS Countries in Perspective," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 11(1), pages 159-184, February.
    15. Genge, Ewa & Bartolucci, Francesco, 2019. "Are attitudes towards immigration changing in Europe? An analysis based on bidimensional latent class IRT models," MPRA Paper 94672, University Library of Munich, Germany.
    16. Maria Cracolici & Francesca Giambona & Miranda Cuffaro, 2014. "Family Structure and Subjective Economic Well-Being: Some New Evidence," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 118(1), pages 433-456, August.
    17. Francesco Bartolucci & Alessio Farcomeni & Luisa Scaccia, 2017. "A Nonparametric Multidimensional Latent Class IRT Model in a Bayesian Framework," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 952-978, December.
    18. Michela Gnaldi & Simone Del Sarto, 2018. "Time Use Habits of Italian Generation Y: Dimensions of Leisure Preferences," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 138(3), pages 1187-1203, August.
    19. Simone Del Sarto & Michela Gnaldi, 2022. "Spare time use: profiles of Italian Millennials (beyond the media hype)," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1403-1428, December.
    20. Michela Gnaldi, 2017. "A multidimensional IRT approach for dimensionality assessment of standardised students’ tests in mathematics," Quality & Quantity: International Journal of Methodology, Springer, vol. 51(3), pages 1167-1182, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:soinre:v:136:y:2018:i:3:d:10.1007_s11205-016-1500-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.