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An imputation method for categorical variables with application to nonlinear principal component analysis

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  • Ferrari, Pier Alda
  • Annoni, Paola
  • Barbiero, Alessandro
  • Manzi, Giancarlo

Abstract

The problem of missing data in building multidimensional composite indicators is a delicate problem which is often underrated. An imputation method particularly suitable for categorical data is proposed. This method is discussed in detail in the framework of nonlinear principal component analysis and compared to other missing data treatments which are commonly used in this analysis. Its performance vs. these other methods is evaluated throughout a simulation procedure performed on both an artificial case, varying the experimental conditions, and a real case. The proposed procedure is implemented using R1.

Suggested Citation

  • Ferrari, Pier Alda & Annoni, Paola & Barbiero, Alessandro & Manzi, Giancarlo, 2011. "An imputation method for categorical variables with application to nonlinear principal component analysis," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2410-2420, July.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:7:p:2410-2420
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    References listed on IDEAS

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    1. Thomas Astebro & Gongyue Chen, 2003. "How to Deal with Missing Categorical Data: Test of a Simple Bayesian Method," Post-Print hal-00477167, HAL.
    2. Pier Ferrari & Paola Annoni & Giancarlo Manzi, 2010. "Evaluation and comparison of European countries: public opinion on services," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(6), pages 1191-1205, October.
    3. James R. Carpenter & Michael G. Kenward & Stijn Vansteelandt, 2006. "A comparison of multiple imputation and doubly robust estimation for analyses with missing data," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 169(3), pages 571-584, July.
    4. White, Ian R. & Daniel, Rhian & Royston, Patrick, 2010. "Avoiding bias due to perfect prediction in multiple imputation of incomplete categorical variables," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2267-2275, October.
    5. Serneels, Sven & Verdonck, Tim, 2009. "Principal component regression for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3855-3863, September.
    6. Siddique, Juned & Belin, Thomas R., 2008. "Using an Approximate Bayesian Bootstrap to multiply impute nonignorable missing data," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 405-415, December.
    7. Christopher Paul & William Mason & Daniel McCaffrey & Sarah Fox, 2008. "A cautionary case study of approaches to the treatment of missing data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 351-372, July.
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    Cited by:

    1. Nadia Solaro & Alessandro Barbiero & Giancarlo Manzi & Pier Alda Ferrari, 2017. "A sequential distance-based approach for imputing missing data: Forward Imputation," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 395-414, June.
    2. Arboretti, Rosa & Bonnini, Stefano & Corain, Livio & Salmaso, Luigi, 2014. "A permutation approach for ranking of multivariate populations," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 39-57.
    3. Pier Alda FERRARI & Alessandro BARBIERO, 2011. "Generating ordinal data," Departmental Working Papers 2011-38, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.

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