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A sequential distance-based approach for imputing missing data: Forward Imputation

Author

Listed:
  • Nadia Solaro

    (Università degli Studi di Milano-Bicocca)

  • Alessandro Barbiero

    (Università degli Studi di Milano)

  • Giancarlo Manzi

    (Università degli Studi di Milano)

  • Pier Alda Ferrari

    (Università degli Studi di Milano)

Abstract

Missing data recurrently affect datasets in almost every field of quantitative research. The subject is vast and complex and has originated a literature rich in very different approaches to the problem. Within an exploratory framework, distance-based methods such as nearest-neighbour imputation (NNI), or procedures involving multivariate data analysis (MVDA) techniques seem to treat the problem properly. In NNI, the metric and the number of donors can be chosen at will. MVDA-based procedures expressly account for variable associations. The new approach proposed here, called Forward Imputation, ideally meets these features. It is designed as a sequential procedure that imputes missing data in a step-by-step process involving subsets of units according to their “completeness rate”. Two methods within this context are developed for the imputation of quantitative data. One applies NNI with the Mahalanobis distance, the other combines NNI and principal component analysis. Statistical properties of the two methods are discussed, and their performance is assessed, also in comparison with alternative imputation methods. To this purpose, a simulation study in the presence of different data patterns along with an application to real data are carried out, and practical hints for users are also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:11:y:2017:i:2:d:10.1007_s11634-016-0243-0
    DOI: 10.1007/s11634-016-0243-0
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    References listed on IDEAS

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    1. Agostino Tarsitano & Marianna Falcone, 2010. "Missing-Values Adjustment For Mixed-Type Data," Working Papers 201015, Università della Calabria, Dipartimento di Economia, Statistica e Finanza "Giovanni Anania" - DESF.
    2. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    3. Nadia SOLARO & Alessandro BARBIERO & Giancarlo MANZI & Pier Alda FERRARI, 2015. "A Comprehensive Simulation Study on the Forward Imputation," Departmental Working Papers 2015-04, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    4. Lounasheimo, Antton, 1999. "The Impact of Human Capital on Economic Growth," Discussion Papers 673, The Research Institute of the Finnish Economy.
    5. Julie Josse & Jérôme Pagès & François Husson, 2011. "Multiple imputation in principal component analysis," 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. 5(3), pages 231-246, October.
    6. 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.
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    Cited by:

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