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Using Generalized Procrustes Analysis for Multiple Imputation in Principal Component Analysis

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  • Joost Ginkel
  • Pieter Kroonenberg

Abstract

Multiple imputation is one of the most highly recommended procedures for dealing with missing data. However, to date little attention has been paid to methods for combining the results from principal component analyses applied to a multiply imputed data set. In this paper we propose Generalized Procrustes analysis for this purpose, of which its centroid solution can be used as a final estimate for the component loadings. Convex hulls based on the loadings of the imputed data sets can be used to represent the uncertainty due to the missing data. In two simulation studies, the performance of Generalized Procrustes approach is evaluated and compared with other methods. More specifically it is studied how these methods behave when order changes of components and sign reversals of component loadings occur, such as in case of near-equal eigenvalues, or data having almost as many counterindicative items as indicative items. The simulations show that other proposed methods either may run into serious problems or are not able to adequately assess the accuracy due to the presence of missing data. However, when the above situations do not occur, all methods will provide adequate estimates for the PCA loadings. Copyright Classification Society of North America 2014

Suggested Citation

  • Joost Ginkel & Pieter Kroonenberg, 2014. "Using Generalized Procrustes Analysis for Multiple Imputation in Principal Component Analysis," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 242-269, July.
    • Handle: RePEc:spr:jclass:v:31:y:2014:i:2:p:242-269
    DOI: 10.1007/s00357-014-9154-y
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    References listed on IDEAS

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    2. Renate S M Buisman & Katharina Pittner & Marieke S Tollenaar & Jolanda Lindenberg & Lisa J M van den Berg & Laura H C G Compier-de Block & Joost R van Ginkel & Lenneke R A Alink & Marian J Bakermans-K, 2020. "Intergenerational transmission of child maltreatment using a multi-informant multi-generation family design," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-23, March.
    3. Sébastien Loisel & Yoshio Takane, 2019. "Comparisons among several methods for handling missing data in principal component analysis (PCA)," 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. 13(2), pages 495-518, June.
    4. Ann Bostrom & Adam L. Hayes & Katherine M. Crosman, 2019. "Efficacy, Action, and Support for Reducing Climate Change Risks," Risk Analysis, John Wiley & Sons, vol. 39(4), pages 805-828, April.

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