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Principal component analysis with missing values: a comparative survey of methods

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Abstract

Principal component analysis (PCA) is a standard technique to summarize the main structures of a data table containing the measurements of several quantitative variables for a number of individuals. Here, we study the case where some of the data values are missing and propose a review of methods which accommodate PCA to missing data. In plant ecology, this statistical challenge relates to the current effort to compile global plant functional trait databases producing matrices with a large amount of missing values. We present several techniques to consider or estimate (impute) missing values in PCA and compare them using theoretical considerations. We carried out a simulation study to evaluate the relative merits of the different approaches in various situations (correlation structure, number of variables and individuals, and percentage of missing values) and also applied them on a real data set. Lastly, we discuss the advantages and drawbacks of these approaches, the potential pitfalls and future challenges that need to be addressed in the future.

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Acknowledgments

We would like to thank Peter Minchin and Jari Oksanen for the invitation to participate to this special issue and Gavin Simpson and an anonymous reviewer for comments on an earlier draft of the manuscript. We would like to warmly thank Ian Wright for freely distributing the GLOPNET data set.

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Authors and Affiliations

  1. Université de Lyon, 69000, Lyon, France

    Stéphane Dray

  2. Université Lyon 1, CNRS, UMR5558, Laboratoire de Biométrie et Biologie Evolutive, 69622, Villeurbanne, France

    Stéphane Dray

  3. Applied Mathematics Department, Agrocampus Ouest, Rennes, France

    Julie Josse

Authors
  1. Stéphane Dray
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  2. Julie Josse
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Correspondence to Stéphane Dray.

Additional information

Communicated by P. R. Minchin and J. Oksanen.

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Dray, S., Josse, J. Principal component analysis with missing values: a comparative survey of methods. Plant Ecol 216, 657–667 (2015). https://doi.org/10.1007/s11258-014-0406-z

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