Imputation of Mixed Data With Multilevel Singular Value Decomposition

• Published in: Journal of computational and graphical statistics 2019-07, Vol.28 (3), p.552-566
• Main Authors: Husson, François, Josse, Julie, Narasimhan, Balasubramanian, Robin, Geneviève
• Format: Article
• Language: English
• Subjects: Agglomeration; Applications; Computer simulation; Datasets; Distributed computation; Hierarchical data; Hospitals; Low-rank matrix estimation; Matrix completion; Multilevel; Multivariate, Multilevel, and Mixture Modelling; Qualitative analysis; Singular value decomposition; Statistical analysis; Statistical methods; Statistics; Systematically and sporadically missing values
• ISSN: 1061-8600; 1537-2715
• DOI: 10.1080/10618600.2019.1585261

Statistical analysis of large datasets offers new opportunities to better understand underlying processes. Yet, data accumulation often implies relaxing acquisition procedures or compounding diverse sources. As a consequence, datasets often contain mixed data, that is, both quantitative and qualitative, and many missing values. Furthermore, aggregated data present a natural multilevel structure, where individuals or samples are nested within different sites, such as countries or hospitals. Imputation of multilevel data has therefore drawn some attention recently, but current solutions are not designed to handle mixed data, and suffer from important drawbacks, such as their computational cost. In this article, we propose a single imputation method for multilevel data, which can be used to complete either quantitative, categorical, or mixed data. The method is based on multilevel singular value decomposition (SVD), which consists in decomposing the variability of the data into two components, the between and within groups variability, and performing an SVD on both parts. We show on a simulation study that in comparison to competitors, the method has the advantages of handling datasets of various size, and being computationally faster. Furthermore, it is the first so far to handle mixed data. We apply the method to impute a medical dataset resulting from the aggregation of several hospitals datasets. This application falls in the framework of a larger project on Trauma patients. To overcome obstacles associated to the aggregation of medical data, we turn to distributed computation. The method is implemented in the R package missMDA. Supplementary materials for this article are available online.