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Low-rank model with covariates for count data with missing values

Author

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  • Robin, Geneviève
  • Josse, Julie
  • Moulines, Éric
  • Sardy, Sylvain

Abstract

A complete methodology called LORI (Low-Rank Interaction), including a Poisson model, an algorithm, and an automatic selection of the regularization parameter, is proposed for the analysis of frequency tables with covariates, including an upper bound on the estimation error. A simulation study with synthetic data suggests that LORI improves empirically on state-of-the-art methods in terms of estimation and imputation. Illustrations show how the method can be interpreted through visual displays with the analysis of a well-known plant abundance data set, and the LORI outputs are seen to be consistent with known results. The relevance of the methodology is also demonstrated through the analysis of a waterbirds abundance contingency table from the French national agency for wildlife and hunting management. The method is available in the R package lori on the Comprehensive Archive Network (CRAN).

Suggested Citation

  • Robin, Geneviève & Josse, Julie & Moulines, Éric & Sardy, Sylvain, 2019. "Low-rank model with covariates for count data with missing values," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 416-434.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:416-434
    DOI: 10.1016/j.jmva.2019.04.004
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    References listed on IDEAS

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    1. de Leeuw, Jan, 2006. "Principal component analysis of binary data by iterated singular value decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 21-39, January.
    2. Fithian, William & Josse, Julie, 2017. "Multiple correspondence analysis and the multilogit bilinear model," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 87-102.
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    2. Bigot, Jérémie & Deledalle, Charles, 2022. "Low-rank matrix denoising for count data using unbiased Kullback-Leibler risk estimation," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    3. Chen, Yunxiao & Li, Xiaoou, 2022. "Determining the number of factors in high-dimensional generalized latent factor models," LSE Research Online Documents on Economics 111574, London School of Economics and Political Science, LSE Library.
    4. P. Chatelain & X. Milhaud, 2024. "Estimation and prediction with data quality indexes in linear regressions," Computational Statistics, Springer, vol. 39(6), pages 3373-3404, September.
    5. Li, Xiao & Matsuda, Takeru & Komaki, Fumiyasu, 2024. "Empirical Bayes Poisson matrix completion," Computational Statistics & Data Analysis, Elsevier, vol. 197(C).

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