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Sparse logistic functional principal component analysis for binary data

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Abstract

Functional binary datasets occur frequently in real practice, whereas discrete characteristics of the data can bring challenges to model estimation. In this paper, we propose a sparse logistic functional principal component analysis (SLFPCA) method to handle functional binary data. The SLFPCA looks for local sparsity of the eigenfunctions to obtain convenience in interpretation. We formulate the problem through a penalized Bernoulli likelihood with both roughness penalty and sparseness penalty terms. An innovative algorithm is developed for the optimization of the penalized likelihood using majorization-minimization algorithm. The proposed method is accompanied by R package SLFPCA for implementation. The theoretical results indicate both consistency and sparsistency of the proposed method. We conduct a thorough numerical experiment to demonstrate the advantages of the SLFPCA approach. Our method is further applied to a physical activity dataset.

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Acknowledgements

This work was supported by Public Health & Disease Control and Prevention, Major Innovation & Planning Interdisciplinary Platform for the “Double-First Class” Initiative, Renmin University of China. This work was supported by the Outstanding Innovative Talents Cultivation Funded Programs 2021 of Renmin University of China.

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Authors and Affiliations

  1. Center for Applied Statistics, School of Statistics, Renmin University of China, Beijing, China

    Rou Zhong & Jingxiao Zhang

  2. School of Economics, Hangzhou Dianzi University, Hangzhou, China

    Shishi Liu

  3. Department of Mathematics and Statistics, University of Calgary, Calgary, Canada

    Haocheng Li

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  1. Rou Zhong
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  2. Shishi Liu
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  3. Haocheng Li
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  4. Jingxiao Zhang
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Correspondence to Jingxiao Zhang.

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Zhong, R., Liu, S., Li, H. et al. Sparse logistic functional principal component analysis for binary data. Stat Comput 33, 15 (2023). https://doi.org/10.1007/s11222-022-10190-3

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