IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v88y2023i3d10.1007_s11336-023-09918-5.html
   My bibliography  Save this article

Multinomial Logistic Factor Regression for Multi-source Functional Block-wise Missing Data

Author

Listed:
  • Xiuli Du

    (Nanjing Normal University)

  • Xiaohu Jiang

    (Nanjing Normal University)

  • Jinguan Lin

    (Nanjing Audit University)

Abstract

Multi-source functional block-wise missing data arise more commonly in medical care recently with the rapid development of big data and medical technology, hence there is an urgent need to develop efficient dimension reduction to extract important information for classification under such data. However, most existing methods for classification problems consider high-dimensional data as covariates. In the paper, we propose a novel multinomial imputed-factor Logistic regression model with multi-source functional block-wise missing data as covariates. Our main contribution is to establishing two multinomial factor regression models by using the imputed multi-source functional principal component scores and imputed canonical scores as covariates, respectively, where the missing factors are imputed by both the conditional mean imputation and the multiple block-wise imputation approaches. Specifically, the univariate FPCA is carried out for the observable data of each data source firstly to obtain the univariate principal component scores and the eigenfunctions. Then, the block-wise missing univariate principal component scores instead of the block-wise missing functional data are imputed by the conditional mean imputation method and the multiple block-wise imputation method, respectively. After that, based on the imputed univariate factors, the multi-source principal component scores are constructed by using the relationship between the multi-source principal component scores and the univariate principal component scores; and at the same time, the canonical scores are obtained by the multiple-set canonial correlation analysis. Finally, the multinomial imputed-factor Logistic regression model is established with the multi-source principal component scores or the canonical scores as factors. Numerical simulations and real data analysis on ADNI data show the proposed method works well.

Suggested Citation

  • Xiuli Du & Xiaohu Jiang & Jinguan Lin, 2023. "Multinomial Logistic Factor Regression for Multi-source Functional Block-wise Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 975-1001, September.
  • Handle: RePEc:spr:psycho:v:88:y:2023:i:3:d:10.1007_s11336-023-09918-5
    DOI: 10.1007/s11336-023-09918-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-023-09918-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s11336-023-09918-5?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Yoshio Takane & Heungsun Hwang & Hervé Abdi, 2008. "Regularized Multiple-Set Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 753-775, December.
    3. Michel Tenenhaus & Arthur Tenenhaus & Patrick J. F. Groenen, 2017. "Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 737-777, September.
    4. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    5. Yehua Li & Naisyin Wang & Raymond J. Carroll, 2013. "Selecting the Number of Principal Components in Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1284-1294, December.
    6. Fei Xue & Annie Qu, 2021. "Integrating Multisource Block-Wise Missing Data in Model Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1914-1927, October.
    7. Michel Tenenhaus, 2011. "Regularized generalized canonical correlation analysis," Post-Print hal-00578321, HAL.
    8. Arthur Tenenhaus & Michel Tenenhaus, 2011. "Regularized Generalized Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 76(2), pages 257-284, April.
    9. Bair, Eric & Hastie, Trevor & Paul, Debashis & Tibshirani, Robert, 2006. "Prediction by Supervised Principal Components," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 119-137, March.
    10. Michel Tenenhaus & Arthur Tenenhaus, 2011. "Regularized Generalized Canonical Correlation Analysis," Post-Print hal-00609220, HAL.
    11. Heungsun Hwang & Kwanghee Jung & Yoshio Takane & Todd Woodward, 2012. "Functional Multiple-Set Canonical Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 48-64, January.
    12. Guan Yu & Quefeng Li & Dinggang Shen & Yufeng Liu, 2020. "Optimal Sparse Linear Prediction for Block-missing Multi-modality Data Without Imputation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1406-1419, July.
    13. Tianxi Cai & T. Tony Cai & Anru Zhang, 2016. "Structured Matrix Completion with Applications to Genomic Data Integration," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 621-633, April.
    14. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    15. Tenenhaus, Arthur & Philippe, Cathy & Frouin, Vincent, 2015. "Kernel Generalized Canonical Correlation Analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 114-131.
    16. Jacques, Julien & Preda, Cristian, 2014. "Model-based clustering for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 92-106.
    17. Hongtu Zhu & Dan Shen & Xuewei Peng & Leo Yufeng Liu, 2017. "MWPCR: Multiscale Weighted Principal Component Regression for High-Dimensional Prediction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1009-1021, July.
    18. Ji Yeh Choi & Heungsun Hwang & Michio Yamamoto & Kwanghee Jung & Todd S. Woodward, 2017. "A Unified Approach to Functional Principal Component Analysis and Functional Multiple-Set Canonical Correlation," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 427-441, June.
    19. Yong He & Xinbing Kong & Long Yu & Xinsheng Zhang, 2022. "Large-Dimensional Factor Analysis Without Moment Constraints," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 302-312, January.
    20. Clara Happ & Sonja Greven, 2018. "Multivariate Functional Principal Component Analysis for Data Observed on Different (Dimensional) Domains," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 649-659, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tenenhaus, Arthur & Philippe, Cathy & Frouin, Vincent, 2015. "Kernel Generalized Canonical Correlation Analysis," Computational Statistics & Data Analysis, Elsevier, vol. 90(C), pages 114-131.
    2. Heungsun Hwang & Gyeongcheol Cho, 2020. "Global Least Squares Path Modeling: A Full-Information Alternative to Partial Least Squares Path Modeling," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 947-972, December.
    3. Kyunghee Han & Pantelis Z Hadjipantelis & Jane-Ling Wang & Michael S Kramer & Seungmi Yang & Richard M Martin & Hans-Georg Müller, 2018. "Functional principal component analysis for identifying multivariate patterns and archetypes of growth, and their association with long-term cognitive development," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-18, November.
    4. Lukáš Malec & Vladimír Janovský, 2020. "Connecting the multivariate partial least squares with canonical analysis: a path-following approach," 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. 14(3), pages 589-609, September.
    5. Shen, Cencheng & Sun, Ming & Tang, Minh & Priebe, Carey E., 2014. "Generalized canonical correlation analysis for classification," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 310-322.
    6. Cruz-Cano, Raul & Lee, Mei-Ling Ting, 2014. "Fast regularized canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 88-100.
    7. Husson, François & Josse, Julie & Saporta, Gilbert, 2016. "Jan de Leeuw and the French School of Data Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 73(i06).
    8. Wang, Wenjia & Zhou, Yi-Hui, 2021. "Eigenvector-based sparse canonical correlation analysis: Fast computation for estimation of multiple canonical vectors," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    9. Evermann, Joerg & Tate, Mary, 2016. "Assessing the predictive performance of structural equation model estimators," Journal of Business Research, Elsevier, vol. 69(10), pages 4565-4582.
    10. Golovkine, Steven & Klutchnikoff, Nicolas & Patilea, Valentin, 2022. "Clustering multivariate functional data using unsupervised binary trees," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    11. Sarstedt, Marko & Hair, Joseph F. & Ringle, Christian M. & Thiele, Kai O. & Gudergan, Siegfried P., 2016. "Estimation issues with PLS and CBSEM: Where the bias lies!," Journal of Business Research, Elsevier, vol. 69(10), pages 3998-4010.
    12. Virta, Joni & Li, Bing & Nordhausen, Klaus & Oja, Hannu, 2020. "Independent component analysis for multivariate functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    13. Michel Tenenhaus & Arthur Tenenhaus & Patrick J. F. Groenen, 2017. "Regularized Generalized Canonical Correlation Analysis: A Framework for Sequential Multiblock Component Methods," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 737-777, September.
    14. Joseph F. Hair & G. Tomas M. Hult & Christian M. Ringle & Marko Sarstedt & Kai Oliver Thiele, 2017. "Mirror, mirror on the wall: a comparative evaluation of composite-based structural equation modeling methods," Journal of the Academy of Marketing Science, Springer, vol. 45(5), pages 616-632, September.
    15. Xinyue Chang & Yehua Li & Yi Li, 2023. "Asynchronous and error‐prone longitudinal data analysis via functional calibration," Biometrics, The International Biometric Society, vol. 79(4), pages 3374-3387, December.
    16. Rosaria Romano & Francesco Palumbo, 2021. "Partial possibilistic regression path modeling: handling uncertainty in path modeling," Computational Statistics, Springer, vol. 36(1), pages 615-639, March.
    17. Florian Rohart & Benoît Gautier & Amrit Singh & Kim-Anh Lê Cao, 2017. "mixOmics: An R package for ‘omics feature selection and multiple data integration," PLOS Computational Biology, Public Library of Science, vol. 13(11), pages 1-19, November.
    18. Saart, Patrick W. & Xia, Yingcun, 2022. "Functional time series approach to analyzing asset returns co-movements," Journal of Econometrics, Elsevier, vol. 229(1), pages 127-151.
    19. Stéphanie Bougeard & Hervé Abdi & Gilbert Saporta & Ndèye Niang, 2018. "Clusterwise analysis for multiblock component methods," 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. 12(2), pages 285-313, June.
    20. Cristina Davino & Vincenzo Esposito Vinzi, 2016. "Quantile composite-based path modeling," 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. 10(4), pages 491-520, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:88:y:2023:i:3:d:10.1007_s11336-023-09918-5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.