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

  • Theory and Methods
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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.

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Acknowledgements

Data collection and sharing for this project was funded by the Alzheimer’s Disease Neuroimaging Initiative (ADNI) (National Institutes of Health Grant U01 AG024904) and DOD ADNI (Department of Defense award number W81XWH-12-2-0012). ADNI is funded by the National Institute on Aging, the National Institute of Biomedical Imaging and Bioengineering, and through generous contributions from the following: AbbVie, Alzheimer’s Association; Alzheimer’s Drug Discovery Foundation; Araclon Biotech; BioClinica, Inc.; Biogen; Bristol-Myers Squibb Company; CereSpir, Inc.; Cogstate; Eisai Inc.; Elan Pharmaceuticals, Inc.; Eli Lilly and Company; EuroImmun; F. Hoffmann-La Roche Ltd and its affiliated company Genentech, Inc.; Fujirebio; GE Healthcare; IXICO Ltd.; Janssen Alzheimer Immunotherapy Research & Development, LLC.; Johnson & Johnson Pharmaceutical Research & Development LLC.; Lumosity; Lundbeck; Merck & Co., Inc.; Meso Scale Diagnostics, LLC.; NeuroRx Research; Neurotrack Technologies; Novartis Pharmaceuticals Corporation; Pfizer Inc.; Piramal Imaging; Servier; Takeda Pharmaceutical Company; and Transition Therapeutics. The Canadian Institutes of Health Research is providing funds to support ADNI clinical sites in Canada. Private sector contributions are facilitated by the Foundation for the National Institutes of Health (www.fnih.org). The grantee organization is the Northern California Institute for Research and Education, and the study is coordinated by the Alzheimer’s Therapeutic Research Institute at the University of Southern California. ADNI data are disseminated by the Laboratory for Neuro Imaging at the University of Southern California. We also thank editors and three anonymous reviews for their constructive comments that helped improve the quality of this article.

Funding

This research is supported by the National Social Science Foundation of China (No.21BTJ044).

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Authors and Affiliations

  1. College of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China

    Xiuli Du & Xiaohu Jiang

  2. Institute of Statistics and Data Science, Nanjing Audit University, Nanjing, 211815, China

    Jinguan Lin

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  1. Xiuli Du
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  2. Xiaohu Jiang
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The Alzheimer’s Disease Neuroimaging Initiative

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Correspondence to Xiuli Du.

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Data used in preparation of this article were obtained from the Alzheimer’s Disease Neuroimaging Initiative (ADNI) database (adni.loni.usc.edu). As such, the investigators within the ADNI contributed to the design and implementation of ADNI and/or provided data but did not participate in analysis or writing of this report. A complete listing of ADNI investigators can be found at: http://adni.loni.usc.edu/wpcontent/uploads/how_to_apply/ADNI_Acknowledgement_List.pdf.

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Du, X., Jiang, X., Lin, J. et al. Multinomial Logistic Factor Regression for Multi-source Functional Block-wise Missing Data. Psychometrika 88, 975–1001 (2023). https://doi.org/10.1007/s11336-023-09918-5

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