Integrative Factor Regression and Its Inference for Multimodal Data Analysis

Abstract

Multimodal data, where different types of data are collected from the same subjects, are fast emerging in a large variety of scientific applications. Factor analysis is commonly used in integrative analysis of multimodal data, and is particularly useful to overcome the curse of high dimensionality and high correlations. However, there is little work on statistical inference for factor analysis-based supervised modeling of multimodal data. In this article, we consider an integrative linear regression model that is built upon the latent factors extracted from multimodal data. We address three important questions: how to infer the significance of one data modality given the other modalities in the model; how to infer the significance of a combination of variables from one modality or across different modalities; and how to quantify the contribution, measured by the goodness of fit, of one data modality given the others. When answering each question, we explicitly characterize both the benefit and the extra cost of factor analysis. Those questions, to our knowledge, have not yet been addressed despite wide use of factor analysis in integrative multimodal analysis, and our proposal bridges an important gap. We study the empirical performance of our methods through simulations, and further illustrate with a multimodal neuroimaging analysis.

Keywords:

• Data integration
• Dimension reduction
• Factor analysis
• High-dimensional inference
• Multimodal neuroimaging
• Principal components analysis

Acknowledgments

The authors thank the editor, the associate editor, and two referees for their constructive comments and suggestions.

Additional information

Funding

Quefeng Li’s research was partially supported by NIH grant R01HL149683. Lexin Li’s research was partially supported by NIH grants R01AG061303, R01AG062542, and R01AG034570.