Abstract

A growth curve model (GCM) aims to characterize how an outcome variable evolves,

develops and grows as a function of time, along with other predictors. It provides a particularly useful framework to model growth trend in longitudinal data. However, the estimation

and inference of GCM with a large number of response variables faces numerous challenges, and

remains underdeveloped. In this article, we study the high-dimensional multivariate-response

linear GCM, and develop the corresponding estimation and inference procedures. Our proposal

involves several innovative components. Specifically, we introduce a Kronecker product structure, which allows us to effectively decompose a very large covariance matrix, and to pool the

correlated samples to improve the estimation accuracy. We devise a highly non-trivial multi-step

estimation approach to estimate the individual covariance components separately and effectively.

We also develop rigorous statistical inference procedures to test both the global effects and the

individual effects, and establish the size and power properties as well as the proper false discovery control. We demonstrate the effectiveness of the new method through both intensive

simulations, and the analysis of a longitudinal neuroimaging data for Alzheimer’s disease.

Information

Preprint No.SS-2024-0307
Manuscript IDSS-2024-0307
Complete AuthorsXin Zhou, Yin Xia, Lexin Li
Corresponding AuthorsYin Xia
Emailsxiayin@fudan.edu.cn

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Acknowledgments

We are grateful to the editor, associate editor, and the two reviewers for their insightful

comments and suggestions, which have greatly improved this manuscript. Xia’s research

was partially supported by NSFC 12331009. Li’s research was partially supported by

NSF CIF-2102227, NIH R01AG080043, and NIH UG3NS140730.

Supplementary Materials

The Supplementary Material contains all technical proofs of the theoretical results and

additional numerical results.

Supplementary materials are available for download.