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arXiv · 2109.05861

Applied Regression Analysis of Correlations for Correlated Data

Jie Hu·Yu Chen·Chenlei Leng·Cheng Yong Tang
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Abstract

Correlated data are ubiquitous in today's data-driven society. While regression models for analyzing means and variances of responses of interest are relatively well-developed, the development of these models for analyzing the correlations is largely confined to longitudinal data, a special form of sequentially correlated data. This paper proposes a new method for the analysis of correlations to fully exploit the use of covariates for general correlated data. In a renewed analysis of the Classroom data, a highly unbalanced multilevel clustered data with within-class and within-school correlations, our method reveals informative insights on these structures not previously known. In another analysis of the malaria immune response data in Benin, a longitudinal study with time-dependent covariates where the exact times of the observations are not available, our approach again provides promising new results. At the heart of our approach is a new generalized z-transformation that converts correlation matrices constrained to be positive definite to vectors with unrestricted support, and is order-invariant. These two properties enable us to develop regression analysis incorporating covariates for the modelling of correlations via the use of maximum likelihood.

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Jie Hu, Yu Chen, Chenlei Leng, Cheng Yong Tang. 2021-09-13. Applied Regression Analysis of Correlations for Correlated Data. https://arxiv.org/abs/2109.05861

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