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Longitudinal studies are also widely used in other medical and social science fields. For instance, in cardiovascular research, they can monitor patients' health over decades to identify risk factors for heart disease, such as high cholesterol or smoking, and evaluate the long-term effectiveness of preventive measures. Similarly, in mental health studies, researchers might follow individuals from adolescence into adulthood to understand the development and progression of conditions like...
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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Functional generalized canonical correlation analysis for studying multiple longitudinal variables.

Lucas Sort1, Laurent Le Brusquet1, Arthur Tenenhaus1

  • 1Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes, Gif-sur-Yvette 91190, France.

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Summary
This summary is machine-generated.

We present functional generalized canonical correlation analysis (FGCCA), a novel statistical framework for analyzing associations between multiple random processes. This robust method handles sparse, irregular data and enables predictive modeling for diverse applications.

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functional datageneralized canonical correlation analysislongitudinal data

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Area of Science:

  • Statistics
  • Data Analysis
  • Multivariate Analysis

Background:

  • Exploring associations between multiple random processes is crucial in many scientific fields.
  • Existing methods may struggle with sparsely or irregularly observed data.
  • A need exists for flexible frameworks accommodating complex data structures.

Purpose of the Study:

  • Introduce functional generalized canonical correlation analysis (FGCCA) as a new statistical framework.
  • Develop a robust method for analyzing associations between multiple joint random processes.
  • Extend the framework for predictive applications by integrating response variables.

Main Methods:

  • Leverage the multiblock regularized generalized canonical correlation analysis (RGCCA) framework.
  • Establish the monotonic property of the FGCCA solving procedure.
  • Incorporate a Bayesian approach for estimating canonical components.
  • Propose an extension for incorporating univariate or multivariate response variables.

Main Results:

  • The proposed FGCCA framework demonstrates robustness to sparse and irregularly observed data.
  • The monotonic property of the solving procedure is theoretically established.
  • A Bayesian estimation approach for canonical components is introduced.
  • The extended FGCCA framework facilitates predictive modeling.

Conclusions:

  • FGCCA offers a powerful and flexible new tool for analyzing complex associations between random processes.
  • The method's robustness and adaptability make it suitable for various real-world datasets.
  • The predictive extension opens avenues for forecasting and classification tasks in data analysis.