Determination of correlations in multivariate longitudinal data with modified Cholesky and hypersphere decomposition...

Area of Science:

• Statistics
• Biostatistics
• Data Science

Background:

• Multivariate longitudinal data analysis presents challenges in identifying important relationships within the generalized autoregressive matrix.
• Existing methods may not efficiently handle the selection of significant elements in complex time-series data.

Purpose of the Study:

• To develop a Bayesian framework for multivariate longitudinal data analysis.
• To focus on the selection of important elements within the generalized autoregressive matrix.
• To provide an accessible R package for implementing the proposed methodology.

Main Methods:

• A Bayesian framework was developed for multivariate longitudinal data.
• An efficient Gibbs sampling algorithm was created for model implementation.
• The methodology was validated through a comprehensive simulation study.
• An R package, MLModelSelection, was developed and made available.

Main Results:

• The proposed Bayesian framework effectively selects important elements in the generalized autoregressive matrix.
• Simulation studies demonstrated the robust performance of the developed approach.
• Application to a nonalcoholic fatty liver disease dataset revealed significant correlations in multiple responses over time.

Conclusions:

• The Bayesian framework offers an effective approach for multivariate longitudinal data analysis and element selection.
• The MLModelSelection R package provides a practical tool for researchers.
• The methodology successfully illustrated joint variability in lung function and body mass index within a clinical context.