Bayesian multivariate sparse functional principal components analysis with application to longitudinal microbiome...

Area of Science:

• Microbiome research
• Statistical modeling
• Functional data analysis

Background:

• Modeling simultaneous temporal dynamics of multiple complex, nonlinear outcomes is crucial in microbiome research.
• Existing Sparse Functional Principal Components Analysis (SFPCA) methods are limited in handling multiple trajectories and their inter-relationships.

Purpose of the Study:

• To introduce multivariate Sparse Functional Principal Components Analysis (mSFPCA) for simultaneous characterization of multiple temporal trajectories and their inter-relationships.
• To extend SFPCA methods for enhanced analysis of complex biological data.

Main Methods:

• mSFPCA models each trajectory as a smooth mean plus weighted modes of variation.
• Utilizes Cholesky decomposition for efficient covariance matrix estimation and ensures positive semi-definiteness.
• Employs mutual information to assess temporal associations across outcome trajectories.
• Implemented as a Bayesian algorithm using R and stan for model selection (PSIS-LOO) and validation.

Main Results:

• mSFPCA enables simultaneous estimation of multiple trajectories, allowing correlated component scores across outcomes.
• The method effectively characterizes temporal dynamics and inter-relationships in complex datasets.
• Bayesian implementation facilitates robust model assessment and selection.

Conclusions:

• mSFPCA provides a powerful, flexible tool for analyzing multivariate temporal data, particularly in microbiome research.
• The model's general utility extends to various real-world applications requiring the analysis of multiple dynamic trajectories.