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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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Bayesian latent factor regression for functional and longitudinal data.

Silvia Montagna1, Surya T Tokdar, Brian Neelon

  • 1Department of Statistical Science, Duke University, Durham, NC 27708, USA. sm234@duke.edu

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Summary
This summary is machine-generated.

This study introduces a novel sparse latent factor regression model for functional data analysis. The method allows predictors to flexibly influence the distribution of curves, enhancing understanding of complex biological trajectories.

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Area of Science:

  • Statistics
  • Functional Data Analysis
  • Biostatistics

Background:

  • Modeling functional data often requires understanding how predictors affect not just the mean curve but also its distribution.
  • Existing methods may lack flexibility in capturing these complex relationships.

Purpose of the Study:

  • To develop a flexible functional response regression model that accommodates predictor-driven changes in curve distributions.
  • To enable basis selection and handle an unknown number of latent factors.

Main Methods:

  • A sparse latent factor regression model is applied to basis coefficients of functional data.
  • Shrinkage priors induce basis selection, and an adaptive-blocked Gibbs sampler estimates the number of latent factors.
  • Predictors are incorporated at the latent variable level, allowing differential impact.

Main Results:

  • The proposed model provides a flexible framework for functional response regression.
  • Simulation studies demonstrate the model's performance.
  • Application to blood pressure trajectories during pregnancy illustrates its utility.

Conclusions:

  • The novel sparse latent factor regression model offers a powerful tool for analyzing functional data where predictor effects on curve distribution are crucial.
  • This approach enhances the ability to model complex biological and health-related trajectories.