Bayesian Latent Factor Regression for Functional and Longitudinal Data
Version of Record online: 24 SEP 2012
© 2012, The International Biometric Society
Volume 68, Issue 4, pages 1064–1073, December 2012
How to Cite
Montagna, S., Tokdar, S. T., Neelon, B. and Dunson, D. B. (2012), Bayesian Latent Factor Regression for Functional and Longitudinal Data. Biometrics, 68: 1064–1073. doi: 10.1111/j.1541-0420.2012.01788.x
- Issue online: 21 DEC 2012
- Version of Record online: 24 SEP 2012
- Received June 2011. Revised January 2012. Accepted May 2012.
- Factor analysis;
- Functional principal components analysis;
- Latent trajectory models;
- Random effects;
- Sparse data
Summary In studies involving functional data, it is commonly of interest to model the impact of predictors on the distribution of the curves, allowing flexible effects on not only the mean curve but also the distribution about the mean. Characterizing the curve for each subject as a linear combination of a high-dimensional set of potential basis functions, we place a sparse latent factor regression model on the basis coefficients. We induce basis selection by choosing a shrinkage prior that allows many of the loadings to be close to zero. The number of latent factors is treated as unknown through a highly-efficient, adaptive-blocked Gibbs sampler. Predictors are included on the latent variables level, while allowing different predictors to impact different latent factors. This model induces a framework for functional response regression in which the distribution of the curves is allowed to change flexibly with predictors. The performance is assessed through simulation studies and the methods are applied to data on blood pressure trajectories during pregnancy.