Approximate bayes random effects models for large datasets
Year: 2010
Type: dissertation
Abstract: Many medical studies collect functional data, such as trajectories in a biomarker over time. It is of interest to estimate the trajectories and identify or predict clinically-important features. Linear mixed effects (LME) models are commonly used in such cases, with non-linear effects easily incorporated through splines. However, for sufficient flexibility, it is often necessary to use adaptive splines in which the number and locations of knots is unknown and potentially varying across subjects. This can be accomplished with MCMC methodology, using reversible jump or stochastic search variable selection. However, such approaches are slow and infeasible to implement routinely, particularly for large data sets. Motivated by methods proposed in the machine learning literature for compressive sensing, we focus on relevant vector machine (RVM) methodology - a fast approximate Bayes functional data analysis approach that relies on sparseness-favouring hierarchical priors for basis coefficients. Recent literature on the use of RVM methodology is restricted to models that assume that the distribution of the basis coefficients is centered at zero with diagonal covariance. However, in many longitudinal and functional data analysis applications, centering at zero is an unrealistic assumption and does not allow shrinkage towards a population-averaged function. In this work, we develop a generalized multi-task relevant vector machine (MT-RVM) methodology that generates sparse functional linear mixed models to estimate both population-average and subject-specific curves. In particular, we first consider an LME model that assumes independent random effects and then extend the approach to a more generalized LME model with correlated random effects. Further, we extend the application of the generalized MT-RVM methodology into multi-level relevant vector machine (ML-RVM) methodology to generate a sparse multi-level functional mixed model. The analysis of basal body temperature curves over the menstrual cycle has been the motivating application for all the developed methods.
Author: James Ciera
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2281207728