Prof. Fang Yao

Department of Statistics, University of Toronto

Title:
Modeling Sparse Generalized Longitudinal Observations With Latent Gaussian Processes 

Abstract: In longitudinal data analysis one frequently encounters non-Gaussian data that are repeatedly collected for a sample of individuals over time. The repeated observations could be binomial, Poisson or of another discrete type or could be continuous. The timings of the repeated measurements are often sparse and irregular. We introduce a latent Gaussian process model for such data, establishing a connection to functional data analysis. The proposed functional methods are nonparametric and computationally straightforward as they do not involve a likelihood. We develop functional principal components analysis for this situation and demonstrate the prediction of individual trajectories from sparse observations. This method can handle missing data and leads to predictions of the functional principal component scores which serve as random effects in this model. These scores can then be used for further statistical analysis, such as inference, regression, discriminant analysis or clustering. We illustrate these methods with longitudinal data on primary biliary cirrhosis and onychomycosis (toenail disease).