Estimation and prediction methods for univariate and bivariate cyclic longitudinal data using a semiparametric stochastic mixed effects model

Abstract

In this thesis, I propose and consider inference for a semiparametric stochastic mixed model for bivariate longitudinal data; and provide a prediction procedure of a future cycle utilizing past cycle information. This thesis is built on the work of Zhang et al (1998) and Zhang, Lin & Sowers (2000). However, the papers are missing big gaps in the theoretical results, are to be applied on univariate longitudinal data, and contain no coverage of prediction of future cycles. We fill in all the gaps in this thesis as well as consider real application of a dataset that contains bivariate longitudinal data. The proposed approach models the mean of outcome variables by parametric fixed effects and a smooth nonparametric function for the underlying time effects, and the relationship across the bivariate responses by a bivariate Gaussian random field and a joint distribution of random effects. The prediction approach is proposed from the frequentist prospective and a prediction density function with predictive intervals will be provided. Simulations studies are performed and a real application of a hormone dataset is considered.