Functional based multi-level flexible models for multivariate longitudinal data

UnrestrictedThe examination of the relationship between ecologic covariates and functionals related to various lung function growth curves is of main interest in studying the long term effects of air pollution on children's health. However, such a modeling process leads to several challenging and unresolved issues such as non-linearity in the growth curves, and the correlation between and within outcomes. In this dissertation, flexible multi-level modeling techniques are proposed using penalized splines to model longitudinal outcomes (e.g. lung functions). This new method not only allows for the flexibility in modeling non-linear growth curves but also allows for joint-modeling of the smoothing parameter and the variance components. Second, the penalized-spline based mixed effects model is extended by modeling multiple outcomes jointly via latent variables approach. Hence, this extended model provides a way of accounting for the correlation between outcomes. All proposed models are implemented in a Bayesian setting. These techniques are illustrated throughout via analysis of data from the Southern California Children's Health Study