UC Irvine

Statistical analyses often examine how two factors may jointly impact an outcome of interest. For example, researchers may want to understand how the impact of a covariate varies over time. A common model for such interactions incorporates a product of the two variables. However, in many application domains, this multiplicative interaction is quite restrictive in shape, and cannot adequately describe the joint relationship of two covariates on an outcome. This dissertation proposes methods to model interactions flexibly, with motivations from two different application domains. Chapter 3 proposes a Bayesian hierarchical model for modeling a flexible interaction between two functional covariates to best assess their impact on a scalar outcome. The resulting model is applied to understanding crop yield as a function of a flexible interaction between soil moisture and vapor pressure deficit. The methods in Chapters 4 and 5 are motivated by a project studying the impacts of early life experience on health outcomes for adolescents and young adults. Chapter 4 presents a Bayesian hierarchical model to model longitudinal data as a function of a flexible interaction between a covariate of interest and time. This model also proposes to improve inferences by combining data from a small well-characterized cohort and a very large but less well-characterized cohort via missing data methods. Lastly, Chapter 5 extends on concepts from Chapter 4 to model quantiles of the response distribution rather than its mean, while preserving the flexible interaction and missing data features of the model. Methods developed in Chapters 4 and 5 are applied to study hippocampus growth over time in adolescents and its association with early life adversity.