Bayesian Perspectives on LongROAD Study: Analyzing Driving Decline and Latent Traits

Abstract

As the overall population lives longer, the driving population gets older and older. Despite the existence of a large body of work studying the relationship between driving and aging, the literature has produced mostly mixed results. The LongROAD study was designed to address some of these questions by collecting data from people over 65 concerning their socio-economic status and their health. In our thesis, we analyze this data and its challenges and discuss Bayesian modeling approaches to model the relationship between aging and driving behaviors using the driving data and the latent traits analyzed in the survey data. In this manuscript, we introduce the velocity field framework to model the evolution of time series in longitudinal datasets and discuss its implementation using Gaussian Processes. We motivate the use of Gaussian Processes by citing existing and new theoretical results, together with providing evidence from simulation studies suggesting the efficacy of this new framework for predictive purposes compared to existing benchmarks. We discuss in detail the differences between velocity and velocity field models, and why the latter may provide an advantage. In our application, we use our model to predict the evolution of driving behaviors with age and see that individuals older than 73 are at higher risk of experiencing sharp declines. In the third chapter of this thesis instead, we focus on the problem of modeling Likert Scale questions. We propose an ordinal latent trait model with fixed cutoffs and a flexible latent Beta distribution. In simulation settings, we show the ability of this model to predict the actual distribution of latent traits at the population level in a variety of settings, compared to existing standard approaches for Likert Scale modeling. Moreover, we prove the ability of the model to correctly identify the parameters of the latent traits whenever the assumptions are met. We use our model in our application to gather a better understanding of the latent traits concerning the driving behaviors in the population of the LongROAD study and show comparable prediction performances at the individual question level. Finally, in Chapter 4 of our thesis, we propose a method to integrate driving and survey data. Specifically, we expand the velocity field framework to allow for heterogeneous trends due to different covariates, observed at different frequencies. We do this by modifying the mean function of the Gaussian Process to allow it to be different across latent traits. We prove in simulated settings the ability of the model to correctly identify the parameters under the right specifications, and whenever the model is over-parametrized. We use this model to predict driving behaviors and evolution for different individuals and show that individuals who are more confident and comfortable with their driving are the ones more likely to experience sharper declines.