Models for Longitudinal Compositional Data Analysis with Applications to Mobility Studies

The study of sustainable mobility is becoming central to urban mobility research. Telephonic data represent an important tool for understanding the current patterns of urban mobility; in the last two decades, they have been increasing both in terms of available amount and descriptive power as a proxy for human mobility. Despite the intrinsic uncertainty given by these noisy data, statisticians have paid little attention in the field. This thesis intertwines the statistical analysis of urban mobility based on telephonic data with longitudinal compositional data analysis, that is, the analysis of parts that constitute a whole, where the relative proportions of components change dynamically. Capturing the dependency between successive compositional observations requires tailored methods to take into account the constrained nature of the data. In Chapter 1, we provide a survey of the main probabilistic and statistical methodologies for the exploitation of telephonic data in the field of urban mobility analysis. In Chapter 2, we provide a new approach based on compositional data for urban mobility, where people’s trajectories are represented in the simplex by the proportions of types of roads in their surroundings as they move. We propose a state-space model for the analysis of compositional time series and a model-based clustering approach for the unsupervised aggregation of those series, to uncover the main patterns of human mobility. In Chapter 3, we focus on an alternative approach to longitudinal compositional data analysis, by modeling the observations directly on the simplex and the longitudinal aspect through generalized estimating equations. This more general model is useful for applications where the dependence on the covariates is the main interest.