Statistical Inference for Complete and Incomplete Mobility Trajectories under the Flight-Pause Model

In this paper, we provide a rigorous formulation of the so-called flight-pause model for human mobility, represented by a collection of random objects we call motions. We provide both the likelihood function corresponding to the general model and a special case we term the standard parameterization. We show how inference on unknown model parameters can be obtained using mobile phone tracking (MPT) data observed at regular time intervals. Since MPT data is frequently incomplete due to operating errors or battery-conservation considerations, we develop the statistical machinery needed to make inferences on model parameters and impute gaps in an observed mobility trajectory under various data collection mechanisms. We show an unusual missing-data scenario that arises in this setting, namely that there is not a one-to-one correspondence between assumptions about the missing data mechanism giving rise to MPT observations and those about the missing data mechanism for the random motions underlying the flight pause model. Thus, the methodology offers a contribution to the literature on missing data under modern measurement technologies. Through a series of simulation studies and a real data illustration, we demonstrate the consequences of missing data and our proposed adjustments under different data collection mechanisms, outlining implications for MPT data collection design.