The utility of multilevel models for continuous-time feature selection of spatio-temporal networks

Abstract

Many models for the analysis of spatio-temporal networks specify time as a series of discrete steps. This either requires evenly spaced measurement times or the aggregation of data into measurement windows. This can lead to the introduction of bias. An alternative is to use continuous-time models, for example, multilevel models. Models capturing complex spatio-temporal variation are often difficult to visualise and interpret. This can be addressed by simplifying the results, for example by extracting ‘features’ of interest (such as maxima or minima) of temporal patterns associated with different network connections.This paper uses simulation to evaluate the accuracy and precision with which b-spline-based multilevel models (a flexible form of continuous-time model that can easily capture complex variation associated with a spatio-temporal network structure) capture the timing and extent of maximum delays to journeys made between pairs of stations in a small railway network.On average models captured the timing and extent of maximum delay with small bias, but there was evidence of overestimation and underestimation of low and high values of these features, respectively. This systematic bias may have partially caused the undercoverage of credible intervals for the pattern features. Alternative model specifications – specifically to capture x-axis random variation, for example – should be considered in future work.