Simultaneous detection of gradual and abrupt structural changes in Bayesian longitudinal modelling using entropy and model fit measures

Abstract

Although individuals may exhibit both gradual and abrupt changes in their dynamic properties as shaped by both slowly accumulating influences and acute events, existing statistical frameworks offer limited capacity for the simultaneous detection and representation of these distinct change patterns. We propose a Bayesian regime-switching (RS) modelling framework and an entropy measure adapted from the frequentist framework to facilitate simultaneous representation and testing of postulates of gradual and abrupt changes. Results from Monte Carlo simulation studies indicated that using a combination of entropy and information criterion measures such as the Bayesian information criterion was consistently most effective at facilitating the selection of the best-fitting model across varying magnitudes of abrupt changes. We found that slight lower entropy thresholds may be helpful in facilitating the selection of longitudinal models with RS properties as this class of models tended to yield lower entropy values than conventional thresholds for reliable classification in cross-sectional mixture models—even under satisfactory parameter recovery and classification results. We fitted the proposed models and other candidate models to the data collected from an intervention study on the psychological well-being (PWB) of college-attending early adults. Results suggested abrupt, regime-related transitions in the intra-individual variability levels of PWB dynamics among some participants following the intervention period. Practical usage of the entropy measure in conjunction with other model selection measures, and guidelines to enhance simultaneous detection of true abrupt and gradual changes are discussed.