Simultaneous detection of gradual and abrupt structural changes in Bayesian longitudinal modelling using entropy and...

Area of Science:

• Statistics
• Psychology
• Behavioral Science

Background:

• Individuals exhibit both gradual and abrupt changes in dynamic properties due to accumulated influences and acute events.
• Existing statistical frameworks have limited capacity for simultaneously detecting and representing these distinct change patterns.
• Accurate modeling is crucial for understanding psychological well-being (PWB) dynamics.

Purpose of the Study:

• To propose a Bayesian regime-switching (RS) modeling framework for simultaneous detection and representation of gradual and abrupt changes.
• To adapt an entropy measure for testing postulates of gradual and abrupt changes.
• To investigate the effectiveness of the proposed framework in analyzing psychological well-being (PWB) dynamics.

Main Methods:

• Developed a Bayesian regime-switching (RS) modeling framework.
• Adapted an entropy measure from the frequentist framework.
• Conducted Monte Carlo simulation studies and applied models to intervention study data on early adults' PWB.

Main Results:

• The combination of entropy and information criterion measures (e.g., Bayesian information criterion) effectively selected the best-fitting model across varying abrupt change magnitudes.
• Lower entropy thresholds aided in selecting longitudinal models with RS properties.
• Abrupt, regime-related transitions in intra-individual variability of PWB dynamics were observed in some participants post-intervention.

Conclusions:

• The proposed Bayesian RS modeling framework and entropy measure facilitate the simultaneous detection and representation of gradual and abrupt changes.
• The entropy measure, used with other model selection criteria, offers practical guidelines for identifying true abrupt and gradual changes.
• Findings suggest potential abrupt shifts in PWB dynamics following interventions.