Representing Sudden Shifts in Intensive Dyadic Interaction Data Using Differential Equation Models with Regime...

Area of Science:

• Social Sciences
• Dynamical Systems Modeling
• Behavioral Dynamics

Background:

• Traditional differential equation models struggle to identify qualitative shifts in system dynamics.
• There's a need for tools to diagnose abrupt changes, their timing, and determinants in complex systems.
• Social scientists increasingly use differential equations to model interdependent variables.

Purpose of the Study:

• To introduce regime-switching differential equation models for representing abrupt changes in dynamic systems.
• To develop a method for diagnosing evidence, timing, and determinants of qualitative shifts in dynamics.
• To model discrete shifts in mother-infant dyad movement dynamics during the Strange Situation Procedure (SSP).

Main Methods:

• Combined the Kim filter with a numerical differential equation solver for estimation.
• Utilized a framework capable of handling both ordinary and stochastic differential equations.
• Employed regime-switching differential equation models to capture behavioral shifts.

Main Results:

• Successfully illustrated the utility of regime-switching differential equations in modeling mother-infant movement dynamics during the SSP.
• Demonstrated shifts between proximity-seeking and exploratory behaviors in infants.
• Monte Carlo simulations evaluated information criteria for diagnosing dynamic shifts.

Conclusions:

• Regime-switching differential equation models offer a powerful framework for analyzing abrupt changes in behavioral dynamics.
• The proposed method effectively captures discrete shifts in complex systems, such as mother-infant interactions.
• This approach enhances the diagnosis of dynamic shifts and their underlying causes in social science research.