Estimation of nonlinear mixed-effects continuous-time models using the continuous-discrete extended Kalman filter

Area of Science:

• Statistics
• Quantitative Psychology
• Computational Neuroscience

Background:

• Intensive longitudinal data often exhibit complex, nonlinear, and heterogeneous change patterns at irregular intervals.
• Modeling such data necessitates continuous-time differential equation models, potentially nonlinear and with mixed effects.
• Current methods for fitting mixed-effects stochastic differential equation (SDE) models, particularly using the continuous-discrete extended Kalman filter (CDEKF), lack thorough investigation regarding efficacy and identification constraints.

Purpose of the Study:

• To analytically inspect the identification constraints of fitting nonlinear mixed-effects SDE models via the CDEKF approach.
• To extend a published emotion model into a nonlinear mixed-effects SDE framework and apply it to ecological momentary assessment (EMA) data.
• To evaluate the feasibility of the proposed CDEKF approach for fitting these complex models through Monte Carlo simulations.

Main Methods:

• Analytical inspection of identification constraints for nonlinear mixed-effects SDE models fitted with CDEKF.
• Extension of an existing emotion model to a nonlinear mixed-effects SDE framework.
• Application of the extended model to irregularly spaced EMA data and validation via Monte Carlo simulation studies.

Main Results:

• The proposed CDEKF approach yields reasonable parameter and standard error estimates for nonlinear mixed-effects SDE models, provided certain identification constraints are satisfied.
• Simulation studies demonstrate the feasibility of the approach under varying conditions.
• The study investigates the impact of sample size, process noise variance, and data spacing on estimation outcomes.

Conclusions:

• The continuous-discrete extended Kalman filter (CDEKF) approach is a viable method for fitting nonlinear mixed-effects stochastic differential equation (SDE) models to intensive longitudinal data.
• Satisfying specific identification constraints is crucial for reliable parameter estimation.
• The findings provide valuable insights for researchers modeling complex dynamic processes with irregularly sampled data.