Abstract: The increased popularity of irregularly spaced intensive longitudinal measurements presents a need for
continuous-time models (i.e., differential equation models) that may be nonlinear in form and include
mixed effects in key dynamic parameters of interest. For fitting such models, innovative estimation
approaches have been proposed but have not been examined in a systematic way. To examine the
existing and potential methods for estimating mixed-effects nonlinear continuous-time models, the
current study implements and improves the accuracy, robustness, and computational efficiency of the
Continuous-Discrete Extended Kalman Filter (CDEKF) approach to fitting a nonlinear stochastic
differential equation model of emotions to data from the Affective Dynamics and Individual Differences
study; and performs a Monte Carlo simulation study to evaluate the strengths and limitations of the
CDEKF approach. Results from the simulation study and empirical application are used to offer practical
suggestions on ways to use the CDEKF approach and the associated continuous-time models to answer
substantive questions that are otherwise cumbersome to test within a discrete-time framework.

Keywords: Continuous-Discrete Extended Kalman Filter (CDEKF), continuous-time models, differential equation models, longitudinal measures