Applying continuous-time models to ecological momentary assessments: A practical introduction to the method and demonstration with clinical data

Ecological momentary assessment (EMA) is a frequently used approach among clinical researchers to collect naturalistic data in real time. EMA data can provide insights into the temporal dynamics of psychological processes. Traditional methods used to analyze EMA data, such as hierarchical linear modeling and multilevel vector auto-regression, paint an incomplete picture of the dynamics of psychological processes because they cannot capture how variables evolve outside predefined measurement occasions. Continuous-time models, an analytical approach that treats variables as dynamical systems that evolve continuously, overcome this limitation. Time advances smoothly in continuous-time models, contrasting with standard discrete-time models in which time progresses in finite jumps. This paper presents a practical introduction to continuous-time models for analyzing EMA data. To illustrate the method and its interpretation, we provide an empirical demonstration of a continuous-time model utilizing EMA data of real-time loneliness and mood states (happiness, sadness, and anxiety) from a clinical sample comprising Veterans with a history of mental illness. Psychological variables, such as feelings of loneliness or sadness, can often change many times throughout the day. However, standard ways of analyzing these variables do not accurately capture these changes and fluctuations. Here, we highlight the benefits of continuous-time models, a method that can capture subtle changes in such psychological variables over time.