Dynamic Structural Equation Modeling with Cycles

Cyclical phenomena are commonly observed in many areas of repeated measurements, especially with intensive longitudinal data. A typical example is circadian (24-hour) rhythm of physical measures such as blood pressure, heart rate, glucose level, and alertness. This paper focuses on positive affect, which is a common measure in psychological studies and for which circadian rhythm has been observed but not analyzed by modern statistical methods. The paper demonstrates that a large new analysis arsenal is available for analysis of cyclical features in intensive longitudinal data. This can help researchers extract more information from their data to get more valid estimates of coupled processes and to get new theoretical insights into circadian rhythms of mood. To assist in this effort, the analyses are based on general models with a rich set of features while still being accessible without an unduly steep learning curve. Scripts for the Mplus software are available for all the analyses presented.