Selection of the Number of Participants in Intensive Longitudinal Studies: A User-Friendly Shiny App and Tutorial for Performing Power Analysis in Multilevel Regression Models That Account for Temporal Dependencies

In recent years, the popularity of procedures for collecting intensive longitudinal data, such as the experience-sampling method, has increased greatly. The data collected using such designs allow researchers to study the dynamics of psychological functioning and how these dynamics differ across individuals. To this end, the data are often modeled with multilevel regression models. An important question that arises when researchers design intensive longitudinal studies is how to determine the number of participants needed to test specific hypotheses regarding the parameters of these models with sufficient power. Power calculations for intensive longitudinal studies are challenging because of the hierarchical data structure in which repeated observations are nested within the individuals and because of the serial dependence that is typically present in these data. We therefore present a user-friendly application and step-by-step tutorial for performing simulation-based power analyses for a set of models that are popular in intensive longitudinal research. Because many studies use the same sampling protocol (i.e., a fixed number of at least approximately equidistant observations) within individuals, we assume that this protocol is fixed and focus on the number of participants. All included models explicitly account for the temporal dependencies in the data by assuming serially correlated errors or including autoregressive effects.