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

Abstract

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.

Daily-Life Social Experiences as a Potential Mediator of the Relationship Between Parenting and Psychopathology in Adolescence

“…In the registration for this study, we described the power analysis that we would perform, following a strategy described by Lafit et al (47). Power was computed by performing the confirmatory analyses described above on 1000 Monte Carlobased simulations, for a three-level model with 10 beeps per day for 6 days and an average compliance rate of 50%, aiming to achieve 0.80 power.…”

Dimensions of Skill Use in the Unified Protocol: Exploring Unique Effects on Anxiety and Depression

“…The fixed effects of this model are specified in the equation: 𝑂𝐴𝑆𝐼𝑆 𝑖𝑡 = 𝛾 00 + 𝛾 01 (𝑈𝑃𝑆𝑈𝑆 𝑖 ) + 𝛾 10 (𝑈𝑃𝑆𝑈𝑆 𝑖𝑡 ) + 𝛾 02 (𝑊𝐴𝐼 𝑖 ) + 𝛾 20 (𝑊𝐴𝐼 𝑖𝑡−1 ) + 𝛾 30 (𝑂𝐴𝑆𝐼𝑆 𝑖𝑡−1 ) + 𝛾 40 (𝑂𝐷𝑆𝐼𝑆 𝑖𝑡 ) + 𝛾 50 (𝑠𝑒𝑠𝑠𝑖𝑜𝑛 𝑖𝑡 ) + 𝛾 03 (𝑠𝑒𝑞 𝑐𝑜𝑛𝑑𝑖𝑡𝑖𝑜𝑛 𝑖 ) + 𝛾 04 (𝑡ℎ𝑒𝑟𝑎𝑝𝑖𝑠𝑡 𝑖 ) + 𝑒 𝑖𝑡 We repeated this process, replacing anxiety and depression, and conducted two further models, replacing UPSUS total scores with all specific UP skills. In these models, we had 80% power to detect medium-to-large sized between-person effects (R 2  .16; Faul et al, 2009) and medium-to-large-sized within-person effects (R 2  .11; Lafit et al, 2021). All code is available at: https://osf.io/7k3ay/?view_only=a86dcc04e64d4d67b83f147b70784e57…”

Ecological Momentary Assessment of Depression in People With Advanced Dementia: Longitudinal Pilot Study

“…Recommendations for determining sample size in intensive longitudinal designs are based on the power of both the within-and between-person sample sizes [27,28]. Despite our smaller between-person sample size (n=12), the within-person sample size (ie, number of repeated observations) is important in detecting the reliability of the random effects and within-person variability and typically requires >50 observations per individual and >1000 observations in total [29][30][31]. With our study design, we aim to achieve a large number of observations well above this cutoff (ie, eight observations per day for 6 weeks, totaling approximately 336 observations per participant), providing sufficient power for our primary within-person analysis [32].…”