Reliability in Continuous Time: Planning for Measurement-Burst and Related Intensive Longitudinal Designs

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The power to detect change in longitudinal studies depends critically on the reliability of the measures of change, but current reliability indices do not adequately isolate sources of between- and within-person variation in complex longitudinal designs, such as those with multiple bursts and irregularly spaced occasions. We define dynamic and equilibrium reliability in a multilevel continuous-time (CT) state-space framework. For Bursti-CT-VAR, a special case of this framework with burst-specific equilibria for multiple-burst data, we split equilibrium reliability into trait and burst-deviation reliability and demonstrate the roles of these coefficients in power planning. We (1) compare these coefficients analytically with familiar ones: discrete-time coefficients and intraclass correlations of two- and three-level models. In Monte Carlo simulations, we (2) show the consequences of analyzing irregularly spaced occasions as regularly spaced, (3) examine how the process's half-life, sample size, and burst configuration affect accuracy and power, and (4) assess how CT designs within measurement bursts affect power.