Experiments in Daily Life: When Causal Within-Person Effects Do (Not) Translate into Between-Person Differences

Intensive longitudinal designs allow researchers to study the dynamics of psychological processes in daily life. Yet, because these methods are usually observational, they do not allow strong causal inferences. A promising solution is to incorporate (micro-)randomized interventions within intensive longitudinal designs to uncover within-person causal effects. However, it remains unclear whether (or how) the resulting within-person causal effects translate into between-person differences in outcomes. In this work, we show analytically and using simulated data that within-person causal effects translate into between-person differences if there are no counteracting forces that modulate this cross-level translation. Three possible counteracting forces that we consider here, are (i) contextual effects, (ii) correlated random effects, and (iii) cross-level interactions. We illustrate these principles using empirical data from a 10-day micro-randomized mindfulness intervention study (n = 91), in which participants were randomized to complete a treatment or control task at each occasion. We conclude by providing recommendations regarding the design of micro-randomized experiments in intensive longitudinal designs, as well as the statistical analyses of data resulting from theses designs.