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Over the last decade, technological advances have provided new opportunities for the collection of longitudinal data, moving from yearly to hourly measurements and thus allowing for new insights into the moment-to-moment dynamics that underly emotional and behavioural processes (Hamaker & Wichers, 2017; Jebb et al., 2015). Alongside changes in data collection methods, statistical models that can adequately capture the complexity of such intensive longitudinal data have also been developed. Among these methods, dynamic structural equation modelling (DSEM) has been gaining on popularity as it is well-suited to capture the within-person dynamics (capturing how for instance emotional processes unfold within an individual) that are likely of interest to behavioural and psychological researchers while also allowing for insights into how between-person differences (capturing factors that differ between people such as gender or genetic predisposition) influence within-person dynamics (Asparouhov et al., 2018; Hamaker et al., 2018; McNeish & Hamaker, 2019).
To date, DSEM has been used to investigate research questions focusing on directional associations between within-person components (Blanke et al., 2021), to gain insights into whether between-person factors (such as ADHD traits) moderate within-person effects (Brown et al., 2022), to evaluate whether within-person effects (such as stress reactivity) mediate the associations between two between-person factors (Speyer et al., 2022) and to investigate mediation effects on the within-person level (McNeish & Mackinnon, 2022). However, at this time, DSEM has not been utilised to investigate moderation effects at the within-person levels, that is whether changes relative to a person’s baseline in a repeatedly measured variable moderate the within-person coupling between two other repeatedly measured variables. Investigating within-person moderation effects can greatly expand our understanding of the moment-to-moment dynamics underlying emotional and behavioural processes. For example, such analyses may help clarify whether being surrounded by more green space rather than concrete compared to a person’s specific average significantly impacts whether an individual experiencing increases in stress subsequently goes on to experience increases in negative affect (Barton & Rogerson, 2017). Thus, investigating within-person moderation effects may be beneficial for the development of interventions by helping us identify amenable factors, such as engaging in a physical activity or improving dietary behaviours, that can help prevent increases in mental health symptoms in response to encountering momentary stressors. Consequently, such analyses are likely to be of interest to developmental researchers. Here, we describe how researchers can implement, test and interpret dynamic interaction effects using dynamic structural equation modelling as implemented in the structural equation modelling software Mplus. We will illustrate the analysis of within-person moderation effects using an empirical example from developmental psychology and discuss how the analysis of such within-person moderation effects can advance our understanding of the processes underlying children’s development.