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Complex social scientific theories are conventionally tested using linear structural equation modelling (SEM). However, the underlying assumptions of linear SEM often prove unrealistic, making the decomposition of direct and indirect effects problematic. Recent advancements in causal mediation analysis can help to address these shortcomings, allowing for causal inference when a new set of identifying assumptions are satisfied. This paper reviews how these ideas can be generalised to multiple mediators, with a focus on the post-treatment confounding and causal ordering cases. Using the potential outcome framework as a rigorous tool for causal inference, the application is the theory of procedural justice policing. Analysis of data from two randomised experiments shows that making similar parametric assumptions to SEMs and using g-computation improves the viability of effect decomposition. The paper concludes with a discussion of how causal mediation analysis improves upon SEM and the potential limitation of the methods.