Identifying Causal Effects in Experiments with Latent Treatments: An Instrumental Variable Approach

Psychological experiments target the causal effects of latent variables, which they cannot manipulate directly. Researchers use manipulation checks to confirm that the latent variable changed, but then estimate the causal effect of the manipulation itself, not that of changes in the target latent variable. We treat the manipulation as an instrumental variable (IV) for the latent treatment, measured by several items, and derive conditions under which the treatment's average causal effect is identified. The resulting assumptions allow for some treatment-effect and loading heterogeneity, and are weaker than those most psychometric applications already make.Because a latent treatment has no unit, the estimand is defined only once a scale is fixed. We define two and work out their identification: an anchored estimand, per unit of one item, and a standardized estimand, per standard deviation of the latent treatment. The latter is more familiar but requires more assumptions and, notably, does not transfer between experiments. We show how to estimate both estimands with off-the-shelf SEM and IV software, and a simulation shows how the estimators behave in realistic samples when individual assumptions fail. Because researchers design the manipulation and choose the items, we close with practical implications.