在存在潜在治疗因素的实验中识别因果效应：一种工具变量方法

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