Causal Inference for Experiments with Latent Outcomes: Key Results and Their Implications for Design and Analysis

Abstract: How should researchers analyze randomized experiments in which the main outcome is measured in multiple ways but each measure contains some degree of error? We describe modeling approaches that enable researchers to identify causal parameters of interest, suggest ways that experimental designs can be augmented so as to make linear latent variable models more credible, and discuss empirical tests of key modeling assumptions. We show that when experimental researchers invest appropriately in multiple outcome measures, an optimally weighted index of the outcome measures enables researchers to obtain efficient and interpretable estimates of causal parameters by applying standard regression methods, and that weights may be obtained using instrumental variables regression. Maximum likelihood and generalized method of moments estimators can be used to obtain estimates and standard errors in a single step. An empirical application illustrates the gains in precision and robustness that multiple outcome measures can provide.