On Identifying Total Effects in the Presence of Latent Variables and Selection bias
This work provides tools for causal inference in observational studies, though it is incremental by building on prior graphical criteria.
The paper tackles the problem of identifying total causal effects when latent variables and selection bias are present, proposing new graphical identifiability criteria based on factor models to address gaps in existing methods.
Assume that cause-effect relationships between variables can be described as a directed acyclic graph and the corresponding linear structural equation model.We consider the identification problem of total effects in the presence of latent variables and selection bias between a treatment variable and a response variable. Pearl and his colleagues provided the back door criterion, the front door criterion (Pearl, 2000) and the conditional instrumental variable method (Brito and Pearl, 2002) as identifiability criteria for total effects in the presence of latent variables, but not in the presence of selection bias. In order to solve this problem, we propose new graphical identifiability criteria for total effects based on the identifiable factor models. The results of this paper are useful to identify total effects in observational studies and provide a new viewpoint to the identification conditions of factor models.