Graphical Models for Identification in Structural Equation Models
- Author(s): Brito, Carlos
- et al.
Structural Equation Models (SEM) is one of the most important tools for causal analysis in the social and behavioral sciences (e.g., Economics, Sociology, etc). A central problem in the application of SEM models is the analysis of Identification. Succintly, a model is identified if it only admits a unique parametrization to be compatible with a given covariance matrix (i.e., observed data). The identification of a model is important because, in general, no reliable quantitative conclusion can be derived from non-identified models.
In this work, we develop a new approach for the analysis of identification in SEM, based on graph theoretic techniques. Our main result is a general sufficient criterion for model identification. The criterion consists of a number of graphical conditions on the causal diagram of the model. We also develop a new method for computing correlation constraints imposed by the structural assumptions, that can be used for model testing. Finally, we also provide a generalization to the traditional method of Instrumental Variables, through the concept of Instrumental Sets.