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Department of Statistics, UCLA

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Graphical Models for Identification in Structural Equation Models


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.

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