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Measurement error is ubiquitous in many variables - from blood pressurerecordings in physiology to intelligence measures in psychology. Structuralequation models (SEMs) account for the process of measurement by explicitlydistinguishing between latent variables and their measurement indicators. Usersoften fit entire SEMs to data, but this can fail if some model parameters arenot identified. The model-implied instrumental variables (MIIVs) approach is amore flexible alternative that can estimate subsets of model parameters inidentified equations. Numerous methods to identify individual parameters alsoexist in the field of graphical models (such as DAGs), but many of these do notaccount for measurement effects. Here, we take the concept of"latent-to-observed" (L2O) transformation from the MIIV approach and develop anequivalent graphical L2O transformation that allows applying existing graphicalcriteria to latent parameters in SEMs. We combine L2O transformation withgraphical instrumental variable criteria to obtain an efficient algorithm fornon-iterative parameter identification in SEMs with latent variables. We provethat this graphical L2O transformation with the instrumental set criterion isequivalent to the state-of-the-art MIIV approach for SEMs, and show that it canlead to novel identification strategies when combined with other graphicalcriteria.

Combining Graphical and Algebraic Approaches for Parameter Identification in Latent Variable Structural Equation Models