  Measurement error is ubiquitous in many variables - from blood pressure
recordings in physiology to intelligence measures in psychology. Structural
equation models (SEMs) account for the process of measurement by explicitly
distinguishing between latent variables and their measurement indicators. Users
often fit entire SEMs to data, but this can fail if some model parameters are
not identified. The model-implied instrumental variables (MIIVs) approach is a
more flexible alternative that can estimate subsets of model parameters in
identified equations. Numerous methods to identify individual parameters also
exist in the field of graphical models (such as DAGs), but many of these do not
account for measurement effects. Here, we take the concept of
"latent-to-observed" (L2O) transformation from the MIIV approach and develop an
equivalent graphical L2O transformation that allows applying existing graphical
criteria to latent parameters in SEMs. We combine L2O transformation with
graphical instrumental variable criteria to obtain an efficient algorithm for
non-iterative parameter identification in SEMs with latent variables. We prove
that this graphical L2O transformation with the instrumental set criterion is
equivalent to the state-of-the-art MIIV approach for SEMs, and show that it can
lead to novel identification strategies when combined with other graphical
criteria.
