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.

翻译：测量误差普遍存在于众多变量中——从生理学中的血压记录到心理学中的智力测量。结构方程模型通过明确区分潜变量及其测量指标，将测量过程纳入考量。用户常将整个结构方程模型拟合至数据，但若部分模型参数无法识别，该过程可能失败。模型隐含工具变量方法作为一种更灵活的替代方案，可在已识别方程中估计模型参数子集。在图模型领域（如有向无环图）中也存在多种识别单个参数的方法，但多数方法未考虑测量效应。本文借鉴MIIV方法中的"潜变量到观测变量"（L2O）转换概念，开发出等价的图论L2O转换，使得现有图论准则可应用于结构方程模型中的潜参数。我们将L2O转换与图论工具变量准则相结合，提出一种用于含潜变量结构方程模型中非迭代参数识别的高效算法。我们证明该基于图论L2O转换与工具集准则的方法等价于当前最先进的MIIV方法，并表明当其与其他图论准则结合时，能催生新型识别策略。