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:在许多变量中,从生理中的血压记录到心理学中的智能测量,测量误差都是无处不在的。结构等式模型(SEMs)通过明确区分潜伏变量及其测量指标来计算测量过程。用户通常将整个SEM与数据相匹配,但如果没有确定一些模型参数,这可能会失败。模型隐含的辅助变量(MIIVs)方法是一个更灵活的替代方法,可以估计确定方程式中模型参数的子集。在图形模型领域(如DAGs)也存在许多确定个别参数的方法,但其中许多不考虑测量效果。在这里,我们从MIIV方法中采用“远程观察”转换(L2O)概念,并开发一个等效的图形L2O变换方法,允许将现有的图形标准应用于SEMs的潜在参数。我们将L2O变换方法与图形化工具变异性标准结合起来,以获得在SEMs与潜伏变量一起识别非隐含参数参数的高效算法。我们证明,这种图形L2O变式L2O与工具设定的标准与工具设定的标准是等同的状态-艺术 MIIV方法。当显示其他图形识别时,可以显示其他的新型战略时,而显示其他的铅识别方法。</s>