Using Phantom Variables in Structural Equation Modeling to Assess Model Sensitivity to External Misspecification
Using Phantom Variables in Structural Equation Modeling to Assess Model Sensitivity to External Misspecification
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DOI：
10.1037/met0000103
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发表时间：
2017-12-01
影响因子：
7
通讯作者：
Hancock, Gregory R.
中科院分区：
文献类型：
--
作者：
Harring, Jeffrey R.;McNeish, Daniel M.;Hancock, Gregory R.
外部错误说明，即结构模型中关键变量的省略，可以从根本上改变一个人在没有这样的变量存在的情况下所做的推断。本文提出了两种处理省略变量的策略，第一种是固定参数方法，将省略变量作为幻象变量合并到模型中，其中所有相关参数值都是固定的；另一种是随机参数方法，在贝叶斯框架下指定所有幻象变量的相关参数值的先验分布。文中讨论了这些方法的逻辑和实现方法，并通过教育心理学文献中的应用实例进行了演示。这种外部错误说明敏感性分析应该成为可测量和潜在变量建模的常规部分，其中所有显著变量的包含可能是有问题的。翻译抽象模型可以被认为是理解总体中数据行为的综合机制。从这个角度来看，该机制的任何不正确程度都构成了错误的说明。本文关注的是外部错误规范--从结构模型中省略关键变量(例如，协变量、中介者)。变量可能不存在，因为其重要性直到进行了研究之后才被揭示(例如，如审查者所建议的)，或者它可能只是在用于辅助数据分析的现有数据集中不可用。然而，如果不加以检查，外部错误说明可能会从根本上改变一个人可能在没有这样的变量存在的情况下做出的推断。提出了两种策略来研究对省略变量的敏感性。第一种是固定参数方法，它将省略的变量作为幻象变量集成到模型中，其中所有关联的参数值都是固定的。第二种策略是贝叶斯框架内的随机参数方法，其中为与参数值相关联的所有幻象变量指定先验分布。这两种方法都允许研究人员通过指定与缺失变量相关的参数值的可能候选者，将实质性领域的专业知识应用于分析模型。更广泛地讨论每种方法背后的理由，然后从教育心理学文献中的一个应用实例来说明它们的实施。我们的结论是，这种外部错误说明敏感性分析应该成为任何可能包含所有显著变量的建模工作的系统性部分。
External misspecification, the omission of key variables from a structural model, can fundamentally alter the inferences one makes without such variables present. This article presents 2 strategies for dealing with omitted variables, the first a fixed parameter approach incorporating the omitted variable into the model as a phantom variable where all associated parameter values are fixed, and the other a random parameter approach specifying prior distributions for all of the phantom variable's associated parameter values under a Bayesian framework. The logic and implementation of these methods are discussed and demonstrated on an applied example from the educational psychology literature. The argument is made that such external misspecification sensitivity analyses should become a routine part of measured and latent variable modeling where the inclusion of all salient variables might be in question.Translational AbstractA model can be thought of as a comprehensive mechanism for understanding the behavior of data in a population. From this perspective, any extent to which that mechanism is incorrect constitutes a misspecification. This article focuses on external misspecifications-the omission of key variables from a structural model (e.g., covariate, mediator). A variable may be absent because its importance was not brought to light until after a study had been conducted (e.g., as suggested by a reviewer) or it simply might be unavailable within an existing dataset being used in a secondary data analysis. Left unchecked, however, external misspecification can fundamentally alter the inferences one might make without such variables present. Two strategies are presented for investigating sensitivity to omitted variables. The first is a fixed parameter approach which integrates an omitted variable into the model as a phantom variable where all associated parameter values are fixed. The second strategy is a random parameter approach within a Bayesian framework in which prior distributions are specified for all of the phantom variables associated parameter values. Both methodologies allow researchers to bring expert knowledge of the substantive domain to bear on the analytic model through specifying likely candidates for the parameter values linked to the missing variables. The reasoning behind each method is discussed more generally before giving way to their implementation on an applied example from the educational psychology literature. Our conclusion is that such an external misspecification sensitivity analysis ought to become a systematic part of any modeling endeavor where the inclusion of all salient variables might be in question.