McDonald Roderick P
Multivariate Behav Res. 2004 Oct 1;39(4):687-713. doi: 10.1207/s15327906mbr3904_5.
Conventional structural equation modeling fits a covariance structure implied by the equations of the model. This treatment of the model often gives misleading results because overall goodness of fit tests do not focus on the specific constraints implied by the model. An alternative treatment arising from Pearl's directed acyclic graph theory checks identifiability and lists and tests the implied constraints. This approach is complete for Markov models, but has remained incomplete for models with correlated disturbances. Some new algebraic results overcome the limitations of DAG theory and give a specific form of structural equation analysis that checks identifiability, tests the implied constraints, equation by equation, and gives consistent estimators of the parameters in closed form from the equations. At present the method is limited to recursive models subject to exclusion conditions. With further work, specific structural equation modeling may yield a complete alternative to the present, rather unsatisfactory, global covariance structure analysis.
传统的结构方程建模拟合模型方程所隐含的协方差结构。这种对模型的处理方式常常会给出误导性的结果，因为整体拟合优度检验并未聚焦于模型所隐含的特定约束。源自珀尔的有向无环图理论的另一种处理方式会检查可识别性，并列出和检验隐含的约束。这种方法对于马尔可夫模型是完整的，但对于具有相关扰动的模型仍不完整。一些新的代数结果克服了有向无环图理论的局限性，并给出了一种特定形式的结构方程分析，该分析会检查可识别性，逐个方程地检验隐含的约束，并从方程中以封闭形式给出参数的一致估计量。目前该方法仅限于受排除条件约束的递归模型。随着进一步的研究，特定的结构方程建模可能会产生一种完全替代当前相当不尽人意的全局协方差结构分析的方法。
