Department of Psychology, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong.
Behav Res Methods. 2011 Sep;43(3):730-45. doi: 10.3758/s13428-011-0088-6.
We propose a two-stage method for comparing standardized coefficients in structural equation modeling (SEM). At stage 1, we transform the original model of interest into the standardized model by model reparameterization, so that the model parameters appearing in the standardized model are equivalent to the standardized parameters of the original model. At stage 2, we impose appropriate linear equality constraints on the standardized model and use a likelihood ratio test to make statistical inferences about the equality of standardized coefficients. Unlike other existing methods for comparing standardized coefficients, the proposed method does not require specific modeling features (e.g., specification of nonlinear constraints), which are available only in certain SEM software programs. Moreover, this method allows researchers to compare two or more standardized coefficients simultaneously in a standard and convenient way. Three real examples are given to illustrate the proposed method, using EQS, a popular SEM software program. Results show that the proposed method performs satisfactorily for testing the equality of standardized coefficients.
我们提出了一种两阶段方法，用于比较结构方程建模（SEM）中的标准化系数。在第 1 阶段，我们通过模型重新参数化将感兴趣的原始模型转换为标准化模型，使得标准化模型中出现的模型参数等同于原始模型的标准化参数。在第 2 阶段，我们对标准化模型施加适当的线性等式约束，并使用似然比检验对标准化系数的相等性进行统计推断。与其他用于比较标准化系数的现有方法不同，所提出的方法不需要特定的建模特征（例如，非线性约束的指定），这些特征仅在某些 SEM 软件程序中可用。此外，该方法允许研究人员以标准且方便的方式同时比较两个或更多标准化系数。使用流行的 SEM 软件程序 EQS 给出了三个实际示例来说明所提出的方法。结果表明，该方法在测试标准化系数的相等性方面表现令人满意。
