ABSTRACT The literature on non-linear structural equation modeling is plentiful. Despite this fact, few studies consider interactions between exogenous and endogenous latent variables. Further, it is well known that treating ordinal data as continuous produces bias, a problem which is enhanced when non-linear relationships between latent variables are incorporated. A marginal maximum likelihood-based approach is proposed in order to fit a non-linear structural equation model including interactions between exogenous and endogenous latent variables in the presence of ordinal data. In this approach, the exact gradient of the approximated observed log-likelihood is calculated in order to attain the approximated maximum likelihood estimator. A simulation study shows that the proposed method provides estimates with low bias and accurate coverage probabilities.

中文翻译：

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序数数据扩展二次结构方程建模的边际最大似然法

摘要 关于非线性结构方程建模的文献很多。尽管如此，很少有研究考虑外生和内生潜在变量之间的相互作用。此外，众所周知，将有序数据视为连续会产生偏差，当包含潜在变量之间的非线性关系时，该问题会加剧。提出了一种基于边际最大似然的方法，以拟合非线性结构方程模型，该模型包括在有序数据存在的情况下外生和内生潜在变量之间的相互作用。在这种方法中，计算近似观测对数似然的精确梯度以获得近似最大似然估计量。