ABSTRACT

There is currently a lack of methods for non-linear structural equation modeling (NSEM) for non-parametric relationships between latent variables when data are ordinal. To this end, a semiparametric approach for flexible NSEMs without parametric forms is developed for ordinal data. An indirect application of a finite mixture of structural equation models (SEMM) is employed for modeling the conditional expected mean of endogenous latent variables. In this context, the latent classes are not to be interpreted as groups of observations belonging to those classes, rather they serve as means to model flexible non-linear functions as locally linear functions which together approximate a globally non-linear function. The proposed method is based on a hybrid of direct maximization and expectation-maximization algorithms. Two simulation studies are performed which show that parameter estimates are associated with low bias and a non-linear functional form is satisfactorily estimated using the proposed approach.

摘要

当前缺乏用于数据有序时潜在变量之间的非参数关系的非线性结构方程建模 (NSEM) 方法。为此，针对序数数据开发了一种用于无参数形式的灵活 NSEM 的半参数方法。结构方程模型 (SEMM) 的有限混合的间接应用用于对内生潜在变量的条件预期平均值进行建模。在这种情况下，潜在类不应被解释为属于这些类的观察组，而是用作将灵活的非线性函数建模为局部线性函数的手段，这些函数共同近似于全局非线性函数。所提出的方法基于直接最大化和期望最大化算法的混合。