The aim of this article is to discuss the reconstruction of the theoretical elements of the structures verified by structural equation models (SEM). The elements of the structures have single-level (one-dimensional) or hierarchical (multi-dimensional) characteristic. The reconstruction of the characteristics of the theoretical elements is very important issue. Poor reconstruction of the theoretical elements, as will be shown, may increase the likelihood of the error of the first kind and lead to the rejection of the correct model. There are such elements which are so complex that verification of the models with their participation would require a huge effort involving trial and finance. If the research concentrates merely on the reconstruction of the characteristics of a particular element, then its construction is crucial. But when the research concentrates on the verification of the model of the process, in which the elements are plentiful and they are connected in a network of mutual dependencies, complexity of the model grows to such an extent that may require thousandths of observations and this can lead to a problem in its estimation. In this case, it becomes necessary to reduce the characteristics of the element to a meta-feature. The article explains how to verify the correctness of the construction of a one-level latent variable, hierarchical latent variable and estimate the variance extracted and reliability of variables. There is also shown how to reduce the hierarchical variable to meta-feature in order to simplify the model and reduce the number of degrees of freedom. There is presented how the construction of meta-features translates into both the reliability of the variable and the fit of the model. The construction of the variables is discussed on the example of the scale of Reaction to stress and the scale of Constraining child’s activity.

中文翻译：

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Problematyka hierarchiczności – wyprowadzenie meta-cech w modelach SEM

本文的目的是讨论通过结构方程模型 (SEM) 验证结构的理论元素的重建。结构的元素具有单级（一维）或分层（多维）特性。重构理论要素的特征是非常重要的问题。正如将要显示的，理论元素的不良重构可能会增加第一类错误的可能性，并导致拒绝正确的模型。这些元素非常复杂，以至于在他们参与下验证模型需要付出巨大的努力，包括试验和资金。如果研究仅仅专注于对特定元素特征的重构，那么它的构建就至关重要。但是当研究集中在过程模型的验证上，其中元素丰富，它们以相互依赖的网络连接，模型的复杂性增长到可能需要千分之一的观察，这可以导致估计出现问题。在这种情况下，有必要将元素的特征简化为元特征。文章解释了如何验证一级潜变量、层次潜变量构建的正确性，以及估计提取的方差和变量的可靠性。还展示了如何将层次变量减少到元特征以简化模型并减少自由度的数量。介绍了元特征的构建如何转化为变量的可靠性和模型的拟合度。变量的构建以压力反应量表和限制儿童活动量表为例进行了讨论。