On the relationship between the higher-order factor model and the hierarchical factor model
On the relationship between the higher-order factor model and the hierarchical factor model
复制标题
DOI：
10.1007/bf02294531
复制
发表时间：
1999-06-01
期刊：
影响因子：
3
通讯作者：
McLeod, LD
中科院分区：
文献类型：
--
作者：
Yung, YF;Thissen, D;McLeod, LD
正式探讨了高阶因子模型与层次因子模型之间的关系。我们证明了Schmid-Leiman变换产生有约束的层次因子解。利用广义Schmid-Leiman变换及其逆变换，我们证明了对于任何无约束的层次因子模型，存在一个等价的高阶因子模型，其直接影响（载荷）来自高阶因子的显变量。因此，高阶因子模型类（不受高阶因子的直接影响）嵌套在无约束层次因子模型类中。根据这些形式化的结果，我们讨论了检验高阶因子模型和一般因子问题的一些启示。注意到关于具有直接影响的高阶因子模型的有效拟合的一个有趣的方面。
The relationship between the higher-order factor model and the hierarchical factor model is explored formally. We show that the Schmid-Leiman transformation produces constrained hierarchical factor solutions. Using a generalized Schmid-Leiman transformation and its inverse, we show that for any unconstrained hierarchical factor model there is an equivalent higher-order factor model with direct effects (loadings) on the manifest variables from the higher-order factors. Therefore, the class of higher-order factor models (without direct effects of higher-order factors) is nested within the class of unconstrained hierarchical factor models. In light of these formal results, we discuss some implications for testing the higher-order factor model and the issue of general factor. An interesting aspect concerning the efficient fitting of the higher-order factor model with direct effects is noted.