Several studies have indicated that bifactor models fit a broad range of psychometric data better than alternative multidimensional models such as second-order models (e.g., Carnivez, 2016; Gignac, 2016; Rodriguez, Reise, & Haviland, 2016). Murray and Johnson (2013) and Gignac (2016) argued that this phenomenon is partially due to unmodeled complexities (e.g., unmodeled cross-factor loadings) that induce a bias in standard statistical measures that favors bifactor models over second-order models. We extend the Murray and Johnson simulation studies to show how the ability to distinguish second-order and bifactor models diminishes as the amount of unmodeled complexity increases. By using theorems about rank constraints on the covariance matrix to find submodels of measurement models that have less unmodeled complexity, we are able to reduce the statistical bias in favor of bifactor models; this allows researchers to reliably distinguish between bifactor and second-order models.

中文翻译：

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寻找纯子模型以改进双因子和二阶模型的区分

多项研究表明，双因子模型比二阶模型等替代多维模型更适合广泛的心理测量数据（例如，Carnivez，2016 年；Gignac，2016 年；Rodriguez、Reise 和 Haviland，2016 年）。Murray 和 Johnson (2013) 以及 Gignac (2016) 认为，这种现象的部分原因是未建模的复杂性（例如，未建模的交叉因子载荷）导致标准统计测量出现偏差，偏向于二阶模型的双因子模型。我们扩展了 Murray 和 Johnson 模拟研究，以展示区分二阶和双因子模型的能力如何随着未建模复杂性的增加而降低。通过使用关于协方差矩阵的秩约束的定理来找到未建模复杂度较低的测量模型的子模型，我们能够减少统计偏差以支持双因子模型；这使研究人员能够可靠地区分双因子模型和二阶模型。