精确探索性双因子分析：一种基于约束的优化方法
Exact Exploratory Bi-factor Analysis: A Constraint-based Optimisation Approach
AI总结：
针对现有探索性双因子分析方法仅能得到近似结构的问题，提出一种基于约束的优化方法，通过将双因子载荷结构转化为等式约束构建连续域约束优化问题，用增广拉格朗日法求解以得到精确结构，经模拟和真实数据验证有效，并可扩展至层次因子分析。
摘要：
双因子分析是验证性因子分析的一种形式，广泛应用于心理与教育测量领域。使用双因子模型需要明确设定观测变量与组因子之间关系的显式双因子结构。在实际应用中，双因子结构有时是未知的，这种情况下就需要探索性的双因子分析方法来确定双因子结构。遗憾的是，目前探索性双因子分析的方法很少，仅有的例外是Jennrich和Bentler（2011, 2012）提出的一种基于旋转的方法。但该方法只能得到近似的双因子结构，因为即使应用硬阈值处理，它也无法生成精确的双因子载荷结构。本文提出了一种基于约束的优化方法，能够从数据中学习精确的双因子载荷结构，解决了基于旋转的方法存在的问题。该方法的核心是将双因子载荷结构数学表征为一组等式约束，从而我们可以将探索性双因子分析问题构建为连续域上的约束优化问题，并使用增广拉格朗日方法求解该优化问题。我们通过模拟研究和一个真实数据示例验证了所提方法的有效性，还讨论了将该方法扩展到探索性层次因子分析的相关内容。相关代码可在https://anonymous.4open.science/r/Bifactor-ALM-method-757D获取。
英文摘要：
Bi-factor analysis is a form of confirmatory factor analysis widely used in psychological and educational measurement. The use of a bi-factor model requires the specification of an explicit bi-factor structure on the relationship between the observed variables and the group factors. In practice, the bi-factor structure is sometimes unknown, in which case an exploratory form of bi-factor analysis is needed to find the bi-factor structure. Unfortunately, there are few methods for exploratory bi-factor analysis, with the exception of a rotation-based method proposed in Jennrich and Bentler (2011, 2012). However, this method only finds approximate bi-factor structures, as it does not yield an exact bi-factor loading structure, even after applying hard thresholding. In this paper, we propose a constraint-based optimisation method that learns an exact bi-factor loading structure from data, overcoming the issue with the rotation-based method. The key to the proposed method is a mathematical characterisation of the bi-factor loading structure as a set of equality constraints, which allows us to formulate the exploratory bi-factor analysis problem as a constrained optimisation problem in a continuous domain and solve the optimisation problem with an augmented Lagrangian method. The power of the proposed method is shown via simulation studies and a real data example. Extending the proposed method to exploratory hierarchical factor analysis is also discussed. The codes are available on ``https://anonymous.4open.science/r/Bifactor-ALM-method-757D".
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
