Rotation to Sparse Loadings Using [Formula: see text] Losses and Related Inference Problems.
Rotation to Sparse Loadings Using [Formula: see text] Losses and Related Inference Problems.
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DOI：
10.1007/s11336-023-09911-y
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发表时间：
2023-06
期刊：
影响因子：
3
通讯作者：
Moustaki, Irini
中科院分区：
文献类型：
--
作者：
Liu, Xinyi;Wallin, Gabriel;Chen, Yunxiao;Moustaki, Irini
关键词：
探索性因子分析（EFA）被广泛应用于研究多变量数据的潜在结构。旋转和正则估计是EFA中常用的寻找可解释加载矩阵的两类方法。在本文中，我们提出了一种新的基于分量损失函数的斜旋转，它与正则估计量密切相关。基于所提出的旋转方法，我们开发了模型选择和后选择推理程序。当真实载荷矩阵稀疏时，该方法在统计精度和计算成本方面优于传统的旋转和正则化估计方法。由于所提出的损失函数是非光滑的，我们开发了一种迭代重加权梯度投影算法来解决优化问题。我们还开发了理论结果，建立了估计、模型选择和选择后推理的统计一致性。我们对所提出的方法进行了评估，并通过仿真研究将其与正则化估计和传统的旋转方法进行了比较。我们用大五人格评估的应用进一步说明了这一点。在线版本包含补充材料，可在10.1007/s11336-023-09911-y获得。
Researchers have widely used exploratory factor analysis (EFA) to learn the latent structure underlying multivariate data. Rotation and regularised estimation are two classes of methods in EFA that they often use to find interpretable loading matrices. In this paper, we propose a new family of oblique rotations based on component-wise loss functions that is closely related to an regularised estimator. We develop model selection and post-selection inference procedures based on the proposed rotation method. When the true loading matrix is sparse, the proposed method tends to outperform traditional rotation and regularised estimation methods in terms of statistical accuracy and computational cost. Since the proposed loss functions are nonsmooth, we develop an iteratively reweighted gradient projection algorithm for solving the optimisation problem. We also develop theoretical results that establish the statistical consistency of the estimation, model selection, and post-selection inference. We evaluate the proposed method and compare it with regularised estimation and traditional rotation methods via simulation studies. We further illustrate it using an application to the Big Five personality assessment. The online version contains supplementary material available at 10.1007/s11336-023-09911-y.
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DOI：
10.1109/tsp.2013.2287685
发表时间：
2013-10-30
期刊：
IEEE transactions on signal processing : a publication of the IEEE Signal Processing Society
影响因子：
--
作者：
Babadi B;Ba D;Purdon PL;Brown EN
通讯作者：
Brown EN
影响因子：
3
作者：
Chen, Yunxiao;Li, Xiaoou;Zhang, Siliang
通讯作者：
Zhang, Siliang
影响因子：
3
作者：
Daubechies, Ingrid;Devore, Ronald;Guentuerk, C. Sinan
通讯作者：
Guentuerk, C. Sinan
影响因子：
2.7
作者：
Chen, Y.;Li, X.
通讯作者：
Li, X.
DOI：
10.1080/01621459.2019.1635485
发表时间：
2019-07-20
影响因子：
3.7
作者：
Chen, Yunxiao;Li, Xiaoou;Zhang, Siliang
通讯作者：
Zhang, Siliang