基于梯度投影的方差最大旋转需要10到500个以上的随机开始加载矩阵以获得最佳性能
Varimax rotation based on gradient projection needs between 10 and more than 500 random start loading matrices for optimal performance
摘要：
梯度投影旋转（GPR）是一种很有前途的方法，旋转因子或分量载荷不同的标准。由于GPR-Varimax的最佳性能的条件是广泛未知的，本模拟研究探讨GPR走向方差最大准则的主成分分析。模拟研究的条件包括两个样本量（n = 100，n = 300），正交简单结构总体模型基于4个分量（3，6，9，12），有和没有Kaiser归一化，以及6个随机开始加载矩阵用于GPR方差最大旋转（1，10，50，100，500，1，000）。当至少使用10个随机矩阵而不是单位矩阵用于开始加载时，GPR-Varimax旋转总是表现得更好。GPR-Varimax对少量组件的效果更好，与较小（n = 100）样本相比，较大（n = 300）样本的效果更好，并且在旋转前对载荷进行Kaiser归一化。为了确保GPR-Varimax在恢复正交简单结构时的最佳（静态）性能，我们建议使用至少10次迭代的起始加载矩阵来旋转多达三个分量，并使用50次迭代来旋转多达六个分量。对于最多9个组分，旋转应基于至少300个病例的样本量、Kaiser标准化和50个以上不同的起始加载矩阵。对于9个以上的分量，GPR方差最大旋转应基于至少300个案例、Kaiser归一化和至少500个不同的起始加载矩阵。
英文摘要：
Gradient projection rotation (GPR) is a promising method to rotate factor or component loadings by different criteria. Since the conditions for optimal performance of GPR-Varimax are widely unknown, this simulation study investigates GPR towards the Varimax criterion in principal component analysis. The conditions of the simulation study comprise two sample sizes (n = 100, n = 300), with orthogonal simple structure population models based on four numbers of components (3, 6, 9, 12), with- and without Kaiser-normalization, and six numbers of random start loading matrices for GPR-Varimax rotation (1, 10, 50, 100, 500, 1,000). GPR-Varimax rotation always performed better when at least 10 random matrices were used for start loadings instead of the identity matrix. GPR-Varimax worked better for a small number of components, larger (n = 300) as compared to smaller (n = 100) samples, and when loadings were Kaiser-normalized before rotation. To ensure optimal (stationary) performance of GPR-Varimax in recovering orthogonal simple structure, we recommend using at least 10 iterations of start loading matrices for the rotation of up to three components and 50 iterations for up to six components. For up to nine components, rotation should be based on a sample size of at least 300 cases, Kaiser-normalization, and more than 50 different start loading matrices. For more than nine components, GPR-Varimax rotation should be based on at least 300 cases, Kaiser-normalization, and at least 500 different start loading matrices.
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