psych :: principal-旋转(主要)组件的顺序和命名说明 [英] psych::principal - explanation for the order and naming of rotated (principal) components

问题描述

让x成为示例数据帧.

set.seed(0)
x <- replicate(4, rnorm(10))

使用psych软件包中的principal功能的PCA将产生:

A PCA using the principal function from the psych package will yield:

> principal(x, nf=4, rotate="none")
...
                       PC1  PC2  PC3  PC4
SS loadings           1.91 1.09 0.68 0.31
Proportion Var        0.48 0.27 0.17 0.08
Cumulative Var        0.48 0.75 0.92 1.00
Proportion Explained  0.48 0.27 0.17 0.08
Cumulative Proportion 0.48 0.75 0.92 1.00

使用varimax准则旋转te PCA解决方案会产生现在名为RCi的新组件，以指示PC已旋转(因此，它们不再是PC).

Rotating te PCA solution using the varimax criterion yields new components now named RCi to indicate that the PCs have been rotated (hence, they are no PCs anymore).

> principal(x, nf=4, rotate="varimax")
...
                       RC4  RC3  RC2  RC1
SS loadings           1.03 1.02 1.00 0.95
Proportion Var        0.26 0.26 0.25 0.24
Cumulative Var        0.26 0.51 0.76 1.00
Proportion Explained  0.26 0.26 0.25 0.24
Cumulative Proportion 0.26 0.51 0.76 1.00

我的问题:为什么现在订单从RC4到RC1，数字从4减少到1.RC仍根据其SS份额进行排序.由于旋转是正交的，所以我不明白这一点. RC名称的顺序传达了哪些有用的额外信息?还是如果旋转是正交的，我会认为顺序是任意的吗?

My question: Why is the order now RC4 to RC1 with the numbers decreasing from 4 to 1. The RCs are still ordered according to their share of SS. As the rotation is orthogonal I do not understand the point. What useful extra information does the order of the RC names convey? Or am I wrong to consider the order as arbitrary if the rotation is orthogonal?

谢谢！

推荐答案

标记， 逻辑是识别旋转的作用.这更多是出于教学原因，而不是其他任何原因.我试图显示原始组件与旋转组件的关系.以您的示例为例，查看负载，而不仅仅是造成差异的原因.

Mark, The logic is to recognize what rotation does. This is more for pedagogical reasons than anything else. I am trying to show the relationship of the original components to the rotated components. To take your example, look at the loadings, not just the variances accounted for.

unrotated:

    PC1   PC2   PC3   PC4 h2       u2
1 -0.77 -0.40  0.39  0.32  1 -6.7e-16
2  0.71 -0.28  0.63 -0.17  1  6.7e-16
3 -0.10  0.93  0.35  0.09  1  6.7e-16
4  0.90 -0.02 -0.13  0.42  1  2.2e-16

Rotated:
    RC4   RC3   RC2   RC1 h2       u2
1  0.95 -0.10 -0.08 -0.29  1 -6.7e-16
2 -0.10  0.97 -0.06  0.22  1  6.7e-16
3 -0.07 -0.06  0.99 -0.05  1  6.7e-16
4 -0.34  0.27 -0.07  0.90  1  2.2e-16

尤其要看变量3和4.在未旋转的解决方案中，它们分别定义PC2和PC1.现在看看旋转的解决方案.这两个仍标记PC2和PC1(并标记为RC2和RC1以反映它们已旋转)，但是当PC4旋转到RC4时，所占的差异已经更改，因为PC4现在吸收了更多的差异. (对于PC3和PC4也是如此，但不清楚.)

In particular, look at variables 3 and 4. In the unrotated solution, they define PC2 and PC1 respectively. Now look at the rotated solution. These two still mark PC2 and PC1 (and are labeled RC2 and RC1 to reflect that they are rotated), but the variances accounted for have changed as PC4 when rotated to RC4 now soaks up more variance. (This is also true for PC3 and PC4 but not as clear.)

我想做的是代表您旋转时发生的情况.将PC1旋转到一个更简单的结构，并变成RC1.

What I am trying to do is represent what happens as you rotate. PC1 is rotated to a simpler structure, and becomes RC1.

然后，由于许多人喜欢按方差的顺序说明其分量，因此我按特征值(即平方和)进行排序.

Then, because many people like to have their components in order of variance accounted for, I sort by the eigen value (sum squares accounted for).

我相信其他程序所做的是旋转和重新标记，以便组件始终称为C1 ... Cn.我只想看看这些组件的来源.

I believe what other programs do is to rotate and relabel so that the components are always called C1 ... Cn. I just like to see where the components came from.

如果您认为这很有用，我可以(最终)将此讨论添加到主体和fa的文档中.

If you think it is useful, I can (eventually) add this discussion to the documentation for principal as well as fa.

账单

这篇关于psych :: principal-旋转(主要)组件的顺序和命名说明的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！