方差最大化旋转

在统计学中, 方差最大化旋转是在主成分分析或因子分析中使用的一种方法，通过坐标变换使各个因子载荷的方差之和最大。通俗地说，就是 (a) 任何一个变量只在一个因子上有高贡献率，而在其它因子上的载荷几乎为0; (b)任何一个因子只在少数变量上有高载荷, 而在其它变量上的载荷几乎为0. 果满足这个条件的因子载荷矩阵称为具有“简单结构”。方差最大化旋转就是用来将载荷矩阵旋转到尽量接近简单结构的方法。从这组变量代表的样本看来，方差最大化旋转找到了一种表示样本的最简单的方法，即每个样本可以用少数变量的函数的线性组合表示。

One way of expressing the varimax criterion formally is this:

$R_{\mathrm {VARIMAX} }=\operatorname {arg} \max _{R}\left(\sum _{j=1}^{k}\sum _{i=1}^{p}(\Lambda R)_{ij}^{4}-{\frac {\gamma }{p}}\sum _{j=1}^{k}\left(\sum _{i=1}^{p}(\Lambda R)_{ij}^{2}\right)^{2}\right).$

where γ = 1 for VARIMAX.

Suggested by Henry Felix Kaiser in 1958, it is a popular scheme for orthogonal rotation (where all factors remain uncorrelated with one another).

A technical discussion of advantages and disadvantages of various rotation approaches are discussed at the website of Columbia University.

Rotation in factor analysis

A summary of the use of varimax rotation and of other types of factor rotation is presented in this article on factor analysis.

Implementations

In the R programming language the varimax method is implemented in several packages including stats (function varimax( )), or in contributed packages including GPArotation or psych.

See also

• 因子分析
• Empirical orthogonal functions
• Q methodology
• 旋转矩阵

External links

• Factor rotations in Factor Analyses by Herve Abdi
• About Varimax
• Properties of Principal Components
• http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/4041/pdf/imm4041.pdf