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psych::principal为了测试目的，我需要以编程方式重现自动（varimax）旋转。

事实证明，对于某些数据，我无法从 再现该旋转psych，因为显然，输出中组件的顺序会随着旋转而改变。

考虑这个可重现的例子：

# some dataset from psych

library(psych)
data("Thurstone")

principal.unrotated <- principal(r = Thurstone, nfactors = 4, rotate = "none")$loa  # calculate unrotated loadings
principal.varimax <- principal(r = Thurstone, nfactors = 4, rotate = "varimax")$loa  # calculate varimax rotated loadings
rot.mat.varimax <- varimax(x = principal.unrotated)$rotmat  # manually calculate varimax rotmat on unrotated loadings
round(x = unclass(principal.unrotated) %*% rot.mat.varimax, digits = 12) == round(x = unclass(principal.varimax), digits = 12)  # works as expected
#>                 [,1] [,2] [,3] [,4]
#> Sentences       TRUE TRUE TRUE TRUE
#> Vocabulary      TRUE TRUE TRUE TRUE
#> Sent.Completion TRUE TRUE TRUE TRUE
#> First.Letters   TRUE TRUE TRUE TRUE
#> 4.Letter.Words  TRUE TRUE TRUE TRUE
#> Suffixes        TRUE TRUE TRUE TRUE
#> Letter.Series   TRUE TRUE TRUE TRUE
#> Pedigrees       TRUE TRUE TRUE TRUE
#> Letter.Group    TRUE TRUE TRUE TRUE


# same procedure using some dataset from another package

library(qmethod)
data("lipset")
Lipset <- cor(x = lipset[[1]], method = "pearson")  # must calculate cor matrix first

principal.unrotated <- principal(r = Lipset, nfactors = 4, rotate = "none")$loa  # calculate unrotated loadings
principal.varimax <- principal(r = Lipset, nfactors = 4, rotate = "varimax")$loa  # calculate varimax rotated loadings
rot.mat.varimax <- varimax(x = principal.unrotated)$rotmat  # manually calculate varimax rotmat on unrotated loadings
round(x = unclass(principal.unrotated) %*% rot.mat.varimax, digits = 12) == round(x = unclass(principal.varimax), digits = 12)  # fails
#>      [,1]  [,2] [,3] [,4]
#> US1 FALSE FALSE TRUE TRUE
#> US2 FALSE FALSE TRUE TRUE
#> US3 FALSE FALSE TRUE TRUE
#> US4 FALSE FALSE TRUE TRUE
#> JP5 FALSE FALSE TRUE TRUE
#> CA6 FALSE FALSE TRUE TRUE
#> UK7 FALSE FALSE TRUE TRUE
#> US8 FALSE FALSE TRUE TRUE
#> FR9 FALSE FALSE TRUE TRUE

round(unclass(principal.varimax)[, c(2,1,3,4)], 12) == round(unclass(principal.unrotated) %*% rot.mat.varimax, 12)  # seems like the ORDER of components is reversed
#>      PC1  PC2  PC3  PC4
#> US1 TRUE TRUE TRUE TRUE
#> US2 TRUE TRUE TRUE TRUE
#> US3 TRUE TRUE TRUE TRUE
#> US4 TRUE TRUE TRUE TRUE
#> JP5 TRUE TRUE TRUE TRUE
#> CA6 TRUE TRUE TRUE TRUE
#> UK7 TRUE TRUE TRUE TRUE
#> US8 TRUE TRUE TRUE TRUE
#> FR9 TRUE TRUE TRUE TRUE
  • 这是预期的行为，如果是，为什么？
  • 我怎样才能避免这种情况？

更新

只是一个小补充：旋转矩阵在两个过程中实际上是相同的：

principal.varimax$rot.mat == rot.mat.varimax

这意味着（有点违反直觉）rot.mat已按原始顺序应用于主要组件的过去版本。

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1 回答 1

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这实际上是这个问题的重复，按（和）中返回的加载顺序，因此被标记。psych::principalpsych::fa

以下是如何psych::principal通过应用相同的 odering 来重现 varimax 旋转：

# using code from within psych::principal, as per this answer: https://stackoverflow.com/questions/16896959/psychprincipal-explanation-for-the-order-and-naming-of-rotated-principal-c
ev.rotated <- diag(t(manual.varimax) %*% manual.varimax)  # find eigenvalues
ev.order <- order(ev.rotated, decreasing = TRUE)  # order by eigenvalues
manual.varimax <- manual.varimax[, ev.order]

round(manual.varimax, 14) == round(principal.varimax, 14)  # works now
#>     [,1] [,2] [,3] [,4]
#> US1 TRUE TRUE TRUE TRUE
#> US2 TRUE TRUE TRUE TRUE
#> US3 TRUE TRUE TRUE TRUE
#> US4 TRUE TRUE TRUE TRUE
#> JP5 TRUE TRUE TRUE TRUE
#> CA6 TRUE TRUE TRUE TRUE
#> UK7 TRUE TRUE TRUE TRUE
#> US8 TRUE TRUE TRUE TRUE
#> FR9 TRUE TRUE TRUE TRUE
于 2015-09-02T09:42:14.290 回答