The sum of the squared loadings will always sum to 1 because they are
standardized by dividing them by the standard deviation of each component. The
terminology for principal components is not as consistent as we could hope.
What princomp() calls loadings is really the structure matrix (the correlation
between each variable and the component). The pattern matrix (often called the
loadings) are the regression coefficients for computing the principal component
scores. You are probably looking for the pattern matrix which is easy to obtain
by multiplying by the standard deviations:
> set.seed(42)
> data <- matrix(runif(100), 20, 5)
> pc <- princomp(data, cor=TRUE)
> loadings(pc)
Loadings:
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
[1,] 0.638 0.249 -0.260 -0.679
[2,] -0.714 0.449 0.298 -0.444
[3,] 0.585 -0.152 0.522 -0.231 0.555
[4,] -0.617 -0.543 -0.564
[5,] -0.496 0.154 0.479 -0.687 -0.172
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
SS loadings 1.0 1.0 1.0 1.0 1.0
Proportion Var 0.2 0.2 0.2 0.2 0.2
Cumulative Var 0.2 0.4 0.6 0.8 1.0
> rowSums(pc$loadings^2)
[1] 1 1 1 1 1
> # Notice that the column sums of the squared loadings all equal 0
> # Now multiply each loading by its standard deviation
> sweep(pc$loadings, 2, pc$sdev, "*")
Loadings:
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
[1,] 0.765 0.275 -0.237 -0.531
[2,] -0.787 0.427 0.271 -0.347
[3,] 0.701 -0.167 0.497 -0.211 0.434
[4,] -0.680 -0.518 -0.515
[5,] -0.594 0.169 0.456 -0.627 -0.134
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
SS loadings 1.436 1.215 0.907 0.832 0.611
Proportion Var 0.287 0.243 0.181 0.166 0.122
Cumulative Var 0.287 0.530 0.712 0.878 1.000
> pc$sdev^2
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
1.4362072 1.2145055 0.9068555 0.8315685 0.6108632
> # Now the sum of the squared loadings equals the
> # squared standard deviation (aka the eigenvalues)
-------------------------------------
David L Carlson
Department of Anthropology
Texas A&M University
College Station, TX 77840-4352
-----Original Message-----
From: R-help [mailto:r-help-boun...@r-project.org] On Behalf Of Marcelo Kittlein
Sent: Monday, September 14, 2015 8:46 AM
To: r-help@r-project.org
Subject: [R] Error in principal component loadings calculation
Hi all
I have been using "princomp" to obtain the principal components of some
data and find that the loadings returned by the function appear to have
some error.
in a simple example if a calculate de pc for a random matrix I get that
all loadings for the different components have the same proportion of
variance
data <- matrix(runif(100), 20, 5)
pc <- princomp(data, cor=TRUE)
loadings(pc)
Loadings:
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
[1,] -0.280 0.510 0.674 -0.217 -0.400
[2,] 0.529 -0.353 -0.694 -0.330
[3,] -0.111 0.563 -0.713 -0.336 -0.222
[4,] -0.530 -0.502 -0.178 0.140 -0.645
[5,] -0.590 -0.215 -0.582 0.516
Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
SS loadings 1.0 1.0 1.0 1.0 1.0
Proportion Var 0.2 0.2 0.2 0.2 0.2
Cumulative Var 0.2 0.4 0.6 0.8 1.0
This keep returning the same proportion of variance for each component
regardless of the data used.
my R version is
> R.Version()
$platform
[1] "x86_64-unknown-linux-gnu"
$arch
[1] "x86_64"
$os
[1] "linux-gnu"
$system
[1] "x86_64, linux-gnu"
$status
[1] ""
$major
[1] "3"
$minor
[1] "2.1"
$year
[1] "2015"
$month
[1] "06"
$day
[1] "18"
$`svn rev`
[1] "68531"
$language
[1] "R"
$version.string
[1] "R version 3.2.1 (2015-06-18)"
$nickname
[1] "World-Famous Astronaut"
some hint would be much appreciated.
Best regards
Marcelo Kittlein
[[alternative HTML version deleted]]
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______________________________________________
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https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
