[R] prcomp() and varimax()
Mike Amato
mikeamato.wi at gmail.com
Thu Apr 4 14:33:26 CEST 2013
Hello,
I am attempting to do a principal components analysis on 15 survey
items. I want to use a varimax rotation on the retained components, but
I am dubious of the output I am getting, and so I suspect I am doing
something wrong. I proceed in the following steps:
1) use prcomp() to inspect all 15 components, and decide which to retain
2) run prcomp() again, using the "tol" parameter to omit unwanted
components
3) pass the output of step 2 to varimax()
My concern is with the reported proportions of variance for the 3
components after varimax rotation. It looks like each of my 3 components
explains 1/15 of the total variance, summing to a cumulative proportion
of 20% of variance explained. But those 3 components I retained should
now be the only components in the analysis, so they should be able to
account for 100% of the explained variance.
I am able to get reliable seeming results using principal() from the
"psych" package, in which the total amount of variance explained by my
retained components does not differ before or after rotation. But
principal() uses varimax(), so I suspect I am either doing something
wrong or misinterpreting the output when using the base package functions.
Am I doing something wrong when attempting to retain only 3 components?
Am I using varimax() incorrectly?
Am I misinterpreting the returned values from varimax()?
Thanks for any help,
Mike
Here is a link to the data file I am using:
https://www.dropbox.com/s/scypebzy0nnhlwk/pca_sampledata.txt
### step 1 ###
> d1 = read.table("pca_sampledata.txt", T)
> m1 = with(d1, ~ g.enjoy + g.look + g.cost + g.fit + g.health +
g.resale + b.withstand + b.satisfy + b.vegetated + b.everyone + b.harmed
+ b.eco + b.ingenuity + b.security + b.proud)
> pca1 = prcomp(m1)
> summary(pca1) #output truncated for this posting
Importance of components:
PC1 PC2 PC3 PC4 PC5 ... PC15
Standard deviation 1.5531 1.3064 1.1695 0.93512 0.92167 ... 0.35500
Proportion of Variance 0.2199 0.1556 0.1247 0.07972 0.07744 ... 0.01149
Cumulative Proportion 0.2199 0.3755 0.5002 0.57988 0.65732 ... 1.00000
### step 2 ###
> pca2 = prcomp(m1, tol=.75)
> summary(pca2) #full output shown
Importance of components:
PC1 PC2 PC3
Standard deviation 1.5531 1.3064 1.1695
Proportion of Variance 0.4397 0.3111 0.2493
Cumulative Proportion 0.4397 0.7507 1.0000
### step 3 ###
> pca3 = varimax(pca2$rotation)
> pca3
> ...
> PC1 PC2 PC3
> SS loadings 1.000 1.000 1.000
> Proportion Var 0.067 0.067 0.067
> Cumulative Var 0.067 0.133 0.200
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