Hello, not understanding the output of prcomp, I reduce the number of
components and the output continues to show cumulative 100% of the
variance explained, which can't be the case dropping from 8 components
to 3.
How do i get the output in terms of the cumulative % of the total
variance, so when i go from total solution of 8 (8 variables in the data
set), to a reduced number of components, i can evaluate % of variance
explained, or am I missing something??
8 variables in the data set
> princ = prcomp(df[,-1],rotate="varimax",scale=TRUE)
> summary(princ)
Importance of components:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
Standard deviation 1.381 1.247 1.211 0.994 0.927 0.764 0.6708 0.4366
Proportion of Variance 0.238 0.194 0.183 0.124 0.107 0.073 0.0562 0.0238
Cumulative Proportion 0.238 0.433 0.616 0.740 0.847 0.920 0.9762 *1.0000*
> princ = prcomp(df[,-1],rotate="varimax",scale=TRUE,tol=.75)
> summary(princ)
Importance of components:
PC1 PC2 PC3
Standard deviation 1.381 1.247 1.211
Proportion of Variance 0.387 0.316 0.297
Cumulative Proportion 0.387 0.703 *1.000*
[[alternative HTML version deleted]]
principal components is a data reduction technique. It looks like you have three axes that account for 100%. Make this reporducible. On Mon, Nov 9, 2009 at 11:37 AM, zubin <binabina at bellsouth.net> wrote:> Hello, not understanding the output of prcomp, I reduce the number of > components and the output continues to show cumulative 100% of the > variance explained, which can't be the case dropping from 8 components > to 3. > > How do i get the output in terms of the cumulative % of the total > variance, so when i go from total solution of 8 (8 variables in the data > set), to a reduced number of components, i can evaluate % of variance > explained, or am I missing something?? > > 8 variables in the data set > > ?> princ = prcomp(df[,-1],rotate="varimax",scale=TRUE) > ?> summary(princ) > Importance of components: > ? ? ? ? ? ? ? ? ? ? ? ? PC1 ? PC2 ? PC3 ? PC4 ? PC5 ? PC6 ? ?PC7 ? ?PC8 > Standard deviation ? ? 1.381 1.247 1.211 0.994 0.927 0.764 0.6708 0.4366 > Proportion of Variance 0.238 0.194 0.183 0.124 0.107 0.073 0.0562 0.0238 > Cumulative Proportion ?0.238 0.433 0.616 0.740 0.847 0.920 0.9762 *1.0000* > > ?> princ = prcomp(df[,-1],rotate="varimax",scale=TRUE,tol=.75) > ?> summary(princ) > > Importance of components: > ? ? ? ? ? ? ? ? ? ? ? ? PC1 ? PC2 ? PC3 > Standard deviation ? ? 1.381 1.247 1.211 > Proportion of Variance 0.387 0.316 0.297 > Cumulative Proportion ?0.387 0.703 *1.000* > > ? ? ? ?[[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list > 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. >-- Stephen Sefick Let's not spend our time and resources thinking about things that are so little or so large that all they really do for us is puff us up and make us feel like gods. We are mammals, and have not exhausted the annoying little problems of being mammals. -K. Mullis
In the first PCA you ask how much variance of the EIGHT (!) variables is
captured by the first, second,..., eigth principal component.
In the second PCA you ask how much variance of the THREE (!) variables is
captured by the first, second, and third principal component.
Of course you need only as many PCs as there are variables to capture 100 %
of the variance. Your "problem" thus comes from the fact that you have
eight
variables in the first PCA, which requires eight PCs to capture 100%, and
that you have only three variables in the second PCA, which naturally only
requires three PCs to capture 100% of the variance.
So it's more, yes, you are missing something in this case, rather than that
something is wrong with the analyses.
HTH,
Daniel
-------------------------
cuncta stricte discussurus
-------------------------
-----Urspr?ngliche Nachricht-----
Von: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] Im
Auftrag von zubin
Gesendet: Monday, November 09, 2009 12:37 PM
An: r-help at r-project.org
Betreff: [R] prcomp - principal components in R
Hello, not understanding the output of prcomp, I reduce the number of
components and the output continues to show cumulative 100% of the variance
explained, which can't be the case dropping from 8 components to 3.
How do i get the output in terms of the cumulative % of the total variance,
so when i go from total solution of 8 (8 variables in the data set), to a
reduced number of components, i can evaluate % of variance explained, or am
I missing something??
8 variables in the data set
> princ = prcomp(df[,-1],rotate="varimax",scale=TRUE)
> summary(princ)
Importance of components:
PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
Standard deviation 1.381 1.247 1.211 0.994 0.927 0.764 0.6708 0.4366
Proportion of Variance 0.238 0.194 0.183 0.124 0.107 0.073 0.0562 0.0238
Cumulative Proportion 0.238 0.433 0.616 0.740 0.847 0.920 0.9762 *1.0000*
> princ = prcomp(df[,-1],rotate="varimax",scale=TRUE,tol=.75)
> summary(princ)
Importance of components:
PC1 PC2 PC3
Standard deviation 1.381 1.247 1.211
Proportion of Variance 0.387 0.316 0.297 Cumulative Proportion 0.387 0.703
*1.000*
[[alternative HTML version deleted]]
______________________________________________
R-help at r-project.org mailing list
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.
Hi: I'm not familar with prcomp but with the principal components function
in bill revelle's? psych package , one can specify the number of
components
one wants to use to build the "closest" covariance matrix? I
don't know
what tol is doing in your example? but it's not doing? that.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
? ? ? ? ? ? ? ? ? ? ? ? ? mark
On Nov 9, 2009, zubin <binabina at bellsouth.net> wrote:
All 8 variables are still in the analysis, i am just reducing the number
of components being estimated i thought..
Example 1 component 8 variables, there is no way 1 component explains
100% of the variance of the 8 variable data set.
> princ = prcomp(df[,-1],rotate="varimax",scale=TRUE,tol=.95)
> summary(princ)
Importance of components:
PC1
Standard deviation 1.38
Proportion of Variance 1.00
Cumulative Proportion 1.00
> summary(princ)
Rotation:
PC1
VIX0 -0.08217686
UUP0 -0.18881983
USO0 0.26647346
GLD0 0.26983923
HYG0 0.60674758
term0 0.18220237
spread0 0.61614047
TNX0 0.18111684
Daniel Malter wrote:
> In the first PCA you ask how much variance of the EIGHT (!) variables
is
> captured by the first, second,..., eigth principal component.
>
> In the second PCA you ask how much variance of the THREE (!) variables
is
> captured by the first, second, and third principal component.
>
> Of course you need only as many PCs as there are variables to capture
100 %
> of the variance. Your "problem" thus comes from the fact
that you have
eight
> variables in the first PCA, which requires eight PCs to capture 100%,
and
> that you have only three variables in the second PCA, which naturally
only
> requires three PCs to capture 100% of the variance.
>
> So it's more, yes, you are missing something in this case, rather
than
that
> something is wrong with the analyses.
>
> HTH,
> Daniel
>
> -------------------------
> cuncta stricte discussurus
> -------------------------
>
> -----Urspr??ngliche Nachricht-----
> Von: [1]r-help-bounces at r-project.org
[[2]mailto:r-help-bounces at r-project.org] Im
> Auftrag von zubin
> Gesendet: Monday, November 09, 2009 12:37 PM
> An: [3]r-help at r-project.org
> Betreff: [R] prcomp - principal components in R
>
> Hello, not understanding the output of prcomp, I reduce the number of
> components and the output continues to show cumulative 100% of the
variance
> explained, which can't be the case dropping from 8 components to
3.
>
> How do i get the output in terms of the cumulative % of the total
variance,
> so when i go from total solution of 8 (8 variables in the data set),
to
a
> reduced number of components, i can evaluate % of variance explained,
or
am
> I missing something??
>
> 8 variables in the data set
>
> > princ = prcomp(df[,-1],rotate="varimax",scale=TRUE)
> > summary(princ)
> Importance of components:
> PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
> Standard deviation 1.381 1.247 1.211 0.994 0.927 0.764 0.6708 0.4366
> Proportion of Variance 0.238 0.194 0.183 0.124 0.107 0.073 0.0562
0.0238
> Cumulative Proportion 0.238 0.433 0.616 0.740 0.847 0.920 0.9762
*1.0000*
>
> > princ =
prcomp(df[,-1],rotate="varimax",scale=TRUE,tol=.75)
> > summary(princ)
>
> Importance of components:
> PC1 PC2 PC3
> Standard deviation 1.381 1.247 1.211
> Proportion of Variance 0.387 0.316 0.297 Cumulative Proportion 0.387
0.703
> *1.000*
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> [4]R-help at r-project.org mailing list
> [5]https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
[6]http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>
>
______________________________________________
[7]R-help at r-project.org mailing list
[8]https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide
[9]http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
References
1. mailto:r-help-bounces at r-project.org
2. mailto:r-help-bounces at r-project.org
3. mailto:r-help at r-project.org
4. mailto:R-help at r-project.org
5. https://stat.ethz.ch/mailman/listinfo/r-help
6. http://www.R-project.org/posting-guide.html
7. mailto:R-help at r-project.org
8. https://stat.ethz.ch/mailman/listinfo/r-help
9. http://www.R-project.org/posting-guide.html
The output of summary prcomp displays the cumulative amount of variance
explained relative to the total variance explained by the principal components
PRESENT in the object. So, it is always guaranteed to be at 100% for the last
principal component present. You can see this from the code in summary.prcomp()
(see this code with getAnywhere("summary.prcomp")).
Here's how to get the output you want (the last line in the transcript
below):
> set.seed(1)
> summary(pc1 <- prcomp(x))
Importance of components:
PC1 PC2 PC3 PC4 PC5
Standard deviation 1.175 1.058 0.976 0.916 0.850
Proportion of Variance 0.275 0.223 0.190 0.167 0.144
Cumulative Proportion 0.275 0.498 0.688 0.856 1.000> summary(pc2 <- prcomp(x, tol=0.8))
Importance of components:
PC1 PC2 PC3
Standard deviation 1.17 1.058 0.976
Proportion of Variance 0.40 0.324 0.276
Cumulative Proportion 0.40 0.724 1.000> pc2$sdev
[1] 1.1749061 1.0581362 0.9759016> pc1$sdev
[1] 1.1749061 1.0581362 0.9759016 0.9164905 0.8503122> svd(scale(x, center=T, scale=F))$d / sqrt(nrow(x)-1)
[1] 1.1749061 1.0581362 0.9759016 0.9164905 0.8503122> cumsum(pc1$sdev^2) / sum((svd(scale(x, center=T, scale=F))$d /
sqrt(nrow(x)-1))^2)
[1] 0.2752317 0.4984734 0.6883643 0.8558386 1.0000000>
> # output in terms of the cumulative % of the total variance
> cumsum(pc2$sdev^2) / sum((svd(scale(x, center=T, scale=F))$d /
sqrt(nrow(x)-1))^2)
[1] 0.2752317 0.4984734 0.6883643>
It's probably better to get prcomp to compute all the components in the
first place, because the SVD is the bulk of the computation anyway (so doing it
again will be slower for large matrices.) Then just look at the most important
principal components. However, there may be a shortcut for computing the values
of D in the SVD of a matrix -- you could look for that if you have demanding
computations (e.g., the sqrts of the eigen values of the covariance matrix of
scaled x: sqrt(eigen(var(scale(x, center=T, scale=F)), only.values=T)$values)).
-- Tony Plate
zubin wrote:> Hello, not understanding the output of prcomp, I reduce the number of
> components and the output continues to show cumulative 100% of the
> variance explained, which can't be the case dropping from 8 components
> to 3.
>
> How do i get the output in terms of the cumulative % of the total
> variance, so when i go from total solution of 8 (8 variables in the data
> set), to a reduced number of components, i can evaluate % of variance
> explained, or am I missing something??
>
> 8 variables in the data set
>
> > princ = prcomp(df[,-1],rotate="varimax",scale=TRUE)
> > summary(princ)
> Importance of components:
> PC1 PC2 PC3 PC4 PC5 PC6 PC7 PC8
> Standard deviation 1.381 1.247 1.211 0.994 0.927 0.764 0.6708 0.4366
> Proportion of Variance 0.238 0.194 0.183 0.124 0.107 0.073 0.0562 0.0238
> Cumulative Proportion 0.238 0.433 0.616 0.740 0.847 0.920 0.9762 *1.0000*
>
> > princ = prcomp(df[,-1],rotate="varimax",scale=TRUE,tol=.75)
> > summary(princ)
>
> Importance of components:
> PC1 PC2 PC3
> Standard deviation 1.381 1.247 1.211
> Proportion of Variance 0.387 0.316 0.297
> Cumulative Proportion 0.387 0.703 *1.000*
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list
> 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.
>