Thanks for the reply. Maybe my problem is that prcomp() and varimax() 
are calculating "cumulative proportion of variance" differently?
When I use the tol parameter with prcomp(), it restricts the number of 
components to 3 and reports that the cumulative variance explained by 
the third component is 100%.
But when I try to pass that 3-component analysis to varimax(), the 
cumulative variance of the third component drops to 20%. The cumulative 
proportion of variance explained by a component should not change 
following rotation, so it seems like it should be either 50% (as in the 
original 15 component model pca1) or else 75% (as in the smaller 
unrotated model pca2). But component 3 in the rotated model (pca3) has a 
value that is neither of those.

I suspect maybe I am not using varimax() correctly? Especially because 
it doesn't make sense that all components in the rotated model (pca3) 
would explain an identical amount of variance- this is real data, so the 
first component should explain more variance than the second, and so on.

Thanks for the help,
Mike



On 4/7/2013 6:38 AM, S Ellison wrote:
>> 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.
> Am I misreading what you just wrote? One percentage (20%) is a proportion of the total variance in the data; the other is the proportion of the variance explained by the model. These are different things; they should not usually be the same.
>
> *******************************************************************
> This email and any attachments are confidential. Any use, copying or
> disclosure other than by the intended recipient is unauthorised. If
> you have received this message in error, please notify the sender
> immediately via +44(0)20 8943 7000 or notify postmaster@lgcgroup.com
> and delete this message and any copies from your computer and network.
> LGC Limited. Registered in England 2991879.
> Registered office: Queens Road, Teddington, Middlesex, TW11 0LY, UK
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

	[[alternative HTML version deleted]]

