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From |
kornbrot <d.e.kornbrot@herts.ac.uk> |

To |
"statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu> |

Subject |
Re: st: PCA and rotation |

Date |
Mon, 28 Dec 2009 11:41:22 +0000 |

Title:

- ALWAYS use factor analysis not principal components, as errors are included in PC anf may differ across replications
- ALWAYS use oblique rotation rather than orthogonal rotation, as otherwise you may miss higher order factors

Makes sens to me.

Other views?

Best

diana

On 21/12/2009 21:33, "Michael I. Lichter" <mlichter@buffalo.edu> wrote:

I recently found that when I extracted components using -pca-, rotated

them using an orthogonal rotation (e.g., -rotate, varimax-), and scored

them using -predict-, the correlations between what I presumed were

uncorrelated factors were actually as high as 0.6. I know that component

scores may be correlated, but this seemed a bit much. Somebody else

noted the same thing a few months ago

(http://www.stata.com/statalist/archive/2009-08/msg00793.html). On the

other hand, I found that factor scores (produced with -factor, pcf-) for

the same data remained virtually uncorrelated after orthogonal rotation.

I therefore assumed that the behavior of rotated PCs was a bug. I

contacted Stata. Isabel Canette told me that I was mistaken. She

referred me to "Methods of Multivariate Analysis" by A. Rencher, Second

Edition,Wiley, 2002, page 403, where Rencher says:

"...If the resulting components do not have satisfactory interpretation,

they can be further rotated, seeking dimensions in which many of the

coefficients of the linear combination and near zero to simplify

interpretation.

However, the new rotated components are correlated, and they do not

successively account for maximum variance. They are, therefore, no

longer principal components in the usual sense, and their routine use

is questionable".

In other words, it's not a bug, it's ... something else. Isabel said

that for this reason Stata discourages the use of rotation after -pca-.

What's odd is that I've seen a number of articles that use varimax

rotations (with Kaiser normalization) of principal components in scale

development. The authors only use the PCA to guide scale development;

they perform further analysis with Cronbach's alpha and create summative

scales rather than using factor scores. Still, their interpretation of

the components are based on rotated component loadings that, at least

from Rencher's perspective, are "questionable".

--

Michael I. Lichter, Ph.D. <mlichter@buffalo.edu>

Research Assistant Professor & NRSA Fellow

UB Department of Family Medicine / Primary Care Research Institute

UB Clinical Center, 462 Grider Street, Buffalo, NY 14215

Office: CC 126 / Phone: 716-898-4751 / FAX: 716-898-3536

*

* For searches and help try:

* http://www.stata.com/help.cgi?search

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Professor Diana Kornbrot

web:

University of Hertfordshire

College Lane, Hatfield, Hertfordshire AL10 9AB, UK

voice: +44 (0) 170 728 4626

fax: +44 (0) 170 728 5073

London N2 0LT, UK

voice: +44 (0) 208 883 3657

mobile: +44 (0) 796 890 2102

fax: +44 (0) 870 706 4997

**Follow-Ups**:**Re: st: PCA and rotation***From:*"Michael I. Lichter" <mlichter@buffalo.edu>

**References**:**st: PCA and rotation***From:*"Michael I. Lichter" <mlichter@buffalo.edu>

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