Re: st: PCA and rotation

[kornbrot <d.e.kornbrot@herts.ac.uk>]

Title: Re: st: PCA and rotation

The following intereesting article recommends

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

Reeve, C. L., & Blacksmith, N. (2009). Identifying g: A review of current factor analytic practices in the science of mental abilities. Intelligence, 37(5), 487-494. http://www.sciencedirect.com/science/article/B6W4M-4WN8H8G-1/2/b92c4e9a744cb75285467c53e906aed6. 

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
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/

---

Professor Diana Kornbrot
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