[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

From |
"Nick Cox" <[email protected]> |

To |
<[email protected]> |

Subject |
RE: st: PCA and rotation |

Date |
Mon, 4 Jan 2010 18:58:21 -0000 |

These recommendations sound tendentious to me, except that no doubt they make much sense in the context of the authors' aims. The idea that factor analysis is _uniformly_ superior to principal component analysis is I think only defensible if your aims are limited to those addressed explicitly by factor analysis. Indeed, even non-experts on intelligence tests can guess that different intelligence factors, if they exist, are most unlikely to be uncorrelated, but there are plenty of contexts (e.g. in meteorology and oceanography) in which orthogonal components are precisely what is desired from a physical point of view. Nick [email protected] Diana Kornbrot 28 Dec 2009 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? On 21/12/2009 21:33, "Michael I. Lichter" <[email protected]> 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". * * 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/

**Follow-Ups**:**RE: st: PCA and rotation***From:*"Verkuilen, Jay" <[email protected]>

- Prev by Date:
**st: RE: Re: Command to identify number of unique individuals** - Next by Date:
**RE: st: PCA and rotation** - Previous by thread:
**st: RE: Re: Command to identify number of unique individuals** - Next by thread:
**RE: st: PCA and rotation** - Index(es):

© Copyright 1996–2024 StataCorp LLC | Terms of use | Privacy | Contact us | What's new | Site index |