If Your aim is to reduce observed data, the PCA is a good choice. However with just 5 variables You are probably looking for latent factors and therefore You should perform exploratory (or the best choice would be confirmatory) factor analysis.

Another question is what is the difference between factor with eigenvalue - 1.01 and 0.98? This is extremely arbitraty and using Kaiser criterion for deciding on this is inappropriate. Try to use more sophisticated methods such as parallel analysis, this would resolve the problem of the number of factors.

Thank you Radoslaw and Khander. Actually, I'm performing both PCA and factor analysis. Results of FA in this case suggest two factors (parallel analysis), and yes all the variables are centered and normalized. I'm just hesitating between varimax or promax rotation. By the way, parallel analysis suggest extracting just one component (but two factors, as I mentioned).

As for my original question, it seems that the matrix above are not the loadings. To get them, each column should be multiplied by the standard deviations in the first line above, so some of the final loadings would be > 0.90, as expected. This is somehow different to the output of other functions performing PCA in R, like principal (psych), which prints the loadings directly. Am I right?

David

Well I think in the case of R, it depends on the package as I mentioned. As you can see above, the output of prcomp() function are not the loadings, as far as I understand.

Thanks!

David, If You are still hesitating which rotation to choose and You are familiar with R, instead of promax try the simplimax rotation. In the promax rotation, the simple target matrix and the target rotation were found in a two-step procedure while simplimax did it simultaneously by finding among all simple target matrices that have a specified number of zero elements. Due to this fact, choosing the best simple target with specified number of zeros was objective. In brief, the main aim of the simplimax rotation is to maximise the simplicity of the rotated pattern.

If You have big cross loadings and Your measure is not well investigated You could use the equamax or facparism rotation and if You do not have cross-loadings - try geomin or quartimax.

Hope this helps.

From what I see, you have HUGE loadings. Anything above 0.3 is a good  loading. Above 0.5 is large. Remember these are correlation coefficients and they cannot be above 1.  So, in PC1, you have all 5 variables loading above 0.3. In PC2, v2, v3 and v4 load well. PC3 v2 loads 0.8! PC4, v1 loads 0.76. PC4, v5 loads 0.76. So, all 5 variables are clearly highly correlated. They have subtle differences, as the factors they load more heavily indicate, but they are all highly correlated. I don't know what they are or which ones are more important to your research, but if you want to reduce the number of variables (which is not very large at this point), pick up the ones loading heavily by themselves in different factors. So, pick v1 in PC4, v3 in PC2, v2 in PC3 and v5 in PC5. Don't use v4 because is highly correlated with all the others without showing marked differentiation. Of course, if you rotate, it might get a different set. Rotation basically changes the reference system so you can get "cleaner" factors, that is, factors that are not as correlated with each other.

http://ocw.jhsph.edu/courses/statisticspsychosocialresearch/pdfs/lecture8.pdf

Thanks Gloria, but I think the matrix above (and therefore the values that you comment) are eigenvectors of the covariance matrix, and should me multiplied by the standard deviations (the line before the matrix, above), to get the actual loadings. Doing so, the loadings are really high for all variables in PC1. And for example the -0.80 you mention in PC3, would become a  ~ -0.40.

I hope to be right. Thanks!!

David

Which software are you using? SPSS gives you the loadings directly as correlation coefficients. Regardless, any loading above 0.3 is good in the Social Sciences. 0.4 is medium. 0.5 and above is high.

Gloriam Guenzburger

can you introduce some references for those numbers(0.3 , 0.4 , 0.5)

cause i used 0.4 in my project, so i need some references

Thanks a lot

Hesam Moradian

Those are values given by professors over the course of several grad courses. They are one of those things, guesstimates by the community over decades. Honestly, I don't think there are hard core data to back them up, other than that in social sciences, data can be so muddled that if you get a correlation over 0.3, you start to take notice, 0.5 looks pretty good and anything above that, it is a slam dunk, given that the maximum is 1.0. I would like to have anything more concrete than that, but that is the nature of the beast. If anybody out there has anything more concrete, please share with the rest of the class. I'd love to see it, seriously.