(2014-Jul-30, 21:07:43)menghu1001 Wrote: Concerning congruence coefficient, after reading this article...

Davenport, E. C. (1990). Significance testing of congruence coefficients: A good idea?. Educational and psychological measurement, 50(2), 289-296.

... I am left with the impression it's very bad method. You should be careful with that. (The version of the paper I have can't allow copy paste, but check the pages 293-295.) The congruence coeff seems to constantly give you very high value even in situations where they should be (theoretically) small, or not high at all.

Can you upload that paper or send it to me? There are other sources that are more sanguine about the CC, e.g., https://media.psy.utexas.edu/sandbox/gro...ruence.pdf In any case, the problems with using Pearson's r in the analysis of factor loadings are even greater.

Quote:Regarding the question of negative loadings, i don't understand your discussion here, both of you. My opinion is that when you have small loadings (such as 0.20 or less) in the 1rst unrotated factor, regardless of the direction, you should remove it because it's a poor measure of this factor.

I don't think the size of the loadings is that important here, only the sign. In scale development, it makes sense to remove indicator variables with small loadings (e.g., <0.3) because the purpose is to come up with a reliable measurement instrument. However, the purpose of Emil's paper is not to develop a scale but to investigate the correlation structure of international socioeconomic differences.

(2014-Jul-31, 20:25:10)Emil Wrote: However, one point. Yes, it is possible that the 2nd factor is almost the same size as the first. I had actually checked this because I initially did some analyses in SPSS before moving to R (it's my first time using R for a project). Here's what one can do in R:

Code:`y_ml.2 = fa(y,nfactors=2,rotate="none",scores="regression",fm="ml") #FA with 2 factors`

y_ml.2 #display results

plot(y_ml.2$loadings[1:54],y_ml$loadings) #plots first factors

cor(y_ml.2$loadings[1:54],y_ml$loadings) #correlation ^

y_ml.3 = fa(y,nfactors=3,rotate="none",scores="regression",fm="ml") #same as above just for 3 factors

y_ml.3

plot(y_ml.3$loadings[1:54],y_ml$loadings)

cor(y_ml.3$loadings[1:54],y_ml$loadings)

One will get the 2 factor and 3 factor solutions using max. likelihood. Apparently the first factor is not completely identical across the nfactors to extract, but almost so. ML1 (with nfactors=1) with ML1 from nfactors=2 and 3 was .999.

With nfactors=2, the 2nd factor was much smaller. Var% for ML1 is about 41%, for ML2 it is about 11%,

With 3, ML1=41%, ML2=10%, ML3=5%.

Discuss that in the paper, and explain why you disregard the other factors. As to the number of factors, use Kaiser's rule (eigenvalue>1) or, if you can, parallel analysis. Are the other factors interpretable based on which variables load strongly on them?