# Thread: Principal Components Analysis (psychology) - negative loadings?

1. ## Principal Components Analysis (psychology) - negative loadings?

Hi there,

I'm attempting to do dimension reduction/data reduction with PCA. The goal is to extract "factor" scores to use as independent variables i further analyses. I'm using SPSS, and I have a large data set with 26 variables (measuring memory performance on various memory tests) and N=400-1000 subjects, depending on which subsample I'm looking at. There is also rather high multicollinearity in the data...

In my preliminary analyses I've extracted 4-5 components, which are rather stable when I cross-check them on other subsamples. However, I'm not sure of which rotation method to use. I would like to use oblique rotation, since all my variables measure memory and components are correlated (some over 0.5). My components are pretty much identical whichever rotation method I use, i.e. the same variables load on the same component. But when I use oblique rotation one of the components only has negative loadings in the pattern matrix. Now I'm very unsure of how to interpret this component? It is negatively correlated with two of the other components, -0.544 and -0.536. What does this really mean?

Now I'm leaning towards using orthogonal rotation just to circumvent the problem, but I have a feeling that just ignoring the problem won't make it go away So I'm trying to figure out what this result is telling me about my data. For the sake of extracting factor scores the rotation method does not seem to make much difference. Perhaps they are the same whichever rotation method one uses?

I would be very thankful for some guidance on this matter. That is, what does a component with only negative loadings after oblique rotation really mean?

I hope someone can help me...

2. my question is quite different from principle componenet analysis.my question is aboyt independent component analysis .
why we are in ICA assume that the components or the sources not gaussian?
i.e. not follow the multivariate norman distribution

3. Hi sara_pu,

Rotation is only used to help us with the interpretation. There aren't any mathematical advantages in one rotation over the other. You just have to use the one that is easiest to interpret. Usually oblique rotations are not easy to interpret, since you have to distinguish between the pattern loadings and the structure loadings, since there is a correlation involved. I imagine this correlation is twisted your values. The oblique rotations are usually used when the orthogonal solutions give some illogical conclusions. Apparently that's not your case, so you should use the rotation with the simplest structure.

Now, osama hamza, I don't really understand what you mean with Independent Principal Components. Usually this analysis is classified within the Analysis of Interdependece, if that's what you man. The core is that there are no distribution assumptions in PCA or Factor Analysis. There are some inference procedures related with PCA that assume multivariate normality, but those are somehow different analysis, not the common PCA.

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