I will, as is my custom, take a step back and ask what it is you are trying to do, exactly. Factor analysis is designed to find latent variables. If you want to find latent variables and cluster them, then what you are doing is correct. But you say you simply want to reduce the number of variables - that suggests principal component analysis, instead.
However, with either of those, you have to interpret cluster analysis on new variables, and those new variables are simply weighted sums of the old ones.
How many variables have you got? How correlated are they? If there are far too many, and they are very strongly correlated, then you could look for all correlations over some very high number, and randomly delete one variable from each pair. This reduces the number of variables and leaves the variables as they are.
Let me also echo @StasK about the need to do this at all, and @rolando2 about the usefulness of finding something different from what has been found before. As my favorite professor in grad school used to say "If you're not surprised, you haven't learned anything".
You are correct. Stata is weird about this. Stata gives different results from SAS, R and SPSS, and it is difficult (in my opinion) to understand why without delving quite deep into the world of factor analysis and PCA.
Here's how you know that something weird is happening. The sum of the squared loadings for a component are equal to the eigenvalue for that component.
Pre-and post-rotation, the eigenvalues change, but the total eigenvalues don't change. Add up the sum of the squared loadings from your output (this is why I asked you to remove the blanks in my comment). With Stata's default, the sum of squared loadings will sum to 1.00 (within rounding error). With SPSS (and R, and SAS, and every other factor analysis program I've looked at) they will sum to the eigenvalue for that factor. (Post rotation eigenvalues change, but the sum of eigenvalues stays the same). The sum of squared loadings in SPSS is equal to the sum of the eigenvalues (i.e. 3.8723 + 1.40682), both pre- and post-rotation.
In Stata, the sum of the squared loadings for each factor is equal to 1.00, and so Stata has rescaled the loadings.
The only mention of this (that I have found) in the Stata documentation is in the estat loadings section of the help, where it says:
cnorm(unit | eigen | inveigen), an option used with estat loadings,
selects the normalization of the eigenvectors, the columns of the
principal-component loading matrix. The following normalizations are
available
However, this appears to apply only to the unrotated component matrix, not the component rotated matrix. I can't get the unnormalized rotated matrix after PCA.
The people at Stata seem to know what they are doing, and usually have a good reason for doing things the way that they do. This one is beyond me though.
(For future reference, it would have made my life easier if you'd used a dataset that I could access, and if you'd included all output, without blanks).
Edit: My usual go-to site for information about how to get the same results for different programs is the UCLA IDRE. They don't cover PCA in Stata: http://www.ats.ucla.edu/stat/AnnotatedOutput/ I have to wonder if that's because they couldn't get the same result. :)
Best Answer
Skewness issue in PCA is the same as in regression: the longer tail, if it is really long relative to the whole range of the distribution, actually behaves like a big outlier—it pulls the fit line (principal component in your case) strongly toward itself because its influence is enhanced; its influence is enhanced because it is so far from the mean. In the context of PCA allowing very skewed variables is pretty similar to doing PCA without centering the data (i.e., doing PCA on the basis of cosine matrix rather than correlation matrix). It is you who decides whether to permit the long tail to influence results so greatly (and let the data be) or not (and transform the data). The issue is not connected with how you do interpretation of loadings.
As you like.
KMO is an index that tells you whether partial correlations are reasonably small to submit data to factor analysis. Because in factor analysis we generally expect a factor to load more than just two variables. Your KMO is low enough. You can make it better if you drop from the analysis variables with low individual KMO values (these form the diagonal of anti-image matrix, you can request to show this matrix in SPSS Factor procedure). Can tranforming variables into less skewed recover KMO? Who knows. Maybe. Note that KMO is important mostly in Factor analysis model, not Principal Components analysis model: in FA you fit pairwise correlations, whereas in PCA you don't.