I have to reduce the number of variables to conduct a cluster analysis. My variables are strongly correlated, so I thought to do
a Factor Analysis PCA (principal component analysis). However, if I use the resulting scores, my clusters are not quite correct (compared to previous classifications in literature).
Can I use the rotation matrix to select the variables with the biggest loads for each component/factor and use only these variables for my clustering?
Any bibliographic references would also be helpful.
My goal: I have to run a clusters analysis with two-step algorithm by SPSS, but my variables are not independents, so I thought about discarding some of them.
My dataset: I am working on 15 scalar parameters (my variables) of 100,000 cases. Some variables are strongly correlated ($>0.9$ Pearson)
My doubt: Since I need only independent variables, I thought to run a Principal Component Analysis (sorry: I wrongly talked about Factor Analysis in my original question, my mistake) and select only the variables with the biggest loadings for each component. I know that the PCA process presents some arbitrary steps, but I found out that this selection is actually similar to the "method B4" proposed by I.T. Jolliffe (1972 & 2002) to select variables and suggested also by J.R. King & D.A. Jackson in 1999.
So I was thinking to select in this way some sub-groups of independent variables. I will then use the groups to run different cluster analysis and I will compare the results.