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. However, if I use the resulting scores of factor analysis, my clusters are not quite correct (compared to previous classifications in literature).
Can I just use the rotated matrix of factor analysis to select the variables with the biggest loads for each factor and use only these variables for my clustering?
Any bibliographic references would also be helpful.
First of all, thank you really for your help.
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.