Variable transformation for factor analysis

Question

When conducting a factor analysis, we need to check the normality and constant variance assumption of the original variables.
If there is HSK existing in the data, can I do different transformations(for example log transformation to x1, squared x2...) to different variables and then conduct the analysis?
Or I should do the same transformation to all variables?

Thanks a lot.

Answer 1

You can certainly apply different transformations to different variables, but it will change the meaning of the results. A key assumption in factor analysis is that the observed measurements are linear combinations of the underlying factors (plus noise). Transforming the observed measurements could have a big influence on the results.