I am new to factor analysis. I inherited a project at work from another team. They took 9 variables that are all Poisson-distributed count random variables and ran a "regular" factor analysis in Stata/SPSS (they did not specifically account for this being count data). The four factors they obtained are each normally distributed continuous variables.
My question is:
Is what they did correct, or are there special factor analysis methods for count data?
Should I be concerned that the factors are a totally different distribution than the original data?
The next step in the project is to set up regression models for each of the factors as the DV. Obviously, if the factors had been in the same family as the original count data, I would be running Poisson or NBD regressions, but after this transformation, I am running linear regressions. Not sure which is the right way to go.
I'd appreciate advice and information that would help me learn more about this. Stata specific information is a plus.