I have a non-ordinal categorical dependent variable with 3 choice outcomes and 20 ordinal categorical predictors and want to do a multinomial logistic regression. However, I want to reduce the predictors to just a few variables with factor analysis. SPSS gives regression factor scores as variables for each of my cases. Do I replace my original 20 predictors with these 5 regression factor score variables, or do the factors need to be on another format before using them as predictors?
Provided that the factor analysis is itself valid, then you can replace your 20 predictors with the 5 factor score variables. That is, there is no special relationship between multinomial logistic regression and factor analysis that makes the application of factor analysis as a way of pre-processing the data invalid.
In terms of the validity of the factor analysis, you may want to use dimension reduction technique that are designed for categorical data. From memory, SPSS has one or two (HOMALS and Categorical Principal Components Analysis).
The other practical challenge is that it is possible that the best predictor variable may end up with relatively little weight in the factor analysis, so it may be useful to only do the factor analysis with variables that are known to have some predictive relationship with your dependent variable.