My data consists of 6 independent variables (continuous and categorical) and 8 dependent variables on likert scale (categorical). I want to use multinomial logistic regression to find out the relationship between dependent and independent variables. I reduced the 8 dependent variables by principal component analysis (factor analysis) into 2 factors.
My question is that could I use the factor results of SPSS or average of factors as dependent variables in logistic regression?
The principal component analysis is for "continuous variables" not for "categorical variables".
The multinomial logistic regression is not for ordinal responses, thus you should use ordinal logistic regression for each dependent variable separately. Or,
Rasch models might be a good choice for your data.
If you have two factors, then you now have two continuous variables from the scoring on the factors, don't you? I'm not quite following how you have categorical variables out of the factor analysis.
If you really want to use multinomial logistic regression, you could make 4 classes using a median split on each factor: hi/hi, hi/lo, lo/hi, lo/lo.
Another approach would be to use each factor as a dependent variable in its own (not logistic) regression.
I don't know about SPSS, but in SAS you can use PROC CATMOD to fit a multivariate response model. For example, these statements fit an ordinal logistic model (specifically, a cumulative logit model) simultaneously to three multinomial responses (DV1, DV2, DV3). There are two categorical predictors (IV1, IV2) and one continuous predictor (IV3).
proc catmod;
response clogits;
direct iv3;
model dv1*dv2*dv3 = iv1 iv2 iv3;
run; quit;
Keep in mind that models like this tend to have a lot of parameters and therefore often have model fitting problems due to sparseness of the data. You may have to simplify the model in some way if you encounter problems. This may require merging categories in the categorical responses and/or predictors, or dropping response variables or predictors altogether.
