My research study is in development economics. My data consist of more than one independent variables (continuous and categorical) as well as more than one dependent variables (categorical 5-point Likert scale). I want to find out their relationships, therefore regression (ordinal logistic) is the best choice.
But the problem is to reduce the dependent variable from many (6 variables) to one. I explored many options such as categorical principal component analysis (CATPCA), principal component analysis (PCA), composite variable (COMP). But using PCA and COMP means considering the data as continuous instead of categorical. However, all lead to a reduced dependent variable (object dimension/factors/composite) that is in continuous data form, for which I have to use linear regression.
If I choose ordinal logistic regression then I have to run it on each dependent variable separately, leading to many models instead of one model for dependent variable.
I just came across the Rasch model. I am not much familiar with it. It seems to fit my data.
My questions are:
Could I use Rasch Model?
If yes then which one, the rating scale or partial credit in rasch model OR Graded response model?
Could I able to get results from it on which I can run regression (linear/ordinal?)?
Which software is best for it means easy to use and free to download?