Using Rasch model to explain relationships between a set of dependent and independent variables

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:

1. Could I use Rasch Model?

2. If yes then which one, the rating scale or partial credit in rasch model OR Graded response model?

3. Could I able to get results from it on which I can run regression (linear/ordinal?)?

4. Which software is best for it means easy to use and free to download?

• The Rasch model (not so-called "models of the Rasch family") is for dichotomous items only, so point 1 can be safely discarded. Now, the question is whether your 6 Likert-type items belong to a unidimensional scale or not. In the latter case, that would slightly complicated things because you would need an explanatory multidimensional IRT model. About the last point you will probably find useful recommendations elsewhere. – chl Jan 18 '12 at 11:37
• You should look into one famous table. It says PCA/CATPCA, Rash/IRT are model continuous latent variable. To model categorical latent you need latent profile or latent class analysis. – ttnphns Jan 18 '12 at 14:54
• @ttnphns I do not follow your point. Where is it stated that the OP does consider latent classes rather than latent traits? – chl Jan 18 '12 at 17:45
• crossreference to OP's other question stats.stackexchange.com/questions/20988/… – Jack Tanner Jan 18 '12 at 17:52
• @ttnphns I didn't notice the previous question, my bad! And now it seems there's some confusion about what you are after, wxa. Do you want to use a measurement model or are you just interested in modeling multivariate relationships between two blocks of data? In the latter case, one way to account for the asymmetrical role played by each block (6 predictors on one side, 6 response variables on the other side) is to use redundancy analysis or PLS-2 regression. (I used to think OP means either "original post" or "original poster", depending on the context) – chl Jan 18 '12 at 22:00