I have a dataset where we are looking to predict an outcome variable using three categorical independent variables (each of which has two indicators). A clumsy way to do this would be to create a new categorical variable with eight levels (e.g., a 1 on this new variable would represent a 1 on each of the original variables; a 2 on this new variable would represent a 1 on original variable 1, a 1 on original variable 2, and a 2 on original variable 3; and so on). Is there a more elegant way to do this, such as with loglinear modeling? I could not find any examples in the Mplus manual related to what we are trying to do.
If you combine them into a nominal variable, you will need to create a set of dummy variable so you will be back to where you are. I would simply use them the way they are or do an 8 group analysis. You might want to post your question on a general discussion forum like SEMNET.