How can I combine nominal with ordinal data to build a unique variable?

Question

I performed an Interview with 44 questions Protocol. The structure of questions is based on 18 variables. Major variables are coming from theory. Every major variable consists of 3,4 or more question items. In fact, I want to compare every major variable with each other and compute a correlation coefficient. Now for analysis, when I want to build major variable with available data, I have a problem. For example: major variable(1) i.e. organizational Justice consists of two nominal data (two questions of interview protocol with nominal categories) and one ordinal (one question of interview protocol with ordinal categories). Similarly,major variable(2): organizational trust consist of three ordinal data and two nominal data. Now my available data are the combination of ordinal and nominal. I don't know how do I merge nominal with ordinal data to build a unique variable? The major variable are based on theory,

Answer 1

I think it would be possible to use factorial analysis (PCA, MCA, ...) on each of your varibles subset so as to create multiple variables (PCA dimensions) which are linear combinations of your initial variables. So if your PCA first dimension yields enough inertia you could use it as a single synthetic variable for all the other and test correlation with it.

The problem being that if your first dimension does not yield a sufficient amount of inertia then that dimension would not really be representative of your initial inertia. Your computed correlation coefficients would then have a weaker meaning.

EDIT : Note that using ordinal variables is a violation of the continuity assumption made for PCA but it is often used anyway.

You should also use MFA (used PCA as it is more renown) as you have both categorical and numeric variables.