I am measuring a concept (such as 'friendship') that is multidimensional in nature.
To capture the multidimensional nature of the concept, I have measured the concept through several aspects, each of which focus on one part (or dimension) of the concept.
Each aspect has several Likert scale items, which I have added together to arrive at sub scores for the aspect. I have then added all the sub scores to arrive at the overall score for the concept.
For example, if the total of the Likert scale items for Aspect A is 6, Aspect B is 3 and Aspect C is 4, then the overall score for the concept (which is made up of A, B and C) is 13.
In this way, the overall score is a single number, which is a unidimensional index. My focus of interest is the overall score (not the sub scores for each aspect).
How do I test the reliability of my index? Would Cronbach's alpha be appropriate in this case?