Creating an index from a number of variables is becoming popular. The indexes generated can have negative values. The question is, it is ok to have a negative index or negative mean for an index created using MCA and PCA?
Jokin Ezenarro , Let's take MCA for example. I am creating an asset index based on 6 binary variables. For each of the six variables, we assign 1 if a person owns that particular asset.
It is a bit more complex in MCA, as you're creating a continuous variable from categorical variables, and the interpretability is more complex. But if the variables can either be -1 or 1, there is no problem in your index being negative.
Of course, you need to take into account how that index is generated and what are you using it for, in order to properly interpret the negative meaning.