Hi Kehksha,

Thank you for asking a very interesting question.

It seems to me that principal components analysis (PCA) is a statistical method to reduce the dimensionality of a multidimensional (many vectors) model in the presence of correlations between the independent variables.

If we take this as a basis for the question, then the number of statistically significant dimensions (in the orthogonal sense) can be used for whatever purpose, including framing questions. In other words, you are statistically reducing the set of supposedly independent variables (the variables on the RHS of a regression equation, for instance) because you have determined that some of those variables are statistically dependent (multicollinear). The main reason for developing a principal component is that component is orthogonal -- that is, statistically independent -- of other variables. Collinearity means that you cannot statistically determine the contribution of each on the dependent variable: so you collapse them on a component that is independent of other variables: Your first principal component. A similar argument can be made for using factor analysis,

So, back to your question. I would not use data reduction methods to reduce the number of questions simply because questions are qualitative, subject to interpretations by different respondents, and may not all lead to being classified as causal independent variables.

I would use PCA after I have developed a theoretically-based model, sampled data at random and -- upon statistical analysis – found that some of my causal variables are statistically dependent on each other. In other words, the correlations make it such that I cannot uniquely ascribe an effect to each of the correlated variables in my model. This is the collinearity problem, simply put.

You might also take a look at eigenvalues and vectors to understand the mathematics of what you are doing. You may want to find other opinions on this issue (going from questions to vectors and matrices).

All the best,

Paolo