How many variables (questions) you have? PCA is easy to be done. 

Dear Davide,

I don't think you should represent the data as a single vector. As far as I know, you should represent your data as samples (people) x variables (questions) and then apply the PCA. I suggest you to use the SPSS program and perform the Confirmatory Factor Analysis with as much PC's as you want.

The output would be the factor loadings, variance explained, commonalities and possible factor rotation (in case your data outcome are not well comprehensive).

Best,

T

https://www.youtube.com/watch?v=iDT0tjU1TWo

Please see the following  article from arxiv, it may help.

https://arxiv.org/abs/1404.1100

Best

HJ

Thanks for your answer fellows.However, my question is trying to questioning an issue that goes beyond the classical PCA theory; I already applied the PCA as you suggest.

If you read the paper or Ross (which is linked above), you will see that he is using PCA to understand how many factors affect the variability of the stock returns, but differently from usual, he gives in input only the stock returns. Yes, he has a matrix because he is using time-series, and it looks something like:

                                           Month 1      Month 2    Month 3

StockPriceCompany1          143            110           154

StockPriceCompany2           243           232           222

StockPriceCompany3           123           125           111

And then he performs a PCA on this matrix, looking for how many factors affect the variability of the stock returns. I would like to perform a similar analysis, but not having time-series of data, I would perform it on a vector instead of a matrix, but the analysis should still be possible to be performed.

The issue is that Ross just presents the results of his analysis, without explaining how we did it.