During my research, I asked several companies to complete a questionnaire to measure they risk maturity. At the end of the questionnaire, each respondent receives a score from 1 to 5 (1=low maturity, 5=high maturity)
Now I want to analyze the results of the questionnaire. The data are then in form of a single vector, where each row is the "score" received by a single participant. On this vector, I want to perform a PCA analysis to find the first 3 PCs.
The idea I want to follow comes from the Arbitrage Pricing Theory (Ross 1976), where the author performs the PCA analysis on the returns of several stocks to understand how many factors influence these returns.
I know that PCA is usually used when I have several dimensions and I want to reduce them finding "factors" as combination of those dimensions. However, Ross in his paper (you can find it attached to this post) uses just the returns to investigate the factors, and I would like to perform a similar analysis on my values to find how many factors can explain the variability of my sample. Even though I now what my objective is, I am not able to get there. Any suggestion?
http://www.top1000funds.com/wp-content/uploads/2014/05/The-Arbitrage-Theory-of-Capital-Asset-Pricing.pdf
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
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