I am currently running a statistical on a complicated set of data and after completing a PCA and deriving with a number of factors (18), I would like to run a multiple regression analysis with them. I have the scores (coefficients) deriving from the PCA could I use those and also those being the dependent variable in my MLR and how would I interpret them correctly ? or could those values only be used as independents (e.g. to predict socioeconomic characteristics) and could not be used in models between them? or would I need to transform them or calculate different values and in what way?
There is no "interpretation" for your regression on PCs as this is only for predictive modeling. USE the PCs not the coefficients. Google regression on principal components for full details. Use whatever variable you want to predict as your DV. If you want to use variable selection on your PCs I suggest adaptive lasso. See the attached and their refer. for details and program sources. Best, David Booth
I am agree with David Eugene Booth comments and suggestions. Depend upon your data (quantitative or qualitative), you need singular values as well as variances obtained via SVD for your analysis. Also kernel PCA is an extension of simple PCA.
Thank you very much for your responses, I have extracted my factors and my data are all in likert scale so they are qualitative, could I calculate scores for each factor by F1= mean (factor loading from rotated component matrix*variable 1...+ factor loading from rotated component matrix* variable 4) according to the selected variables on my factor and run my multiple regression with the F1, F2 ... scores as independents?
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