Hello everybody.

I have a few questions on the principal component regression. The latter consists of three steps which are well summarized here: https://en.wikipedia.org/wiki/Princi...ent_regression


1 - I was wondering how to compute back the coefficient estimates for the original regressors (third step). To my understanding, the coefficients of the original explanatory variables shall be derived from the eigenvalues associated to each original variable for the principal components, however, I am struggling to perform this transformation in Stata.

2 - The second question is more methodological. Indeed, in Step 2, do you think it is feasible to use the multinomial logit estimator, rather than OLS? Or maybe this would make step 3 impossible since the non-linear nature of the mlogit estimator would mess up things too much (?)

3 - Last, I just kindly wanted to ask if in the second step (OLS/mlogit(?) estimation) you could also utilize additional regressors besides the scores of the principal components obtained from the PCA. Nonetheless, I am afraid that this would prevent to derive the coefficient estimates in the third step, since in step 2 it is specified that estimated regression coefficients should be with "dimension equal to the number of selected principal components".

Thank you very much who whoever would like to help me clarifying these 3 doubts.

Kodi