I have a project in which I need to perform orthogonal regression in a multiple regression case. For the non-multiple case, I've found Teetor's R Cookbook suggests using principle components:
reg_orth = prcomp( ~ y + x, data=ds[train,]) reg_orth_slope = reg_orth$rotation[2,1]/reg_orth$rotation[1,1] reg_orth_int = reg_orth$center- reg_orth_slope * reg_orth$center reg_orth_pred = ds[test,'y'] * reg_orth_slope + reg_orth_int
This is fine and seems to work great, but I actually have 5 independent variables that I want to use to predict my dependent variable. I tried to consider what is done to compute the slope and intercept, above, but with 5 independent variables, I'm not sure what to do.
I would have thought orthogonal regression would be quite common, but I'm not finding any information on it in the multiple regression case.