pfr_old vs pfr

[JH-Stat]

Hi,

I am seeking your expertise regarding the differences between the 'pfr_old' and 'pfr' functions. Specifically, when I applied the 'pfr_old' function for functional regression with a scalar (non-binary numeric value) outcome without adjusting for other variables, it produced non-constant coefficients. However, upon adjusting for variables such as age and gender, the same function yielded constant estimated coefficients, even after experimenting with different hyperparameters like 'kz' and 'kb'. In contrast, the 'pfr' function provided non-constant results, which aligns with our intuition.

Could you provide some insight into why this discrepancy might occur? Additionally, are there fundamental differences between 'pfr_old' and 'pfr' that might warrant discontinuing the use of one over the other?

I apologize if my understanding appears limited, and I genuinely appreciate any guidance you can provide. Thank you for taking the time to read and consider my request.