Does STATA kick out fitted estimates from the LOESS procedure? I know it typically kicks out some parameters, but can't remember how easy it would be to hand calculate values from output if it does provide line estimates. I ignorantly just think of LOESS as a moving average.
I hope in your study,data are more telling/conclusive, the above image and analyses don't really seem to reflect much and the LOESS seems to mis-direct readers. I may say for the above image, if they had enough data, they may have wanted to have a hold out set to validate model conclusions.
In STATA will you have to run two LOESS models and merge results or does it have a by or strata option? Since you likely just need line points to plot, unlike linear regression where you would just need intercept, step change, and two slopes. Could you create the plot if you were using linear regression? So, I guess my question is, can you not get the estimates or is the issue just creating the plot?