I am trying to run a weighted least squares model that looks something like this (but could be different):
$y = \beta_0 + \beta_1 x + \beta_2 log(x) + \epsilon$
with weights $w_1, w_2, ..$
However, I know, from external knowledge, that whatever the model the outcome must asymptotically converge to a constant for large values of $x$. How can I get an OLS estimate with this constraint.
As an example, let's say if I knew the asymptote $c$, then I can add two fake data points to my model, with very high values of $x$ and very high weights $w$ and $y=c$, and run the normal WLS model and it would give me what I need - except I don't know the value of $c$. Is there a way to impose this constraint - maybe through adding a custom error term to the model?