My question comes from a statistical problem I am bumping into but I think it is more a math question than a stats question, therefore I post it here.
Anyway, I have a Structural Equation Model that includes several links. However, some of the links are non-linear. I tried a whole bunch of stuff with polynomials but that is just not working. I have now created several non-linear least square regression models that fit the non-linearity quite good. I now want to use these exponential equations from these models to transform my data so it become linear after which I want to use it in my linear Structural Equation Model.
So there is variable $S$ which is dependent on variable $G$ which is dependent on variable $T$. $S$ and $G$ are non-linear related and $G$ and $T$ are non-linear related too.
Variable $S$ is related to $G$ in the following way:
$sqrt(S) = a(1+sqrt(G))^{-b}$
Variable $G$ is related to $T$ in the following way:
$sqrt(G) = c(1+T)^{-d}+e$
I need to transform $S$ in a way that it becomes linear with $G$, using these equations. However, $G$ needs to be transformed first so $S$ is actually a function of the transformed $G$. Hence, both equations need to be used to transform $S$ because:
$sqrt(S) = a(1+sqrt((c(1+T)^{-d}+e)))^{-b}$
I need to transform both the $G$ and $S$ variable. The problem is that I have tried a few things, but I am just not confident that I am doing it right. Please help!