I would like to fit a non-linear model that looks like the following: $V(g)=a*A(g)/(b*B(g)+c*C(g))$, where $g$ represents a gene, $a$, $b$ and $c$ are coefficients of $A(g)$, $B(g)$, $C(g)$, which are simple functions of $g$ that don't need to be optimized.
As I have many genes ($>1000$), my goal is to set up the coefficients $a$, $b$, and $c$, such that correlation between $V(g)$ and another given value $DE(g)$ is maximized.
I can do simple iteration for this; e.g.
for i in range(a): for j in range(b): calculate V(g) for all genes with a=i and b=j calculate spearman correlation between all V(g) and all DE(g). take i,j pair that make the maximum spearman correlation value.
- But are there R packages that people usually use for this purpose?
- Since number of parameters are already set, I don't think I need to do cross-validation, do I?