I wish to model the following relationship $$Y \sim af_1(X) + bf_2(X) + cf_3(X) + ..., Y \in [0,1]$$ where $Y$ is a response (a percentage divided by 100) and $X$ is a covariate which I want to model using those $f$-basis functions. The study's interest lies in the effect that covariate $X$ has on $Y$.
Based on what I have gathered from google, perhaps Beta regression? Presumably zero-inflated since I have $Y = 0$ at times?
Or something else, like some sort of GLM/GAM model? Any recommendations?
EDIT: I forgot to mention: apart from the fixed covariate $X$ effect, I intend to include some random effects.