Proportion Predictive Model with Bi-modal distribution

I am building a model that predicts a proportion: $y_i \sim f(x_{1,i}, x_{2,i},.., x_{n,i})$, where $y_i \in [0,1]$.

One thing I find is that 40% of the observations have $y_i=0$. For the remaining 60%, if I plot $logit^{-1}(y_i)$, it looks like a nice bell curve.

My question here is if I should really build two models. The first model is a logistic regression that predicts if $y_i=0$ and the second model predicts $y_i$ when $y_i>0$.

To put it together, if the logistic regression gives an estimate that with $P(y_i>0|x)$ that my $y_i$ is not 0, and my second regression gives me $E[y_i|x_, y_>0]$, then $E[y_i|x_i]= E[y_i|x_i,y_i>0] P(y_i>0)$

Does this sound acceptable? Is there any other/better way to handle the bi-modal distribution of $y$?

• The description in your second paragraph is a little ambiguous and might be aided by a plot of what you're trying to describe. The proposal in your third paragraph sounds quite similar to a common approach. Search for zero-inflated models. – Glen_b -Reinstate Monica Jul 12 '15 at 0:34