# Does there exist zero-inflated linear regression?

I have a non-count data with huge number of zeros in the target variable. I need to fit a model being a mixture of Dirac delta function and normal distribution parametrized by mean $$X\beta$$ and variance $$\sigma^2$$, with mixing proportion $$\pi$$, i.e.

$$y \sim \left\{ \begin{array}{cl} 0 & \text{ with probability }\pi \\ \mathcal{N}\left(X \beta, \sigma^2 \right) & \text{ with probability } 1-\pi\end{array} \right.$$

to account for the excess zeros. Could you provide me with any references about such models? Or maybe there is some approach that is better, then the above, for continuous, zero-inflated data?

• If you have a genuine expectation that the true distribution is indeed a zero-inflated normal, then just fit that model and be done with it. Whether other approaches are better depends on whether the expectation/evidence that some other choice of distribution is a better approximation to nature. Edited to add: it seems an odd sampling process that both deals with continuous data and has a huge number of integers (zeros) in it. Jun 1, 2017 at 14:35
• @user43849 the process that produces such data is very easy to imagine: think of some kind of device that is idle for most of the time, but sometimes fires some continuous signals.
– Tim
Jun 1, 2017 at 14:43
• Interestingly, the Wiki excerpt of the zero-inflation tag says there is zero-inflated normal regression. Not that this would help, but I find it curious. Jun 1, 2017 at 14:46
• @RichardHardy I wasn't able to find any references dealing with such models, this is how the question emerged...
– Tim
Jun 1, 2017 at 14:51
• In Epidemiology, this is a common problem and the term for such variables is "spike at zero". However, all methods that I am aware of are assuming non-negative values. But maybe the term helps to find extensions to negative values. May 25, 2021 at 16:10