Alternatives to multilevel model with log transformed outcome I'm working with linear mixed-effects model in Stata. Dataset has three levels of 100k observations, nested in 500 regions, nested in 70 regions. 
Currently my modelling strategy is to use three-level model with random intercepts by lev2 and lev3 for (lev2 nested within lev3):
mixed y i.x1 i.x2 || lev3: || lev2:

My outcome y is log transformed to bring it more to normality (heavily skewed data on cost).
However, the dataset contains ~2% of observations where outcome is zero and cannot be log transformed.
What other solution could I use in order to be able to handle zero outcomes?

Update 1: Following this post on The Stata Blog, it might be possible to use Poisson model instead:
meglm y i.x1 i.x2 || lev3: || lev2:, family(poisson) link(log) vce(robust)

This solution however might not work in multilevel framework.

Update 2: Revisiting this problem I came across several papers that used negative binomial regression to analyze cost. Example can be found here (with more on PubMed
Langton JM, Reeve R, Srasuebkul P, Haas M, Viney R, Currow D, et al. (2016) Health service use and costs in the last 6 months of life in elderly decedents with a history of cancer: a comprehensive analysis from a health payer perspective. Br J Cancer, 114(11):1293–302. http://dx.doi.org/10.1038/bjc.2016.75
 A: This is a great use case for the inverse hyperbolic sine transformation [1], [2]:
$$
\log\left( y + \sqrt{y^2 + 1} \right)
$$

Except for very small values of y, the inverse sine is approximately equal to log(2yi) or log(2)+log(yi), and so it can be interpreted in exactly the same way as a standard logarithmic dependent variable. ... But unlike a log variable, the inverse hyperbolic sine is defined at zero.



*

*http://chrisblattman.com/2011/11/15/if-you-know-what-ln1income-is-and-why-its-a-headache-you-should-read-this-post

*http://worthwhile.typepad.com/worthwhile_canadian_initi/2011/07/a-rant-on-inverse-hyperbolic-sine-transformations.html
A: It is not uncommon to offset a variable by a constant prior to taking its log when it cannot be log-transformed directly (for example because some observations are 0 and would map to $-\infty$). 
For example, you could offset all of the observations for the variable by 1 and therefore have a log-transformed variable that is a positive reel. All the observation that are 0 in your original dataset will become $log(0 + 1) = 0$
You can find a thorough description of this issue in this related question.
