Correct glmer distribution family and link for a continuous zero-inflated data set Data set details: 
Zeros are "real" (volume)
Data set is heavily left skewed (even when zeros are excluded)
Response is continuous (volume)
Can anyone recommend a distribution family and link that I can use for glmer?
Alternatively, can assumptions of normality be ignored in this case (if I'm using lmer?)


 A: Assuming that you are describing conditional and not marginal distributions (i.e., if your response variable is y then hist(mydata$y) will not typically give you what you want; you should be concerned with the distribution around the expected values):


*

*Changing the link function won't help you; it determines the dependence of location on predictors, not the conditional distribution

*I would recommend a two-stage approach; use a binomial model to fit zero vs. non-zero, then use either a Gamma model (probably with a log link, it's much more stable than the canonical inverse link) or (more flexibly) transform your non-zero values to make them approximately Normal.

*There are very few distributional models for positive data that admit zeros (Gamma, Weibull, log-Normal all give likelihood=zero for data exactly equal to zero, at least for some parameter regimes [LN always, Gamma and Weibull for shape<1]; in any case they don't account for a point mass (spike) at zero.

*Similarly, some data transformations (Box-Cox) will break with non-positive data, others (Yeo-Johnson) won't break, but won't handle a pile of zeros gracefully.

*The only real downside of the two-stage model is that the zero-vs-nonzero and conditional-if-nonzero models are completely independent.

*If you want to stick with the Gaussian assumption, you could do something nonparametric (bootstrapping or permutation tests) to try to make your results robust to violations of distributional assumptions.

*You could try a model based on a Tweedie distribution; check out the cpglmm function from the cplm package.

