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In the literature I found that for the count data with a lot of zeros so-called zero-inflated distributions (models) and so-called hurdle-at-zero distributions (models) could be used. The differences between those two are well described on stackexchange

What is the difference between zero-inflated and hurdle distributions (models)?

But what kind of models could be used if the data are not count data type (positive integer) but still zero inflated? Like for example exploring the coverage (%) of lichens on pre-defined part of tree trunk.

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They're still called "zero-inflated" models when modifying continuous distributions; there's zero-inflated gamma, zero-inflated lognormal, and so on.

For continuous proportions such as you describe, a zero-inflated beta model might be used (though it's not the only possibility, it's probably the most common by some distance).

If 100% coverage in that predefined part is possible, you might instead use 0-1 inflated beta models (sometimes called 0-and-1 inflated beta models; the search above finds some links for these as well), or if some other density between 0 and 1 is more suitable, some other form of 0-1-inflated continuous model.

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  • $\begingroup$ Thank you. I also found out that it is possible to produce mixed effect models for zero-inflated data with R package glmmADMB. Instructions are available here: glmmadmb.r-forge.r-project.org/glmmADMB.pdf $\endgroup$ – Eco06 Jul 21 '15 at 6:36

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