Choice of transformation for my data set

Question

My data set contains the percentage cover of various plant species, on a rocky substrate. The problem I am having is that the substrate was often completely bare of any plant life. Due to this, a large proportion of the quadrats that I used contained zero percentage cover, which leads me to having heavily right-skewed data.

Therefore, I have to transform my data before I am able to calculate an ANOVA test. I originally went ahead with using the Arcsine transformation, but this still leaves my data right skewed, however, if I do log10 the distribution is normal.

The answer might seem obvious, but the majority of the online material I look at insists on using Arcsine for percentage cover, but this does not normalise my distribution as well as log10 does. Which one should I use?

Answer 1

It is rarely necessary to obtain normally distributed data to perform inference or even prediction. An issue with performing an arbitrary change of variable is that the effects are hard to interpret, or even uninterpretable. For instance, if an arcsine transformation is applied to the effects, on what unit is the outcome? For that reason I would not recommend Box-Cox transformations, although methodologically they identify an optimal change of variable for obtaining normally distributed outcomes. Given the ratio-nature of the outcome, log transforms (of any base power) confer the benefit of estimating a geometric mean difference. The log of 0 is undefined, however. Your "0 cover" cases are dropped from the analysis. But perhaps you should consider a type of structural/0 inflated model: first for the binomial probability of having any cover, then (of the non-zero cover groups), what the geometric mean difference(s) is/are between sites (or whatever comparative features you have identified).

Answer 2

I am having to deal quite often with the same kind of analysis. Since the data are percentages (i.e. percent cover) the ideal way, in my opinion, is to use beta regression using the betareg package in R for example. However, since zeros are part of our life when doing vegetation surveys, betareg cannot be used as it requires the interval (0,1). Hence, I moved to zero-inflated beta regression models via the gamlss package (see also my question here). This package comes with a lot of other useful distributions. However, it becomes problematic when you have factor levels (e.g. treatments) and you want to do for example Tukey adjusted multiple means comparisons. @rvl who wrote the emmeans package provided preliminary support to do this, however, with a word of caution. Note though that for betareg models the emmeans package works perfectly well.

What I sometimes do to reduce the amount of zeros, is to sum species percentages across those species that I can group into herbaceous species, woody species, native species, non-native species, etc. That will in my case often reduce the amount of zeros substantially in the dataset. Then I can follow up with an ad-hoc scaling procedure that moves the remaining zeros into the (0,1) interval (as suggested in Smithson & Verkuilen (see betareg vignette)):

[...] if y also assumes the extremes 0 and 1, a useful transformation in practice is (y·(n−1) + 0.5)/n where n is the sample size (Smithson and Verkuilen 2006).

The next set of tools to analyze vegetation cover data would be Bayesian, as implemented in the zoib package for example. However, I haven't explored the Bayesian models yet but it's certainly on the to-do list.