My data is right skewed and I don't have independent observations, which statistical model should I use in R?

Question

I have biomass data collected at 3 different distances from 42 different ant mounds (at the edge of the mound, 1m and 4m away). In total there's 42 ant mounds, from 11 plots at 5 different elevations (the samples is unevenly distributed by elevation, where the highest elevation only consist of 3 mounds and the lowest of 18 mounds). My response (biomass) is continuous and my explanatory is categorical (Distance).

The question I want to answer is "How does ants affect the surrounding vegetation in a tundra environment?".

My data is not normally distributed, my observations are clearly not independent and I also have some zeros. I assume that I therefore can not use ANOVA, linear models or linear mixed models nor transform my data to fit a linear model? I have tried to use GLMM, but as you may also tell, my dataset is quite small which have resulted in a lot of error messages in R. I also want to account for other variables that might affect the biomass, like soil temperature and soil moisture. So of my understanding GLMM would be the way, but how will I manage that with my small dataset that contains zeros? Are there other models I should consider?

(I have also tried Wilcoxon signed rank test between the distances, but that I guess is not a robust model, it doesn't account for other variables affecting the biomass.)

Thank you!

Answer 1

As far as I understood, the statistical unit in your study is the ant mound. Furthermore, the response is biomass, measured at all ant mounds. The explanatory variables are:

• elevation (with respect to the sea level)
• distance (from mounds edge)

Since you seem to be interested in the relationship between the response and the two explanatory variables, I suggest starting out from the classical linear regression (see lm command in R), perhaps including also quadratic terms.

If, after doing some model checking you find that linear regression is not suitable, you can try generalized linear models. A possible starting model could be the Gamma (see glm command in R). However, if you have zeros, the gamma regression will run and in this case, you have two choices:

1. manually inflate the zeros by some small values (say 0 + 0.001, or whatever you think is small enough and below the detectable range)
2. use an inflated gamma regression model (for a possible implementation check Rfast2 package of R)