I am a long time user of the forum but first time poster. My question is unrelated to a specific dataset but on the internal workings of a PERMANOVA in R (
vegan package) vs a nested linear model in R (linear mixed model, package
nlme). I will explain step by step what my concern is.
Lately I have been working on ecological experiments with complex designs, meaning that we have several sampling times, two spatially nesting variables and two treatments with two levels each. However, the number of replicates per treatment combination was of 4. This means that the number of degrees of freedom (or, in other words, independent data points) that we have in order to perform tests were extremely limited.
When performing a linear model on one of our response variables with all the aforementioned explanatory variables and covariates, including two spatial nests, the test could not be performed due to lack of degrees of freedom (this was identical for the
lmer and the
However, reading the statistical analyses of other similar experiments in the literature, I came across the PERMANOVA test. The experiments had the same number of replicates and comparatively complicated designs, and therefore I decided to test them. I am aware that the PERMANOVA test is multivariate in opposition of the univariate nature of the linear model, but it can be used with a single response variable. This unique response variable is transformed into a distance matrix and the analysis is performed.
To my surprise, the test worked correctly, with absolutely no errors in the output. However, I am not sure if I can confidently use this test until I understand why the number of degrees of freedom was not enough for the linear model whereas it was enough for the PERMANOVA. My only educated guess is that is related to the permutational nature of the test, but I could not find an answer neither in the original literature explaining the PERMANOVA test nor in papers or online forums.