Random effects ordination
into an R command line when you’re connected to the internet.
In standard ordination analyses, the positions of the sample units (e.g. a lake, a trap, a quadrat, etc.) in ordination space are implicitly treated as fixed effects. The practical consequences of this is that ordinations provide no ability to make inferences about sample units that were not observed but in the same statistical population. In other words, if sample units are fixed effects then we’re implicitly assuming that we’ve sampled the entire population. For comparison,
sex is probably a good fixed effect because we can be pretty sure that males, females, hermaphrodites (and maybe some more options if we’re talking about plants) are the only options. But when we’re talking about
sample units, its rare that we’ve got all of them, so to treat them as fixed effects seems at best weird and at worst wrong. Besides weirdness, prediction about un-sampled quadrats (say) becomes impossible if quadrats are treated as fixed effects.
So try it out and let me know how it goes!