Permutation scheme for nested data

[PeBarcik]

Hello all!

I'm having trouble deciding what is the best way to analyse my data.

Here is the description of my study:
I have 6 locations (blocks) over the country. In each location, I have 3 plots. Each plot has one treatment, so basically in each location I have the 3 treatments that I'm studying. Inside each plot, I took 4 samples (to have a greater sampling size of my treatments, although I know they are non-independent, and thus require a permutation scheme for a correct analysis).
My objective is to compare treatments, so I don't want to compare samples inside a plot. I want to compare plots, and take into considerantion that they are inside blocks (Locations).

For that, I came with this permutation scheme:

perm <- with(data_Q, how(nperm = 999,
                         plots = Plots(strata = Plot, type = "free"),
                         within = Within(type = "none"),
                         blocks = Location))

Does this satisfy my objectives?

Also, and I apologize if this is not in the correct place, if I were to use a Linear Mixed Model with this nested data, how would I have to do it to satisfy my objectives?

I came up with this:

lmer(Y ~ X + (1 | Location) + (0 + X | Location) + (1 | Location:Plot))

Should I exclude the (1|Location:Plot) ?
Should I include (0 + X|Location:Plot) ?

Thank you!

[gavinsimpson]

Yes, your permutation design is an appropriate way to permute data in a design-based framework. You don't say what model you are fitting so I can't comment on whether the deisgn is appropriate given the model.

As for your lmer() questions, I don't see why (you haven't explained and this Q&A is not the right place for a LMM discussion) you would want uncorrelated random slopes and intercepts. Also, don't you want (1 | Location / Plot), as Plot is nested in Location, though perhaps A / B evaluates to A:B, I'd need to check.

[gavinsimpson]

@jarioksa You are reading a lot into what I said. If you want an abundance-based analysis, Bray Curtis can include some composition. If you want a compositional analysis, it can bring in some abundance. More than if we used Euclidean / Manhattan or Chi-square as the dissimilarity directly. This is on raw data.

Transformations change all of this; we had Hellinger as a transformation well before it was available as an actual dissimilarity in vegdist(), and that is a Euclidean distance on transformed distance, but as the data are normalized by the row totals it is compositional even though we use it with RDA. The problem with BC is that I don't know what it is doing in general (i.e. you'd need to verify how much of the $d_{ij}$ is compositional and how much is abundance (size) based for each data set, and no one does that). Of course, if you transform the data beforehand you will force say a compositional view - BC on Wisconsin double standardized data is quite different from BC on raw data, which is what most people blindly do. We don't offer to do metaMDS-like transforms in adonis2() unlike in dbrda() and capscale(), so most naive users won't be doing what is arguably better practice. Perhaps we should add metaMDSdist argument to adonis2().

I don't think we should do every analysis with CA/CCA exactly because we can be interested in things other than compositional differences. A lot of the examples I use for teaching use RDA and log-transformed (log1p()) responses, so I'm certainly not advocating for a CA/CCA-only world.

The problem I see with the approach from many users that we see asking questions about vegan (here, on the vegan GitHub, or SO and CV) is that they just default to PERMANOVA and Bray-Curtis because that's what they see others doing and/or BC is the default.

You will note I suggested they use dbrda() instead of adonis2() if they want to use a dissimilarity. I did point out a slight issue with dissimilarity-based methods in that the species scores are added as a secondary step (i.e. in a supplementary vein, as we do in PCA/CA/PCO/NMDS + envfit() or Canoco's supplementary variables). Whether that's a problem for the OP is something only they can answer; I don't know what their research question is. But it is a valid point to be aware of.

As the OP was asking about constrained methods I didn't mention metaMDS().

[PeBarcik]

Thank you so much @gavinsimpson and @jarioksa for your answers and the discussion provided. Unfortunately, I'm quite new to this subject, and cannot answer if I must use dissimilarity, and if adding the species scores as a secondary step is a problem or not. But I'll be aware of your recomendations, and research further into those.
Once again, I appreciate your time and effort put in this Q&A.

[gavinsimpson]

@PeBarcik If you are going to be doing this analysis then it is incumbent upon you to figure out these things before you do the analysis, whether you are new to these kinds of methods or not.

[PeBarcik]

Yes, you are right. If I were to have more questions regarding these topics, should I open another discussion on the vegan repository or keep sending in this Q&A?

[gavinsimpson]

If I were to have more questions regarding these topics, should I open another discussion on the vegan repository or keep sending in this Q&A?

If the question is about vegan specifically then do ask there in the discussions as a Q&A. Likewise if it is about permute specifically, ask here. But if it is a more general statistical question, ask on CrossValidated.