[R-sig-eco] Two way Splitplot non-parametric ANOVA type test

[Felipe Calleja UCR]

Hello,

I'm looking for some help establishing a mixed model non-parametric ANOVA
using R, for a split plot design I've made for an experiment of saltmarsh
germination. I'll explain as clear as possible the experimental design and
afterwards what I've done and my doubts. Hope you can help me.

The experiment consists in meassuring the germination percentage and length
of one species in variable conditions of salinity, immersion time and
presence of other species. I sow seeds in soil core's, that are inside
plastic boxes that are filled periodically with saline water. There are
three factors: salinity (3 levels: 0, 5 and 18), immersion time (3 levels:
0, 20, 40%), species treatment (2 levels: Baccharis (or Juncus), Baccharis
+ Juncus). Inside each box there are 6 cores that combine in a complete
random design the factors of immersion and species treatment. The box is
filled with water at one of the levels of salinity. Thus, I'm using a split
plot design with salinity as the whole plot factor, and immersion and
species treatment as the subplot factors. All factors are considered fixed.
Each box is repeated 10 times.

To simplify the array, I'm interest in making bivariate tests using only
the whole plot factor Salinity, and the sub-plot factor Immersion, using
only the cores that had one species sown (removing the competition
element).



For one of the dependent variables I measured, the conditions of normality
and homoestacity are not fulfilled, so I'm thinking about using a
non-parametric test to analyze the data. But after Reading a lot of papers,
books and forum entries, I can’t clear my head on how to address the
analysis.



I’m basically interested in the main and interactions effects of a model
that I think should look like this: y ~wholeplotFactor*subplotFactor  +
(1|Subject:Wholeplotfactor). The interaction effect I think I did manage to
calculated adequately with the npIntFactRep package (
https://cran.r-project.org/web/packages/npIntFactRep/index.html), but as it
says in the documentation, it only yields results for the interaction in
the mixed design. Not the main effects.



I've used the nparLD (
https://cran.r-project.org/web/packages/nparLD/nparLD.pdf), and for one
species it yields what I think are good results, but for the other one it
rises the warning that the covariance matrix is singular, so I’m looking
for a different approach for the analysis. Does having the covariance
matrix singular invalidates the whole analysis? Or just the interaction
results? I mean, could I use this function for the main effects and the
npIntFactRep for the interactions separately?


Finally I’ve tried with the rlme package
(https://www.rdocumentation.org/packages/rlme/versions/0.5/topics/rlme),

but can’t make it work because it does not recognizes the nested
element of the model (refering to (1|Subject:WholeplotFactor) ).

It rises the error  “ Error: Column `1 | Repetition:Salinity_num` not found”.


Besides the questions regarding the nparLD package, I don’t really have a
specific question for you, just the request for some guidance about options
for analyzing this data. I’m kind of lost in the really wide nonparametric
splitplot ANOVA world and would appreciate very much some guide.



If there’s anyone interested in the case, I can send the data in another
mail so you can see more details.



Thanks a lot in advance, any tip is very well appreciated.





*Felipe Calleja Apéstegui*

*Predoctoral researcher*



*Instituto de Hidráulica Ambiental "IH Cantabria"*

*C/ Isabel Torres, Nº 15*

*Parque Científico y Tecnológico de Cantabria*

*39011 Santander (España)*

*www.ihcantabria.es <http://www.ihcantabria.es/>*

*Tel:  +34 942 20 16 16 Ext. 1153*

*Fax: +34 942 26 63 61*

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