Gian, The marginal tests for one-term models had a problem in vegan 2.5-1 and vegan 2.5-2. This is fixed in vegan 2.5-3, so please upgrade. (It never occurred to me that people would use marginal tests for one-term models where the fitted model is compared against the empty model, and that case was not handled correctly: any other test — total or sequential — should yield identical results in this case and marginal tests make no sense).
I haven’t even considered implementing type-XXX tests in vegan::adonis. The function uses standard R stats functions which only allow sequential tests or tests of marginal terms (ignoring non-marginal main effects when there are interactions). However, if you are interested in interaction term A:B, your really should inspect the model A+B+A:B. It makes no sense in any sense to study model A:B without the main effects. That would give misleading results for A:B. The interpretation of ~A:B is based on standard R stats::model.matrix() in vegan, and these seem to expand a bit differently for factors A & B and continuous variables A & B. So beware, brother beware. Use stats::model.matrix() to see how they really unfold in your case. Cheers, Giari On 1 Nov 2018, at 20:10, Gian Maria Niccolò Benucci <gian.benu...@gmail.com<mailto:gian.benu...@gmail.com>> wrote: Thank you very much Steve, I really appreciate you answer. I do not want to drop the main effects out form the model, I was just trying to understand how adonis works. I was more confused on how to use the adonis function correctly rather than on the theory that is behind it. I have an almost "fully crossed" design (that was the plan, the fact is that I have to remove 2 samples because of the poor sequencing results) with two factors "Growhouse" and "Stage" in this case. I am of course interested in the effect of the main factors, but I also wanted to see if there was a significant interaction and if my developmental stage (i.e. mature or young) was influenced by where my organism where growing (i.e. growhouse 1 or 2). Iif I do as you said, Type I SS for ~ A + B + A*B depends on order so... it is sequential SS(A) SS(B|A) SS(A*B|A B) The interaction is not significant, so maybe worth in this case perform a Type II test directly? adonis(t(otu_fungi_out) ~ Stage + Growhouse + Stage : Growhouse, data=metadata_fungi_out, permutations=9999) Call: adonis(formula = t(otu_fungi_out) ~ Stage + Growhouse + Stage:Growhouse, data = metadata_fungi_out, permutations = 9999) Permutation: free Number of permutations: 9999 Terms added sequentially (first to last) Df SumsOfSqs MeanSqs F.Model R2 Pr(>F) Stage 1 0.4877 0.48769 2.7060 0.10408 0.0238 * Growhouse 1 0.3765 0.37647 2.0889 0.08034 0.0561 . Stage:Growhouse 1 0.2171 0.21708 1.2045 0.04633 0.2376 Residuals 20 3.6045 0.18023 0.76925 Total 23 4.6857 1.00000 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 adonis(t(otu_fungi_out) ~ Growhouse + Stage + Stage : Growhouse, data=metadata_fungi_out, permutations=9999) Call: adonis(formula = t(otu_fungi_out) ~ Growhouse + Stage + Stage:Growhouse, data = metadata_fungi_out, permutations = 9999) Permutation: free Number of permutations: 9999 Terms added sequentially (first to last) Df SumsOfSqs MeanSqs F.Model R2 Pr(>F) Growhouse 1 0.3765 0.37647 2.0889 0.08034 0.0563 . Stage 1 0.4877 0.48769 2.7060 0.10408 0.0271 * Growhouse:Stage 1 0.2171 0.21708 1.2045 0.04633 0.2364 Residuals 20 3.6045 0.18023 0.76925 Total 23 4.6857 1.00000 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Thank you, Gian On Thu, 1 Nov 2018 at 11:06, Steve Brewer <jbre...@olemiss.edu<mailto:jbre...@olemiss.edu>> wrote: Gian, I am bit confused by what your concern is. First, if the imbalance is not that severe, the approach you take to analyzing a two-way permanova (type I, type II, type III ss) is not going to matter that much. Indeed, if the design were balanced, they would give you identical results. Second, regardless of the lack of balance, for the models y ~ A + B + A:B and y ~ B + A + A:B, the test for the interaction will be the same. So, I don’t understand why you would want to drop the main effects from the model, effectively combining them with interaction. That doesn’t make any sense to me. The problem is with the tests of the main effects. My advice is to run both models (i.e., A first, then B first) using type I ss. As mentioned, both models will give you the same interaction result. If the interaction is all that you’re interested in, problem solved. Interpret only the interaction and and ignore the main effects. If the interaction is not significant and low, then interpret only the main effects, focusing only on the second main effect in each of the differently-ordered models (which are equivalent to Type II ss tests). And these results will tell you pretty the same thing as type III tests if there is little or no interaction. I would not worry about trying to estimate the main effects while controlling for the interaction (Ellen’s question), which cannot be done using type I or type II SS in 2-way permanova using adonis. But why would you want to? The lack of a balanced design results in the main effects and the interaction not being independent of one another. Forcing that independence by using type III ss can only work by essentially "throwing away" some of the information associated with the main effects, possibly resulting in an overly conservative test. The lower the interaction, however, the less is thrown away and the less it matters. Steve Stephen Brewer jbre...@olemiss.edu<mailto:jbre...@olemiss.edu> Professor Department of Biology PO Box 1848 University of Mississippi University, Mississippi 38677-1848 Brewer web page - https://jstephenbrewer.wordpress.com<https://jstephenbrewer.wordpress.com/> FAX - 662-915-5144<tel:662-915-5144> Phone - 662-202-5877<tel:662-202-5877> On Oct 31, 2018, at 5:45 PM, Gian Maria Niccolò Benucci < gian.benu...@gmail.com<mailto:gian.benu...@gmail.com>> wrote: Thank you Jari, So to test if there are significant interaction I should use Stage:Growhouse i.e. A:B. This will test the interaction and main effects that are marginal and so removed. How matters then if I include by="margin" or not? The R2 are the same (please see below) but the p-value changes. I assume the second way is most correct, is it? *> adonis2(t(otu_fungi_out) ~ Stage : Growhouse, data=metadata_fungi_out, permutations=9999)* Permutation test for adonis under reduced model Terms added sequentially (first to last) Permutation: free Number of permutations: 9999 adonis2(formula = t(otu_fungi_out) ~ Stage:Growhouse, data = metadata_fungi_out, permutations = 9999) Df SumOfSqs R2 F Pr(>F) Stage:Growhouse 3 1.0812 0.23075 1.9998 0.0211 * Residual 20 3.6045 0.76925 Total 23 4.6857 1.00000 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 *> adonis2(t(otu_fungi_out) ~ Stage : Growhouse, data=metadata_fungi_out, by = "margin", permutations=9999)* Permutation test for adonis under reduced model Marginal effects of terms Permutation: free Number of permutations: 9999 adonis2(formula = t(otu_fungi_out) ~ Stage:Growhouse, data = metadata_fungi_out, permutations = 9999, by = "margin") Df SumOfSqs R2 F Pr(>F) Stage:Growhouse 3 1.0812 0.23075 1.9998 0.006 ** Residual 20 3.6045 0.76925 Total 23 4.6857 1.00000 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Cheers, Gian On Tue, 30 Oct 2018 at 05:47, Jari Oksanen <jari.oksa...@oulu.fi<mailto:jari.oksa...@oulu.fi>> wrote: Hello Gian, These formulae expand into different models. Compare model.matrix(~ Stage:Growhouse, data=metadata_fungi_out) model.matrix(~ Stage*Growhouse, data=metadata_fungi_out) The first model (Stage:Growhouse) will also contain (implicitly) main effects and all these terms are marginal and can be removed, whereas the latter Stage*Growhouse expands to explicit main effects and interaction effects, and only the interaction effects are marginal and can be removed. This is also reflected in the degrees of freedom in your anova table: In the first case Stage:Growhouse has 3 df, and in the latter only 1 df (and the main effects ignored had 2 df). Ciao, Giari On 29 Oct 2018, at 19:11, Gian Maria Niccolò Benucci < gian.benu...@gmail.com<mailto:gian.benu...@gmail.com>> wrote: Hello Jari, It is a little bit confusing. If A*B unfolds in A+B+A:B then A:B is the real interaction component. So, which if the code below will test the variance for the interaction alone? adonis2(t(otu_fungi_out) ~ *Stage : Growhouse*, data=metadata_fungi_out, by = "margin", permutations=9999) Permutation test for adonis under reduced model Marginal effects of terms Permutation: free Number of permutations: 9999 adonis2(formula = t(otu_fungi_out) ~ Stage:Growhouse, data = metadata_fungi_out, permutations = 9999, by = "margin") Df SumOfSqs R2 F Pr(>F) Stage:Growhouse 3 1.0812 0.23075 1.9998 1e-04 *** Residual 20 3.6045 0.76925 Total 23 4.6857 1.00000 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 adonis2(t(otu_fungi_out) ~ *Stage * Growhouse*, data=metadata_fungi_out, by = "margin", permutations=9999) Permutation test for adonis under reduced model Marginal effects of terms Permutation: free Number of permutations: 9999 adonis2(formula = t(otu_fungi_out) ~ Stage * Growhouse, data = metadata_fungi_out, permutations = 9999, by = "margin") Df SumOfSqs R2 F Pr(>F) Stage:Growhouse 1 0.2171 0.04633 1.2045 0.2443 Residual 20 3.6045 0.76925 Total 23 4.6857 1.00000 The results is clearly very different. Also, in a normal adonis call I didn't have any significance for the interaction that I have instead if I use A:B. So ~ A*B will not test for interactions at all? *adonis*(t(otu_fungi_out) ~ Stage * Growhouse, data=metadata_fungi_out, permutations=9999) Call: adonis(formula = t(otu_fungi_out) ~ Stage * Growhouse, data = metadata_fungi_out, permutations = 9999) Permutation: free Number of permutations: 9999 Terms added sequentially (first to last) Df SumsOfSqs MeanSqs F.Model R2 Pr(>F) Stage 1 0.4877 0.48769 2.7060 0.10408 0.0247 * Growhouse 1 0.3765 0.37647 2.0889 0.08034 0.0542 . Stage:Growhouse 1 0.2171 0.21708 1.2045 0.04633 0.2507 Residuals 20 3.6045 0.18023 0.76925 Total 23 4.6857 1.00000 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Thank you! Gian On Tue, 16 Oct 2018 at 08:54, Jari Oksanen <jari.oksa...@oulu.fi<mailto:jari.oksa...@oulu.fi>> wrote: On 16/10/18 11:23, Torsten Hauffe wrote: "adonis2(speciesdataset~A*B, by="margin") but then only the effect of the interaction is tested." This is not entirely correct. adonis2(speciesdataset~A:B, by="margin") would test the interaction alone. ~A*B unfolds to ~A+B+A:B Well, it was correct: the only **marginal** effect in ~A+B+A:B is A:B (A and B are not marginal), and by = "margin" will only analyse marginal effects. Cheers, Jari Oksanen On Tue, 16 Oct 2018 at 11:51, Ellen Pape <ellen.p...@gmail.com<mailto:ellen.p...@gmail.com>> wrote: Hi all, I don't know whether this is the correct mailing group to address this question: I would like to perform a 2-way permanova analysis in R (using adonis in vegan). By default you are performing sequential tests (by="terms"), so when you have 2 or more factors, the order of these factors matter. However, since I wanted to circumvent this, I chose for the option by="margin" (adonis2(speciesdataset~A*B, by="margin")) but then only the effect of the interaction is tested. On the "help page" of anova. cca it says: "if you select by="margin" -> the current function only evaluates marginal terms. It will, for instance, ignore main effects that are included in interaction terms." My question now is: can I somehow get the main effects tested anyhow, when the interaction term is not significant? 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