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 FAX - 662-915-5144 Phone - 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? Thanks, Ellen [[alternative HTML version deleted]] _______________________________________________ R-sig-ecology mailing list R-sig-ecology@r-project.org<mailto:R-sig-ecology@r-project.org> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology [[alternative HTML version deleted]] _______________________________________________ R-sig-ecology mailing list R-sig-ecology@r-project.org<mailto:R-sig-ecology@r-project.org> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology _______________________________________________ R-sig-ecology mailing list R-sig-ecology@r-project.org<mailto:R-sig-ecology@r-project.org> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology [[alternative HTML version deleted]] _______________________________________________ R-sig-ecology mailing list R-sig-ecology@r-project.org<mailto:R-sig-ecology@r-project.org> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology -- Gian Maria Niccolò Benucci, Ph.D. Postdoctoral research associate Michigan State University Department of Plant, Soil and Microbial Sciences 1066 Bogue Street 48825 East Lansing, MI Lab: +1 (517) 844-6966 Email: gian.benu...@gmail.com<mailto:gian.benu...@gmail.com> *----- Do not print this email unless you really need to. Save paper and protect the environment! -----* [[alternative HTML version deleted]] _______________________________________________ R-sig-ecology mailing list R-sig-ecology@r-project.org<mailto:R-sig-ecology@r-project.org> https://stat.ethz.ch/mailman/listinfo/r-sig-ecology [[alternative HTML version deleted]] _______________________________________________ R-sig-ecology mailing list R-sig-ecology@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-ecology
