Parameter estimates from adonis2 model

[egmurrell]

Hello! I am running a PERMANOVA analysis on a dataset with two main effects and an interaction. I would like to print the means and standard errors of the parameter estimates for the model (intercept, each main effect, the interaction effect). Could someone please tell me what code I need to do this?

If the code does not exist for adonis2 models, is there an alternative package I can use that will run PERMANOVA and also print the model parameter estimates?

[technocrat]

Providing a reprex. See the FAQ like the following to illustrate the question will have better chances of attracting useful answers.

For example

library(vegan)
#> Loading required package: permute
#> Loading required package: lattice
#> This is vegan 2.6-4
# from help(adonis2)
data(dune)
data(dune.env)
## default test by terms
adonis2(dune ~ Management*A1, data = dune.env)
#> Permutation test for adonis under reduced model
#> Terms added sequentially (first to last)
#> Permutation: free
#> Number of permutations: 999
#> 
#> adonis2(formula = dune ~ Management * A1, data = dune.env)
#>               Df SumOfSqs      R2      F Pr(>F)   
#> Management     3   1.4686 0.34161 3.2629  0.002 **
#> A1             1   0.4409 0.10256 2.9387  0.018 * 
#> Management:A1  3   0.5892 0.13705 1.3090  0.198   
#> Residual      12   1.8004 0.41878                 
#> Total         19   4.2990 1.00000                 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## overall tests
adonis2(dune ~ Management*A1, data = dune.env, by = NULL)
#> Permutation test for adonis under reduced model
#> Permutation: free
#> Number of permutations: 999
#> 
#> adonis2(formula = dune ~ Management * A1, data = dune.env, by = NULL)
#>          Df SumOfSqs      R2      F Pr(>F)    
#> Model     7   2.4987 0.58122 2.3792  0.001 ***
#> Residual 12   1.8004 0.41878                  
#> Total    19   4.2990 1.00000                  
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

### Example of use with strata, for nested (e.g., block) designs.
dat <- expand.grid(rep=gl(2,1), NO3=factor(c(0,10)),field=gl(3,1) )
dat
#>    rep NO3 field
#> 1    1   0     1
#> 2    2   0     1
#> 3    1  10     1
#> 4    2  10     1
#> 5    1   0     2
#> 6    2   0     2
#> 7    1  10     2
#> 8    2  10     2
#> 9    1   0     3
#> 10   2   0     3
#> 11   1  10     3
#> 12   2  10     3
Agropyron <- with(dat, as.numeric(field) + as.numeric(NO3)+2) +rnorm(12)/2
Schizachyrium <- with(dat, as.numeric(field) - as.numeric(NO3)+2) +rnorm(12)/2
total <- Agropyron + Schizachyrium
dotplot(total ~ NO3, dat, jitter.x=TRUE, groups=field,
        type=c('p','a'), xlab="NO3", auto.key=list(columns=3, lines=TRUE) )

Y <- data.frame(Agropyron, Schizachyrium)
mod <- metaMDS(Y, trace = FALSE)
plot(mod)
### Ellipsoid hulls show treatment
with(dat, ordiellipse(mod, field, kind = "ehull", label = TRUE))
### Spider shows fields
with(dat, ordispider(mod, field, lty=3, col="red"))

### Incorrect (no strata)
adonis2(Y ~ NO3, data = dat, permutations = 199)
#> Permutation test for adonis under reduced model
#> Terms added sequentially (first to last)
#> Permutation: free
#> Number of permutations: 199
#> 
#> adonis2(formula = Y ~ NO3, data = dat, permutations = 199)
#>          Df SumOfSqs      R2      F Pr(>F)
#> NO3       1 0.054321 0.17481 2.1185   0.16
#> Residual 10 0.256420 0.82519              
#> Total    11 0.310741 1.00000
## Correct with strata
with(dat, adonis2(Y ~ NO3, data = dat, permutations = 199, strata = field))
#> Permutation test for adonis under reduced model
#> Terms added sequentially (first to last)
#> Blocks:  strata 
#> Permutation: free
#> Number of permutations: 199
#> 
#> adonis2(formula = Y ~ NO3, data = dat, permutations = 199, strata = field)
#>          Df SumOfSqs      R2      F Pr(>F)   
#> NO3       1 0.054321 0.17481 2.1185   0.01 **
#> Residual 10 0.256420 0.82519                 
#> Total    11 0.310741 1.00000                 
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

^{Created on 2023-03-18 with reprex v2.0.2}

What this illustrates that I have to guess what package is being used. I choose {vegan} because it is top hit among packages for adonis2. But the problem is that adonis2 returns a “permutational MANOVA” (formerly “nonparametric MANOVA”), not a "parametric MANOVA". Plus I am unsure how the data used compares to the data you have in mind.