How can the effect size of a PERMANOVA be calculated? - r

Question

I use the "vegan" package to perform a PERMANOVA (adonis2()), and I also want to calculate the effect size (ω²). For this, I tried to use omega_squared() from the "effectsize" package, but I failed. I think it does not understand the output table, specifically the part with the mean squares. Is it possible to fix this or do I have to calculate manually?
library(vegan)
#> Lade nötiges Paket: permute
#> Lade nötiges Paket: lattice
#> This is vegan 2.6-4
library(effectsize)
data(dune)
data(dune.env)
ado <- adonis2(dune ~ Management, data = dune.env, permutations = 100)
ado
#> Permutation test for adonis under reduced model
#> Terms added sequentially (first to last)
#> Permutation: free
#> Number of permutations: 100
#>
#> adonis2(formula = dune ~ Management, data = dune.env, permutations = 100)
#> Df SumOfSqs R2 F Pr(>F)
#> Management 3 1.4686 0.34161 2.7672 0.009901 **
#> Residual 16 2.8304 0.65839
#> Total 19 4.2990 1.00000
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
w2 <- omega_squared(ado)
#> Error in `[[<-.data.frame`(`*tmp*`, "Mean_Square", value = numeric(0)): Ersetzung hat 0 Zeilen, Daten haben 3
interpret_omega_squared(w2)
#> Error in interpret(es, rules): Objekt 'w2' nicht gefunden
Created on 2022-11-15 with reprex v2.0.2
EDIT
I tried to do it manually:
library(vegan, quietly = T, warn.conflicts = F)
#> This is vegan 2.6-4
library(effectsize)
library(dplyr, quietly = T, warn.conflicts = F)
library(tibble)
library(purrr)
data(dune)
data(dune.env)
ado <- adonis2(dune ~ Management, data = dune.env, permutations = 100)
w2 <- omega_squared(ado) # Does not work
#> Error in `[[<-.data.frame`(`*tmp*`, "Mean_Square", value = numeric(0)): Ersetzung hat 0 Zeilen, Daten haben 3
interpret_omega_squared(w2) # Does not work
#> Error in interpret(es, rules): Objekt 'w2' nicht gefunden
ado_tidy <- tibble( # manually create Adonis test result table
parameter = c("Management", "Residual", "Total"),
df = ado %>% pull("Df"), # Degree of freedom
ss = ado %>% pull("SumOfSqs"), # sum of squares
meansqs = ss / df, # mean squares
p_r2 = ado %>% pull("R2"), # partial R²
f = ado %>% pull("F"), # F value
p = ado %>% pull("Pr(>F)") # p value
)
ado_tidy
#> # A tibble: 3 x 7
#> parameter df ss meansqs p_r2 f p
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 Management 3 1.47 0.490 0.342 2.77 0.00990
#> 2 Residual 16 2.83 0.177 0.658 NA NA
#> 3 Total 19 4.30 0.226 1 NA NA
# Formula:
# W2 = (DFm * (F - 1)) / ((DFm * (F - 1)) + (DFm + 1))
W2 <- abs(
(ado_tidy %>% pull(df) %>% chuck(3) * (ado_tidy %>% pull(f) %>% chuck(1) - 1)) /
((ado_tidy %>% pull(df) %>% chuck(3) * (ado_tidy %>% pull(f) %>% chuck(1) - 1) +
ado_tidy %>% pull(df) %>% chuck(3) + 1)
)
)
W2
#> [1] 0.6267099
interpret_omega_squared(W2, rules = "field2013")
#> [1] "large"
#> (Rules: field2013)
Created on 2022-11-15 with reprex v2.0.2
Hopefully, the equation is correct...

Answer 1

Here is the MicEco::adonis_OmegaSq function edited so that it works both with the current vegan::adonis2 and deprecated vegan::adonis:
#' Calculate (partial) Omega-squared (effect-size calculation) for PERMANOVA and add it to the input object
#'
#' #param adonisOutput An adonis object
#' #param partial Should partial omega-squared be calculated (sample size adjusted). Default TRUE
#' #return Original adonis object with the (partial) Omega-squared values added
#' #import vegan
#' #export
adonis_OmegaSq <- function(adonisOutput, partial = TRUE){
if(!(is(adonisOutput, "adonis") || is(adonisOutput, "anova.cca")))
stop("Input should be an adonis object")
if (is(adonisOutput, "anova.cca")) {
aov_tab <- adonisOutput
aov_tab$MeanSqs <- aov_tab$SumOfSqs / aov_tab$Df
aov_tab$MeanSqs[length(aov_tab$Df)] <- NA
} else {
aov_tab <- adonisOutput$aov.tab
}
heading <- attr(aov_tab, "heading")
MS_res <- aov_tab[pmatch("Residual", rownames(aov_tab)), "MeanSqs"]
SS_tot <- aov_tab[rownames(aov_tab) == "Total", "SumsOfSqs"]
N <- aov_tab[rownames(aov_tab) == "Total", "Df"] + 1
if(partial){
omega <- apply(aov_tab, 1, function(x) (x["Df"]*(x["MeanSqs"]-MS_res))/(x["Df"]*x["MeanSqs"]+(N-x["Df"])*MS_res))
aov_tab$parOmegaSq <- c(omega[1:(length(omega)-2)], NA, NA)
} else {
omega <- apply(aov_tab, 1, function(x) (x["SumsOfSqs"]-x["Df"]*MS_res)/(SS_tot+MS_res))
aov_tab$OmegaSq <- c(omega[1:(length(omega)-2)], NA, NA)
}
if (is(adonisOutput, "adonis"))
cn_order <- c("Df", "SumsOfSqs", "MeanSqs", "F.Model", "R2",
if (partial) "parOmegaSq" else "OmegaSq", "Pr(>F)")
else
cn_order <- c("Df", "SumOfSqs", "F", if (partial) "parOmegaSq" else "OmegaSq",
"Pr(>F)")
aov_tab <- aov_tab[, cn_order]
attr(aov_tab, "names") <- cn_order
attr(aov_tab, "heading") <- heading
if (is(adonisOutput, "adonis"))
adonisOutput$aov.tab <- aov_tab
else
adonisOutput <- aov_tab
return(adonisOutput)
}
source() this function and it should work. In my test it gave the same results for both adonis2 and adonis.