[R] Permutations in RDA for repeated measures, using how()

[Margot Neyret]

Dear all,

I am using RDA to study plant communities in various land uses (variable LU with values M, U, etc.). For each land use, I sample 3 to 5 fields (M1, M2, U1, U2, etc). I make 5 measurements for both plant communities and environmental variables in each field.
I repeat the process every 6 months to study the effect of time and season (D16 for dry season 2017, R16 for rainy season 2016, etc). For field M1 for instance, I have the values for the field_in_season M1-D16, M1-R16, M1-D17.

My 5 measurements are interdependent; and there is also temporal dependance for the field_in_season within the fields.

When I want to test the significance of my RDA, I should thus constrain the permutation to take this into account.

If I am correct (if not please tell me so), in linear models I should write :
> lme(Y ~ X, random = ~1|Field_in_season/Field)

>From various reads, I understand that in RDA I should not only use the strata = Plot argument, but allow for permutation of measurements within field_in_season, and for permutations among Field_in_season. So that would be :

> rda_repeated = anova(rda(Community~LU + Humidity, data = env), by = 'term', permutation = how(within = Within(type = "series", mirror = TRUE), plots = Plots(strata = Field_in_season, type = "series"), blocks = Field))

Is that right ? In the output I get very similar results and “Permutation : free” in both cases, which dos not seem right.

Thanks,
Margot

——————
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> Community = matrix(ncol = 10,nrow = 1350)
> colnames(Community) = letters[1:10]
> for (i in letters[1:10]){
> Community[,i] = rpois(135, 3)
}

> Season = rep(c('D16', 'R16','D17'), each = 450)
> LU = rep(c('M', 'U', 'O'), each = 15, length.out = 1350)
> Field = paste(LU, rep(c(1:3), each = 50), sep = '')
> Field_in_season = paste(Field,Season, sep = '-')
> Humidity = rnorm(n=1350, mean = 100)
> env = data.frame(Season, LU, Field, Field_in_season)

> library(FactoMineR)

> anova(rda(Community~LU + Humidity, data = env), by = 'term’) # Without specification for permutations

> anova(rda(Community~LU + Humidity, data = env), by = 'term’, # With restricted permutations
permutation = how(within = Within(type = "series", mirror = TRUE),
plots = Plots(strata = Field_in_season, type = "series"),
blocks = Field))

Permutation test for rda under reduced model
Terms added sequentially (first to last)
Permutation: free
Number of permutations: 999

Model: rda(formula = Community ~ LU + Humidity, data = env)
Df Variance F Pr(>F)
LU 2 0.4427 9.7954 0.001 ***
Humidity 1 0.0283 1.2508 0.247
Residual 1346 30.4150
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


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