Calculate PERMANOVA (Permutational Multivariate Analysis of Variance)

These functions perform PERMANOVA to assess the significance of group differences based on a specified dissimilarity matrix. The results can be returned directly or added to metadata in an object of class TreeSummarizedExperiment.

getPERMANOVA(x, ...)

addPERMANOVA(x, ...)

# S4 method for class 'SingleCellExperiment'
getPERMANOVA(x, ...)

# S4 method for class 'SummarizedExperiment'
getPERMANOVA(x, assay.type = "counts", formula = NULL, col.var = NULL, ...)

# S4 method for class 'ANY'
getPERMANOVA(x, formula, data, method = "bray", test.homogeneity = TRUE, ...)

# S4 method for class 'SummarizedExperiment'
addPERMANOVA(x, name = "permanova", ...)

Arguments

x

TreeSummarizedExperiment.

...

additional arguments passed to vegan::adonis2.

by: Character scalar. Specifies how significance is calculated. (Default: "margin")
na.action: function. Action to take when missing values for any of the variables in formula are encountered. (Default: na.fail)
full Logical scalar. should all the results from the homogeneity calculations be returned. When FALSE, only summary tables are returned. (Default: FALSE)
homogeneity.test: Character scalar. Specifies the significance test used to analyse vegan::betadisper results. Options include 'permanova' (vegan::permutest), 'anova' (stats::anova) and 'tukeyhsd' (stats::TukeyHSD). (Default: "permanova")

assay.type

Character scalar. Specifies which assay to use for calculation. (Default: "counts")

formula

formula. If x is a SummarizedExperiment a formula can be supplied. Based on the right-hand side of the given formula colData is subset to col.var.

col.var and formula can be missing, which turns the CCA analysis into a CA analysis and dbRDA into PCoA/MDS.

col.var

Character scalar. When x is a SummarizedExperiment,col.var can be used to specify variables from colData.

data

data.frame or coarcible to one. The covariance table including covariates defined by formula.

method

Character scalar. A dissimilarity metric used in PERMANOVA and group dispersion calculation. (Default: "bray")

test.homogeneity

Logical scalar. Should the homogeneity of group dispersions be evaluated? (Default: TRUE)

name

Character scalar. A name for the results that will be stored to metadata. (Default: "permanova")

Value

getPERMANOVA returns the PERMANOVA results or a list containing the PERMANOVA results and homogeneity test results if test.homogeneity = TRUE. addPERMANOVA adds these results to metadata of x.

Details

PERMANOVA is a non-parametric method used to test whether the centroids of different groups (as defined by the formula or covariates) are significantly different in terms of multivariate space.

PERMANOVA relies on the assumption of group homogeneity, meaning the groups should be distinct and have similar variances within each group. This assumption is essential as PERMANOVA is sensitive to differences in within-group dispersion, which can otherwise confound results. This is why the functions return homogeneity test results by default.

The functions utilize vegan::adonis2 to compute PERMANOVA. For homogeneity testing, vegan::betadisper along with vegan::permutest are utilized by default, which allow testing for equal dispersion across groups and validate the homogeneity assumption.

PERMANOVA and distance-based redundancy analysis (dbRDA) are closely related methods for analyzing multivariate data. PERMANOVA is non-parametric, making fewer assumptions about the data. In contrast, dbRDA assumes a linear relationship when constructing the ordination space, although it also employs a PERMANOVA-like approach to test the significance of predictors within this space. dbRDA offers a broader scope overall, as it provides visualization of the constrained ordination, which can reveal patterns and relationships. However, when the underlying data structure is non-linear, the results from the two methods can differ significantly due to dbRDA's reliance on linear assumptions.

Examples


data(GlobalPatterns)
tse <- GlobalPatterns

# Apply relative transformation
tse <- transformAssay(tse, method = "relabundance")
# Perform PERMANOVA
tse <- addPERMANOVA(
    tse,
    assay.type = "relabundance",
    method = "bray",
    formula = x ~ SampleType,
    permutations = 99
    )
# The results are stored to metadata
metadata(tse)[["permanova"]]
#> $permanova
#> Permutation test for adonis under reduced model
#> Marginal effects of terms
#> Permutation: free
#> Number of permutations: 99
#> 
#> adonis2(formula = formula, data = data, permutations = 99, method = ..1, by = by, na.action = na.action)
#>            Df SumOfSqs      R2      F Pr(>F)   
#> SampleType  8   8.2466 0.73109 5.7773   0.01 **
#> Residual   17   3.0332 0.26891                 
#> Total      25  11.2798 1.00000                 
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> $homogeneity
#>            Df    Sum Sq    Mean Sq        F N.Perm Pr(>F) Total variance
#> SampleType  8 0.4996524 0.06245655 5.807135     99   0.01      0.6824898
#>            Explained variance
#> SampleType          0.7321024
#> 

# Calculate dbRDA
rda_res <- getRDA(
    tse, assay.type = "relabundance", method = "bray",
    formula = x ~ SampleType, permutations = 99)
# Significance results are similar to PERMANOVA
attr(rda_res, "significance")
#> $permanova
#>            Df SumOfSqs        F Pr(>F) Total variance Explained variance
#> Model       8  8.24659 5.777341  0.001       11.27982          0.7310924
#> SampleType  8  8.24659 5.777341  0.010       11.27982          0.7310924
#> Residual   17  3.03323       NA     NA       11.27982          0.2689076
#> 
#> $homogeneity
#>            Df    Sum Sq    Mean Sq        F N.Perm Pr(>F) Total variance
#> SampleType  8 0.4996524 0.06245655 5.807135     99   0.01      0.6824898
#>            Explained variance
#> SampleType          0.7321024
#>

Calculate PERMANOVA (Permutational Multivariate Analysis of Variance)

Arguments

Value

Details

See also

Examples