PyPerMANOVA

Implementation of permutational multivariate analysis of variance in Python

Intro

Permutational multivariate analysis of variance (PerMANOVA) is a semi-parametric statistical method. It is described as "a geometric partitioning of multivariate variation in the space of a chosen dissimilarity measure", with p-values obtained using "appropriate distribution-free permutation techniques".

The script implements the simplest version - one-way PerMANOVA, and doesn't require much additional packaging.

The full tutorial is given in Tutorial Jupyter Notebook.

How-to

To conduct the analysis, use the permutational_analysis unction from PyPerMANOVA. It takes the following parameters:

• data : pandas DataFrame a numerical dataframe of N x M size
• mapping : iterator, dictionary, or pd.DataFrame will map columns (or indices) of data to group
• column : if mapping is pd.DataFrame, column in mapping to map columns (or indices) of data

It takes the following key arguments:

• by : string, optional What orientation is taken to produce a distance matrix. Can be either via column, or via row. Default is column.
• norm : string, optional If the data is normalized before constructing a distance matrix. Can be normalized with respect to "row"s or "column"s, or doesn't need to be normalized (None). Default is row.
• metric : string, optional Valid distance metric with which to construct a distance matrix. Default is "euclidean".
• permutations : int, optional Number of permutations used to calculate P value. Default is 999.

It returns the following results:

• permanova_result : pd.DataFrame, result of perMANOVA in the form of dataframe, with the following columns
  • "Pval" - the P value
  • "eta-sqr" - eta squared
  • "F" - F statistic
• posthoc_result : pd.DataFrame, result of post hoc perMANOVAs in the form of dataframe, with the following columns
  • "A","B - the test done between
  • "Pval" - the unadjusted P value
  • "bonf" - bonfferoni corrected P value
  • "eta-sqr" - identical to Pearson R square
  • "F" - F statistic
  • "t" - t statistic

Notes:

The possible values for metric parameter are found on https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.pdist.html And they include the following metrics : ‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘cityblock’, ‘correlation’, ‘cosine’, ‘dice’, ‘euclidean’, ‘hamming’, ‘jaccard’, ‘jensenshannon’, ‘kulsinski’, ‘kulczynski1’, ‘mahalanobis’, ‘matching’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘yule’

Use whatever metric you deem appropriate.

References

https://doi.org/10.1002/9781118445112.stat07841