manocca 2.0.1

MANOCCA: Multivariate ANalysis of Conditional CovAriance

MANOCCA

Multivariate ANalysis of Conditional CovAriance

MANOCCA tests whether a predictor X is associated with the covariance structure of multivariate outcomes Y, adjusting for covariates C:

Cov(Y) ~ X + C

Unlike MANOVA (which tests mean effects) or univariate approaches, MANOCCA isolates changes in correlations/covariances between outcomes. The test is orthogonal to mean and variance effects.

Reference: Boetto C. & Aschard H. (2024). Briefings in Bioinformatics, 25(4).
https://academic.oup.com/bib/article/25/4/bbae272/7690346

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Installation

pip install manocca

Or with conda (once the feedstock is available on conda-forge):

conda install -c conda-forge manocca

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Quick start

import numpy as np
from manocca import MANOCCA, MANOVA, UNIVARIATE, Explainer

rng = np.random.default_rng(42)
N, K = 1000, 10

X = rng.binomial(1, 0.4, (N, 1)).astype(float)   # binary predictor
C = rng.standard_normal((N, 3))                   # covariates
Y = rng.standard_normal((N, K))                   # outcomes

# Inject a covariance effect: Y0 and Y1 become correlated when X=1
mask = X.flatten() == 1
Y[mask, 0] += 1.5 * Y[mask, 1]

# Test Cov(Y) ~ X + C
model = MANOCCA(predictors=X, outputs=Y, covariates=C, n_comp=20)
model.test()
print(f"MANOCCA p-value: {model.p[0, 0]:.4e}")   # should be significant

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Classes

Class	Tests	Description
MANOCCA	Cov(Y) ~ X + C	Core covariance test
MANOVA	Mean(Y) ~ X + C	Classical multivariate mean test
UNIVARIATE	Y_j ~ X + C	Univariate baseline (per outcome)
Explainer	—	Interprets a fitted MANOCCA model

MANOCCA

model = MANOCCA(
    predictors,          # ndarray or DataFrame (N, n_p)
    outputs,             # ndarray or DataFrame (N, k), k >= 2
    covariates=None,     # ndarray or DataFrame (N, n_c), optional
    n_comp=None,         # number of PCA components (default: k)
    apply_qt=True,       # quantile-transform products before PCA
    use_pca=True,        # reduce with PCA (recommended for large k)
    corr_bias=False,     # subtract additive mean-effect bias
    n_jobs=1,            # parallel workers (-1 = all cores)
)
model.test()
model.p                  # ndarray (n_p, 1) — p-values per predictor

Explainer

exp = Explainer(model)

# P-value vs. number of PCA components
p_curve, grid = exp.power_pc_kept("predictor_name", grid=range(1, 21))

# Which pairwise covariances drive the signal?
importances = exp.feature_importances("predictor_name", n_comp=10)

# Per-outcome contribution
contrib = exp.split_contribution(importances)

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Algorithm

1. Compute all k(k−1)/2 pairwise products of (optionally QT-transformed) outcomes.
2. Reduce dimensionality with PCA; apply a second QT to the components.
3. Residualize the components against covariates C.
4. Run a Wilks' Lambda MANOVA of the residuals against each predictor in X.

See the paper for details on the bias-correction mode (corr_bias=True), which makes the test orthogonal to additive mean effects without QT or PCA.

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Citation

@article{boetto2024manocca,
  author  = {Boetto, Christophe and Aschard, Hugues},
  title   = {{MANOCCA}: Multivariate ANalysis of Conditional CovAriance},
  journal = {Briefings in Bioinformatics},
  volume  = {25},
  number  = {4},
  year    = {2024},
  doi     = {10.1093/bib/bbae272},
}

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License

MIT © Christophe Boetto, Hugues Aschard