Log-Contrast Models Overview

Log-Contrast Models Overview#

Microbiome counts have no absolute scale: a sample sequenced twice as deeply gives twice the counts and exactly the same biology. Log-contrast models are built for that — they work in log-ratios and require the coefficients to sum to zero, so the fit depends on the balance between taxa rather than on any number the sequencing run happened to produce.

../../_images/compositional-simplex-zero-sum.png

Fig. 10 Scale invariance and the zero-sum constraint. See Appendix: Mathematical Background for the formulation it comes from.#

The formulation#

Relative abundances sum to a constant, so a composition occupies a simplex rather than the whole of Euclidean space. A log-contrast model works around that in three steps:

  • transform the counts with the centered log-ratio (CLR) or another log-ratio map;

  • fit a regularized regression or classifier in the transformed space;

  • read the coefficients as changes in relative abundance.

The same three steps serve a continuous response and a categorical one.

Contents#

1. Data preparation#

Transform a count table to log-ratios, aggregate it on the taxonomy, append environmental covariates, and split it into training and test sets.

2. Regression models#

Predict a continuous outcome (temperature, pH) from community composition:

  • Log-Contrast Regression: CLR-transformed features, without the taxonomy

  • trac: aggregates features along the taxonomic hierarchy before selection

3. Classification models#

Predict a categorical outcome such as disease status or habitat type:

  • Log-Contrast Classification: the same design matrix against a categorical response

  • trac: identifies predictive taxonomic groups, not only individual features

4. Advanced topics#

  • Concomitant Formulation: joint estimation of the coefficients and the noise level, for data with heterogeneous variance

5. Interpretation#

What a fitted log-contrast model does and does not say about the community.

Key concepts#

Log-Ratio Transformations: convert compositional data to unrestricted space

  • CLR (Centered Log-Ratio): the usual choice; centres each sample on its geometric mean

  • ALR (Additive Log-Ratio): divides by one component taken as the reference

Regularization: prevents overfitting in high-dimensional microbiome data

  • L1 penalty (Lasso): drives coefficients to exactly zero and so selects a subset of features

  • Stability selection: keeps the features whose selection probability across subsamples clears a threshold

trac (tree-aggregation of compositional data): uses phylogenetic structure

  • trac computes adaptive weights from the taxonomic hierarchy

  • It groups related taxa, so a coefficient attaches to a clade

Prerequisites#

  • Install the plugins, following Installation.

  • Read the description of the Atacama dataset.

  • You will need a working knowledge of regression and classification.

Reading order#

Begin with Data Preparation, then take the branch that matches your response variable: