Regression: Predicting Continuous Outcomes

Log-contrast regression fits a regularized model to log-transformed compositional data and returns the taxa, or the taxonomic groups, whose balance tracks a continuous response: temperature, pH, or any other environmental or clinical measurement.

Two workflows

Log-Contrast Regression

• CLR transformation and covariates, no taxonomy

• Faster to fit

• Suited to exploratory work

• Choose it when taxonomic relationships are not part of the question

trac: Regression with taxonomic information

• Aggregates predictors along the taxonomic hierarchy through adaptive weights

• Attaches coefficients to named clades

• Groups feature selection phylogenetically

• Choose it for results you intend to publish

Heterogeneous variance

The concomitant formulation estimates the noise scale jointly with the coefficients. Use it when the residual variance is not constant — see Concomitant Formulation.

Worked example

Both workflows predict average soil temperature from the Atacama desert microbiome dataset and report which taxa track the temperature gradient.

Prerequisites

Work through Data Preparation first.

Reading order

1. Fit without taxonomy in Log-Contrast Regression.

2. Refit with clade-aggregated predictors in trac.

3. Read the selected coefficients with the Interpretation guide.