A transformation-free linear regression for compositional outcomes and predictors.

Area of Science:

• Statistics
• Data Science
• Biostatistics

Background:

• Compositional data, representing parts of a whole, are prevalent across scientific disciplines.
• Existing models for compositional data often rely on complex transformations, hindering interpretation.
• A need exists for simpler, more interpretable models for compositional regression analysis.

Purpose of the Study:

• To develop a novel, transformation-free linear regression model for compositional outcome and predictor variables.
• To provide a model that is interpretable in the compositional space and robust to various data-generating mechanisms.
• To enable the analysis of compositional data, including those with zero or one values.

Main Methods:

• Developed a linear regression model based on estimating equations, avoiding complex log-ratio transformations.
• The model expresses the compositional outcome as a Markov transition from the compositional predictor.
• Introduced permutation tests for assessing linear independence and equality of effect sizes.

Main Results:

• The proposed model offers a simple interpretation of relationships between compositional variables.
• It effectively handles compositional data containing zeros and ones in both outcomes and covariates.
• The model demonstrated accurate capture of compositional data relationships in education and medical research datasets.

Conclusions:

• The transformation-free linear regression model provides a significant advancement for analyzing compositional data.
• Its interpretability and robustness make it a valuable tool for researchers in diverse fields.
• The model facilitates a more accessible and accurate understanding of compositional data structures.