A LATENT VARIABLE MIXTURE MODEL FOR COMPOSITION-ON-COMPOSITION REGRESSION WITH APPLICATION TO CHEMICAL RECYCLING

Area of Science:

• Statistics
• Data Analysis
• Compositional Data Analysis

Background:

• Compositional data analysis frequently involves regression, often requiring complex log-ratio transformations.
• Existing transformation-free models are limited to a single compositional predictor, restricting their applicability.
• Interpreting models with log-ratio transformations can be challenging.

Purpose of the Study:

• To develop an extended transformation-free regression model for handling multiple compositional predictors.
• To address the limitations of existing methods in analyzing complex compositional datasets.
• To provide a more interpretable regression framework for compositional data.

Main Methods:

• A novel extension of the transformation-free regression model using a latent variable mixture.
• A modified expectation-maximization algorithm for parameter estimation.
• Conformal inference for generating prediction limits on the compositional response.

Main Results:

• The proposed model effectively accommodates two or more compositional predictors.
• Estimated model parameters demonstrate natural and interpretable meanings.
• The methodology is successfully applied to hydrothermal liquefaction (HTL) data.

Conclusions:

• The developed methodology offers a powerful and interpretable alternative for regression with multiple compositional predictors.
• The approach simplifies the analysis of complex compositional data without relying on log-ratio transformations.
• The study highlights potential extensions for even broader applications in compositional data analysis.