When predictors sum to a constant: Trade-off effect analysis using a regression model based on isometric log-ratio...

Area of Science:

• Statistics
• Data Analysis

Background:

• Standard regression models fail with constant predictor sums (proportional/ipsative data).
• Existing reduced-rank regression models have rigid linearity/symmetry assumptions, ignoring data composition.
• Compositional data analysis requires methods that respect the nature of the data.

Purpose of the Study:

• To propose a novel method, isometric-log-ratio-transformed trade-off analysis (ITEA), for analyzing trade-off effects in compositional data.
• To address limitations of linearity and symmetry in previous methods.
• To provide a more flexible and interpretable approach for proportional and ipsative data.

Main Methods:

• Predictors are transformed using isometric log-ratio coordinates via sequential binary partitioning.
• Trade-off effects are estimated using regression on these transformed coordinates.
• Trade-off effect is defined as the change in the dependent variable, with confidence intervals derived.

Main Results:

• ITEA yields more flexible and interpretable trade-off effect results compared to Davison et al. (2022).
• Results are robust to variations in orthonormal bases.
• Empirical validation using a forced-choice questionnaire demonstrates ITEA's validity.

Conclusions:

• ITEA offers a statistically sound and interpretable method for analyzing trade-off effects in compositional data.
• The method overcomes limitations of traditional regression and prior reduced-rank models.
• ITEA has practical applications and potential for further extensions in data analysis.