Relative importance analysis of correlated predictors in aquatic veterinary science: Application to an abalone...

Relative importance refers to the process of quantifying how much each predictor in a linear regression model contributes to explaining the outcome variation. In veterinary science, linear regression is widely applied as an analytical tool, allowing researchers to examine relationships between predictors and outcomes of interest in animal populations.

This study aims to provide an introduction to statistical approaches for quantifying the relative importance of correlated predictors. This study focuses exclusively on statistical procedures implemented in R software that are applicable to linear regression within veterinary science. Additionally, the study demonstrates relative importance analysis for correlated predictors using the abalone dataset as an example.

This study evaluates several statistical approaches for assessing predictor importance, including Shapley value-based decomposition, Genizi method, relative weights analysis, and dominance analysis.

The shell weight of abalone was consistently ranked as the most influential predictor in predicting the ring count, which serves as a proxy for abalone age, across all methods. The Proportional Marginal Variance Decomposition (PMVD) metric showed overlapping importance among predictors, while the Genizi metric provided clear separation between all predictors. The Genizi metric and relative weight method consistently produced narrow confidence intervals (CIs) across all estimates, while the PMVD produced wider bootstrap intervals, Lindeman, Merenda, and Gold (LMG) method showed moderate variability, indicating a slight difference in estimates across both metrics.

Shell weight is the most dominant predictor of ring count, serving as a proxy for the age of abalone. Both the relative weights and the Genizi method performed well, resulting in narrow CIs. Dominance analysis provided deeper hierarchical insights into predictor importance but requires greater computational resources, particularly for complex models.

Abalone dataset, Correlated predictors, Dominance analysis, Relative weights analysis, Shapley value.