Impact Range Assessment (IRA): An Interpretable Sensitivity Measure for Regression Modelling

While regression models capture the relationship between predictors and the response variable, they often lack intuitive accompanying methods to understand the influence of predictors on the outcome. To address this, we introduce an interpretability method called Impact Range Assessment (IRA), which quantifies the maximal influence of each predictor by measuring the total potential change in the response variable, across the predictor range. Validation using synthetic linear and nonlinear datasets demonstrates that relevant predictors produced higher IRA values than irrelevant ones. Moreover, repeated evaluations produced results closely aligned with those from the single-execution analysis, confirming the robustness of the method. A case study using a model that predicts pellet quality demonstrated that the IRA provides a simple and intuitive approach to interpret and rank predictor influence, thereby improving model transparency and reliability.

💡 Research Summary

The paper introduces Impact Range Assessment (IRA), a novel, model‑agnostic sensitivity measure designed to quantify the maximal influence of each predictor in a regression model by evaluating the total possible change in the response variable across the observed range of that predictor. The authors motivate the need for an intuitive, computationally efficient method that can be applied to both linear and nonlinear regression models, noting that existing approaches—such as coefficient inspection, feature importance scores, local derivative‑based sensitivity, and global variance‑based methods (Sobol, Morris)—either suffer from scale dependence, lack of interpretability, or high computational cost.

IRA operates in five steps. First, a focus predictor is selected. Second, the predictor’s minimum and maximum values are divided into M evenly spaced points (interpolation). Third, K background observations are drawn with replacement from the training data. Fourth, for each background observation, the focus predictor is replaced by each of the M interpolated values while all other predictors remain unchanged, yielding M modified input rows per background observation. Fifth, the trained regression model predicts the response for all modified rows; the range (max – min) of predictions for each background observation is computed, and the IRA value for the predictor is the average of these K ranges. Mathematically,

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