Integrated Machine Learning and Statistical Interpretation of Malachite Green Removal by SDBS-Modified Ostrich Bone Waste: A Comparative Random Forest, Bayesian Regression, and LMG Analysis

The development of sustainable adsorbents and reliable predictive tools for dye-contaminated wastewater treatment remains an important challenge in environmental engineering. In this study, the adsorption of malachite green (MG) dye onto sodium dodecyl benzene sulfonate (SDBS)-modified ostrich bone waste was investigated using an integrated modeling framework combining Lindeman–Merenda–Gold (LMG) analysis, Bayesian Regression (BR), and Random Forest (RF) modeling. 52 experimental conditions (each measured in triplicate) were analyzed to evaluate the influence of pH, contact time, initial dye concentration, temperature, adsorbent dosage, and SDBS dosage on dye removal efficiency. The three modeling approaches consistently identified pH and contact time as the two most influential operational variables, whereas the relative importance of initial dye concentration and adsorbent dosage differed among the methods. BR quantified the direction and uncertainty of predictor effects, yielding posterior coefficients of 0.650 (95% CrI: 0.365–0.935) for pH, 0.467 (95% CrI: 0.263–0.672) for contact time, and −0.517 (95% CrI: −0.759 to −0.272) for initial dye concentration. Under internal validation, RF yielded an OOB R2 of 0.822, an RMSE of 11.79 pp, and an MAE of 7.85 pp, whereas BR evaluated by LOOCV yielded an R2 = 0.417, an RMSE = 21.31 pp, and an MAE = 16.42 pp. Because different validation protocols were used, these internal estimates are not directly comparable. More stringent group-aware validation resulted in under leave-one-series-out validation; neither model achieved positive skill (pooled R2 = −0.382 for RF; BR R2 was strongly negative, driven mainly by extrapolation when the initial-concentration series was held out), while across the six single-series rotations, R2 was negative in five for both models (RF positive only when the C0 series was held out; BR best when the pH series was held out, R2 = 0.410). These results demonstrate that the models capture relationships within the investigated experimental domain but have limited generalization to experimental series or operating regions not represented in model development. The results confirm the potential of SDBS-modified ostrich bone waste (OBW) as an effective and sustainable adsorbent for malachite green removal and demonstrate that the proposed integrated modeling framework therefore enabled complementary assessment of variable importance, probabilistic predictor effects, and predictive behavior within and across the investigated experimental domain.