A Hybrid Machine Learning Framework for Ordinal Classification Using Ordinal Logistic Regression and Calibrated Support Vector Machines

Abstract

Ordinal classification of global CO₂ emission growth requires models that accommodate ordering, nonlinearity, imbalance, and temporal dependence. This study proposes a probability-level hybrid framework combining ordinal logistic regression (OLR) and a calibrated support vector machine (SVM), using fixed equal-weight fusion (HSM) and adaptive ordinal attention (AOA–HSM). Performance was assessed through 9,000 simulations spanning linear, mixed, and nonlinear mechanisms at n=100,300,500, and through 59 annual observations (1965–2023) with expanding-window temporal validation yielding 30 held-out predictions. OLR provided the strongest ordinal discrimination in linear and mixed settings, whereas HSM was generally more stable; AOA–HSM improved probability quality in selected nonlinear settings. Empirically, calibrated SVM achieved the highest accuracy (0.667), ordinal random forest the highest QWK (0.441), and AOA–HSM the best LogLoss (0.855) and Brier score (0.515). No method dominated all criteria, indicating that adaptive probability fusion is most useful when probabilistic reliability under nonlinear heterogeneity is prioritized.