Multi-Channel Objective Incompatibility in Drift–Diffusion Models: A Diagnostic Stress Test Across Accuracy and Reaction-Time Channels

This technical note investigates a structural question within Drift–Diffusion Models (DDM):Do different objective reductions define equivalent parameter geometries when evaluated under full probabilistic likelihood? Using synthetic datasets generated under known DDM parameters, we compare full trial-level maximum likelihood estimation with independently optimized reduced objectives: accuracy-only (ACC), correct reaction-time mean (RTc), and error reaction-time mean (RTe). Each reduced objective can locally match its targeted observable. However, when evaluated under full likelihood, the resulting parameter configurations exhibit systematic and channel-specific divergence. These divergences persist across generative regimes and do not vanish as sample size increases. Because data are generated under the same DDM structure used for fitting, the observed effects cannot be attributed to model misspecification or sampling fluctuation. The findings indicate that objective reduction induces structural reparameterization rather than simple scalar loss. Distinct evaluation channels correspond to distinct geometric projections of the likelihood surface. The analysis is strictly diagnostic and introduces no new modeling framework, optimization method, or prescriptive procedure.