§ Abstract
Processing speed theories propose that cognitive operation rate constrains higher-order reasoning performance through linear coupling, while resource allocation theories predict nonlinear patterns where different cognitive systems become limiting at different performance levels. Despite extensive research linking processing speed and reasoning, the functional form of this relationship remains empirically underspecified, with important theoretical implications for understanding cognitive architecture. We tested competing linear and nonlinear models (exponential, piecewise linear, and smooth cubic spline) using 556,776 participants across three independent cognitive assessment batteries, applying cross-validation procedures and practical significance thresholds to adjudicate between theoretical accounts.Linear models were consistently selected across all twelve battery-outcome-predictor combinations, with nonlinear alternatives showing effectively zero improvement in predictive accuracy. Processing speed explained 7.4-16.0% of variance in reasoning performance, while working memory moderation effects contributed less than 0.08% of additional variance, indicating predominantly additive rather than interactive relationships between these cognitive constructs. However, sensitivity analyses revealed that these conclusions depended critically on Trail Making Test operationalization: log-transformed completion times yielded linear speed-reasoning relation- ships, whereas raw seconds produced nonlinear patterns with substantial model improvements. Cross-battery analyses further demonstrated that three of four speed-reasoning relationships exhibited battery-specific parameters, indicating limited generalizability across measurement contexts.These findings reveal that theoretical conclusions regarding processing speed’s role in reasoning depend fundamentally on measurement operationalization choices rather than reflect-ing stable cognitive architecture properties. When Trail Making Test times are log-transformed, results support linear processing speed theory, but this support dissolves under alternative operationalizations that produce contradictory functional forms. Transformation dependency represents a critical boundary condition for interpreting speed-cognition relationships and challenges the generalizability of functional form conclusions across different assessment batteries and operationalization conventions.