Reading Cognition as Decisions Unfold in Words: A Factorized Inverse Decision Model

Inverse decision modeling infers latent properties of decision processes from observed behavior, but existing formulations rely primarily on action trajectories. In verbalized cognitive tasks, task execution also produces response dynamics that action-only formulations leave unmodeled, such as verbal production, interaction, and hesitation. We propose a factorized inverse decision model (FIDM) that decomposes each individual's task-execution likelihood into an action factor and an effort factor, governed by separate individual-specific parameters. From raw verbal transcripts, a language model produces structured task-execution traces for factorized inference. On data from 400 older adults performing a grocery-shopping dialog task for cognitive screening, controlled recovery shows selective estimation of the intended factors, while matched semi-synthetic conditions show that FIDM preserves action-execution distinctions even when aggregate behavioral summaries are matched. Action evidence further localizes task-defined deviations across participants. In cognitive-status classification, FIDM provides information complementary to clinical scores, trajectory summaries, and frozen language representations, with consistent gains across all evaluated baselines in the binary setting.