Rethinking Parameter Invariance in Cognitive Modeling

A central promise of cognitive modeling is that model parameters can capture psychological quantities that generalize beyond the setting in which they were estimated. Yet when the same parameter value works across tasks, it is not always clear what has generalized. We distinguish accommodation, in which several tasks can be represented adequately by a common value, from transfer, in which a value selected without the target remains adequate there. Accommodation can hold even when bidirectional transfer fails, and this separation persists without sampling noise. When tasks favor different values, joint fitting may find a compromise that represents them well even though the values favored by the tasks when fitted separately do not transfer. Successful transfer is also more revealing when the target places meaningful constraints on the value being tested. Formal analyses and simulations show that the evidential meaning of parameter stability depends on how the value was selected and what the target could have revealed about it. Together, these results motivate a rethinking of parameter invariance in cognitive modeling and of what cross-task stability can establish about psychological generalization. This is a preprint of a manuscript submitted for publication. It has not been peer reviewed.