aguirreg

Carry-over effects are modeled as the impact of the prior stimulus upon the current stimulus. Ideally, the model would examine the effect of the prior neural state upon the response to the current stimulus. Unfortunately, an independent measure of the prior neural state of the system is generally not available in fMRI studies.¹⁾ Instead, the effect of the prior stimulus is used. A possible concern is that the the same prior stimulus (t-1) might leave the neural system in two different amplitude states (perhaps, dependent upon the effect of the stimulus that preceded the prior stimulus; e.g., the stimulus two back; t-2). For example, the t-1 stimulus may have been the same (along some relevant modeled dimension) as the t-2 stimulus, and thus the neural state is relatively adapted. Presentation then of the current (t) stimulus may result in a different signal response depending upon the prior neural state. If this effect were unbalanced across the possible stimulus pairings, it could introduce bias (the effect being dependent upon the particular sequence used and how second-order transitions were distributed across first-order transitions).

This possibility is best accounted for by employing a sequence with second-order counterbalancing. This will ensure that the neural amplitude state of the system prior to the current stimulus is always balanced across the possible transitions from the prior to current stimulus (presuming that the systematic neural state of the system prior to the current stimulus is entirely determined by the t-2 stimulus).

Thanks to Shivakumar (Shiva) Vishwanathan of UC Santa Barabara for prompting this discussion.