Formal model for describing simultaneous chaining behavior
Greg Jensen, Drew Altschul, H. S. Terrace · Figshare · 2016
The decision tree that govern an animal’s “progress” through the list in a single trial. Each choice made by the subject has a probability of being correct p1, p2, etc., such that the probability of completing a 4-item list (and thus earning a reward) is (p1•p2•p3•p4). Since specifying each pi permits the likelihood to be calculated, posterior distributions for these probabilities can be estimated. (B). The asymmetric bounded logistic function, used to model each choice probability pi in humans (who lacked prior experience, and so had to learn the categories while doing the task). This function is defined in terms of peak learning rate (governed by m), a slope (governed by s), a floor term denoting starting performance (governed by f), and a twist parameter that influenced the asymmetry in learning speeds early vs. late during learning (governed by v). (C). Examples of the conditional probabilities pi for each of the four choices. Note that p3 begins higher than p1 because, should a subject get to the third choice, only two items will remain, making it a 50/50 chance. p4 is modeled as a constant value near 1.0. (D). Joint probabilities associated with reaching different choice points, using the four probability function in panel C. (E). Average expected progress in the list, computed by taking the sums of the joint probabilities in panel D. Thus, given a function for each choice probability pi, one can also model the progress made by participants.