Representing uncertainty in the Rescorla-Wagner model: Blocking, the redundancy effect, and outcome base rate

It is generally assumed that the Rescorla and Wagner (1972) model adequately accommodates the full results of simple cue competition experiments in humans (e.g. Dickinson et al., 1984), while the Bush and Mosteller (1951) model cannot. We present simulations that demonstrate this assumption is wrong in at least some circumstances. The Rescorla-Wagner model, as usually applied, fits the full results of a simple forward cue-competition experiment no better than the Bush-Mosteller model. Additionally, we present a novel finding, where letting the associative strength of all cues start at an intermediate value (rather than zero), allows this modified model to provide a better account of the experimental data than the (equivalently modified) Bush-Mosteller model. This modification also allows the Rescorla-Wagner model to account for a redundancy effect experiment (Uengoer et al., 2013); something that the unmodified model is not able to do. Furthermore, the modified Rescorla-Wagner model can accommodate the effect of varying the proportion of trials on which the outcome occurs (i.e. the base rate) on the redundancy effect (Jones et al., 2019). Interestingly, the initial associative strength of cues varies in line with the outcome base rate. We propose that this modification provides a simple way of mathematically representing uncertainty about the causal status of novel cues within the confines of the Rescorla-Wagner model. The theoretical implications of this modification are discussed. We also briefly introduce free and open resources to support formal modelling in associative learning. Keywords: associative learning, prediction error, uncertainty, modelling, blocking, redundancy effect, open science.