Modelling generalisation gradients as augmented Gaussian functions

Studying generalisation of associative learning requires analysis of response gradients measured over a continuous stimulus dimension. In human studies, there is often a high degree of individual variation in the gradients, making it difficult to draw conclusions about group-level trends with traditional statistical methods. Here, we demonstrate a novel method of analysing generalisation gradients based on hierarchical Bayesian curve-fitting. This method involves fitting an augmented (asymmetrical) Gaussian function to individual gradients and estimating its parameters in a hierarchical Bayesian framework. We show how the posteriors can be used to characterise group differences in generalisation and how classic generalisation phenomena such as peak shift and area shift can be measured and inferred. Estimation of descriptive parameters can provide a detailed and informative way of analysing human generalisation gradients.