Multilevel modelling of simultaneity judgements discriminates between observer models and reveals how participants’ strategy influences the window of subjective synchrony

Abstract

When experimenters vary the timing between two intersensory events, and participants judge their simultaneity, a non-standard (i.e. non-sigmoidal, non-monotonic) psychometric function is obtained. Typically, this function is first characterised (i.e. fitted with a model) for each participant separately, before parameters that maximise the likelihood of the model are utilised (e.g. compared across conditions) in the second stage of a two-step inferential procedure. Often, the width of the psychometric function is interpreted as representing sensitivity to asynchrony, and/or ascribed theoretical equivalence to a window of multisensory temporal binding. Here, we adopt an alternative inferential approach in which a single (principled) Bayesian multilevel model is fitted to data from the entire group and across several conditions at once. In a simple experiment in which 19 participants were sometimes asked to be more conservative in their simultaneity judgements, we demonstrate how the width of the simultaneity function is prone to strategic change and thus questionable as a measure of either sensitivity or multisensory binding. By repeating our analysis with three different recently advocated models (two that imply a decision based on subjective asynchrony, and one that generates changes in perceived synchrony from the correlation between filtered responses to sensory inputs) we provide templates for a range of alternatives within the Bayesian multilevel framework, and find that one of the three models, which hypothesises Gaussian latency noise and difficulty maintaining the stability of decision criteria across trials, provides the most plausible account for this data set.