Reaction Time "Mismatch Costs" Change with the Likelihood of Stimulus-Response Compatibility

Abstract

Dyadic interactions require dynamic correspondence between one's own movements and those of the other agent. This mapping is largely viewed as imitative, with the behavioural hallmark being a reaction-time cost for mismatched actions. Yet the complex motor patterns humans enact together extend beyond direct-matching, varying adaptively between imitation, complementary movements, and counter-imitation. Optimal behaviour requires an agent to predict not only what is likely to be observed but also how that observed action will relate to their own motor planning. In 28 healthy adults, we examined imitation and counter-imitation in a task that varied the likelihood of stimulus-response congruence from highly predictable, to moderately predictable, to unpredictable. To gain mechanistic insights into the statistical learning of stimulus-response compatibility, we compared two computational models of behaviour: (1) a classic fixed learning-rate model (Rescorla-Wagner reinforcement [RW]) and (2) a hierarchical model of perceptual-behavioural processes in which the learning rate adapts to the inferred environmental volatility (hierarchical Gaussian filter [HGF]). Though more complex and hence penalized by model selection, the HGF provided a more likely model of the participants' behaviour. Matching motor responses were only primed (faster) in the most experimentally volatile context. This bias was reversed so that mismatched actions were primed when beliefs about volatility were lower. Inferential statistics indicated that matching responses were only primed in unpredictable contexts when stimuli-response congruence was at 50:50 chance. Outside of these unpredictable blocks the classic stimulus-response compatibility effect was reversed: Incongruent responses were faster than congruent ones. We show that hierarchical Bayesian learning of environmental statistics may underlie response priming during dyadic interactions.

Keywords: Bayesian active inference; Counter-imitation; Heirachical Gaussian filter; Imitation; Learning; Predictive coding; Reaction time; Rescorla–Wagner.

Fig. 1

Behavioural paradigm showing manipulation of the SR (SR) congruence with diagram of the task trials, with all combinations of cues and stimuli depicted, producing matching or mismatching SR pairs and the timing of trial events. The final frames of example stimulus videos are shown

Fig. 2

Example sequences of 400 trial across 10 blocks for the behavioural task, demonstrating our block-wise manipulation of the likelihood of SR congruence. The order of changing likelihoods (red dotted line, plotted as the probability of a matching SR pair) was counterbalanced across participants with two alternative sequences (compare the top and bottom plots show block orders 1 and 2). Within each block a random order of trials was generated for each participant. Example runs of trial types for each block sequence are displayed in purple (1= SR match, 0= mismatch), and this served as a binary input for computational models. (Colour figure online)

Fig. 3

Representation of the perceptual and response models of the HGF (adapted from Marshall et al., 2016). Beliefs are represented in probability distributions arranged hierarchically, with the updating of each level influenced by the estimate in the level above. The perceptual model tracks the participant’s learning of task structure in three levels: the trial-wise encoding of SR pairs (x₁), the probability of SR congruence (x₂) and the volatility of this tendency over time (x₃), for the current trial t. Omega and theta (ω, ϑ) are parameters that couple the levels and control the rate of belief updating for that participant. The response model maps the participant's trial-wise beliefs onto the observed changes in log reaction time (RT), with decision noise captured by zeta (ζ, Gaussian noise term). (Colour figure online)

Fig. 4

Mean reaction-time difference for match–mismatch, with negative values indicating a “mismatch cost.” The dark purple circles and error bars show the group mean with ±95% confidence intervals around the group mean. Transparent dots represent individual participant means. ** denotes Bonferroni-corrected p < .001, NS = not significant. Note. The greyed shading for the probability contexts of p(SR match) 0.1 and 0.9 indicates that these were not included in the statistical tests for the effect of probability on RT differences due to the fewer number of trials. (Colour figure online)

Fig. 5

A Difference in log model evidence (LME) for HGF and RW models for each participant. Positive values indicate model evidence favours the HGF. B Dirichlet density describing the probability of model 1 (HGF model) given the data y (log RT). The shaded area representing the exceedance probability of the HGF being more likely than the Rescorla–Wagner model; variational Bayes estimates of the Dirichlet parameters of each model: α_HGF = 29, α_RW = 1;〈r〉conditional expectations of the probabilities of the two models

Fig. 6

Two example trial-by-trial trajectories of HGF estimates for each block sequences (A and B) given binary input (purple dots, Level 1) and block-wise probability of match trial (dashed red lines, Level 1) of expected input (orange), learning rate (black); Level 2: tendency (yellow) volatility (green, Level 3). (Colour figure online)

Fig. 7

Mean and distribution of volatility estimates by block condition (probability context) with error bars showing 95% CI, overlayed on individual subject’s mean volatility estimate

Fig. 8

Reaction-time modelling in an example participant. A Observed reaction times for a participant completing Block Sequence 2. Predicted reaction times for the (B) HGF and (C) RW models. (Colour figure online)

Fig. 9

Comparison of estimated and observed mean reaction times using the drift-diffusion model with either HGF or RW perceptual parameters. A Subject-wise mean estimates of RT from the diffusion decision models based on either the RW (orange) and the HGF (blue) against the observed (purple) mean reaction time. Overall group mean estimated versus observed reaction time is plotted at the end. B Mean reaction times for SR compatibility with observed (purple), against the estimated values for response models with parameters derived from the HGF (blue), and RW (orange) perceptual models. (Colour figure online)