Estimating the distribution of sensorimotor synchronization data: A Bayesian hierarchical modeling approach

The sensorimotor synchronization paradigm is used when studying the coordination of rhythmic motor responses with a pacing stimulus and is an important paradigm in the study of human timing and time perception. Two measures of performance frequently calculated using sensorimotor synchronization data are the average offset and variability of the stimulus-to-response asynchronies-the offsets between the stimuli and the motor responses. Here it is shown that assuming that asynchronies are normally distributed when estimating these measures can result in considerable underestimation of both the average offset and variability. This is due to a tendency for the distribution of the asynchronies to be bimodal and left skewed when the interstimulus interval is longer than 2 s. It is argued that (1) this asymmetry is the result of the distribution of the asynchronies being a mixture of two types of responses-predictive and reactive-and (2) the main interest in a sensorimotor synchronization study is the predictive responses. A Bayesian hierarchical modeling approach is proposed in which sensorimotor synchronization data are modeled as coming from a right-censored normal distribution that effectively separates the predictive responses from the reactive responses. Evaluation using both simulated data and experimental data from a study by Repp and Doggett (2007) showed that the proposed approach produces more precise estimates of the average offset and variability, with considerably less underestimation.