Parameter Estimation of Linear Sensorimotor Synchronization Models: Phase Correction, Period Correction, and Ensemble Synchronization

Linear models have been used in several contexts to study the mechanisms that underpin sensorimotor synchronization. Given that their parameters are often linked to psychological processes such as phase correction and period correction, the fit of the parameters to experimental data is an important practical question. We present a unified method for parameter estimation of linear sensorimotor synchronization models that extends available techniques and enhances their usability. This method enables reliable and efficient analysis of experimental data for single subject and multi-person synchronization. In a previous paper (Jacoby et al., 2015), we showed how to significantly reduce the estimation error and eliminate the bias of parameter estimation methods by adding a simple and empirically justified constraint on the parameter space. By applying this constraint in conjunction with the tools of matrix algebra, we here develop a novel method for estimating the parameters of most linear models described in the literature. Through extensive simulations, we demonstrate that our method reliably and efficiently recovers the parameters of two influential linear models: Vorberg and Wing (1996), and Schulze et al. (2005), together with their multi-person generalization to ensemble synchronization. We discuss how our method can be applied to include the study of individual differences in sensorimotor synchronization ability, for example, in clinical populations and ensemble musicians.

Implementation of the bGLS Method
For more information see in Timing & Time Perception, Special issue on Rhythm Production and Perception (RPPW):
Jacoby, N., Tishby, N., Repp, B. H., Ahissar, M., & Keller, P. E. (2015). Parameter estimation of linear
sensorimotor synchronization models: Phase correction, period correction and ensemble synchronization. Timing Time Percept., 3, 52-87.
and
Jacoby, N., Keller, P. E., Repp, B. H., Ahissar, M., & Tishby, N. (2015). Lower bound on the accuracy
of parameter estimation methods for linear sensorimotor synchronization models. Timing Time
Percept., 3, 32-51.

Nori.viola@gmail.com
Please cite this paper if you are using this package:
Nori Jacoby, Naftali Tishby, Bruno H. Repp, Merav Ahissar and Peter E. Keller (2015)

IMPORTANT: This code is currently (12/14) in beta.
Critical updates will be forthcoming.

ALL CODE BY: Nori Jacoby (nori.viola@gmail.com)