Error Correction Processes in Temporal Pattern Production

Abstract

A second-order autoregressive model for error correction is applied to measurements of synchronized tapping by an expert and a nonexpert subject for a wide range of patterns, ranging from simple off-beat tapping to a complex polyrhythm. The model can be seen as an extension of the first order approach of Vorberg and Wing and, also, as a linearized version of a general nonlinear model proposed by the author in another publication. The central measured variable is the asynchrony between presented tone and produced tap. General relations for the asynchrony autocovariance functions are derived, as well as covariance-based expressions for first- and second-order autoregressive error correction parameters. A second method of error parameter estimation, based on "local" binned calculations, is also presented. Combination of the two methods, buttressed by simulations, allows effective characterization of the time series' order and parameter values, and experimental support for the model is found to be strong in all cases. Error correction processes prove to be predominantly first order; second (and possibly higher) order effects occur predominantly under conditions of expertise and relatively high task demands. Expertise in tapping (as determined from these two subjects) is found to lead to reduced bias, reduced asynchrony and interonset variance, and, with the exception of a single case, increased values of error correction parameters relative to untrained performance. In a clear majority of cases where it could be tested, both the AR1 error correction parameter alpha, and the asynchrony and interonset standard deviations showed a strong tendency towards a linear relationship with tapping period. Copyright 1998 Academic Press.