Inference on variance components of autocorrelated sequences in the presence of drift

A generative model for measuring latent timing structure in motor sequences

Motor variability often reflects a mixture of different neural and peripheral sources operating over a range of timescales. We present a statistical model of sequence timing that can be used to measure three distinct components of timing variability: global tempo changes that are spread across the sequence, such as might stem from neuromodulatory sources with widespread influence; fast, uncorrelated timing noise, stemming from noisy components within the neural system; and timing jitter that does not alter the timing of subsequent elements, such as might be caused by variation in the motor periphery or by measurement error. In addition to quantifying the variability contributed by each of these latent factors in the data, the approach assigns maximum likelihood estimates of each factor on a trial-to-trial basis. We applied the model to adult zebra finch song, a temporally complex behavior with rich structure on multiple timescales. We find that individual song vocalizations (syllables) contain roughly equal amounts of variability in each of the three components while overall song length is dominated by global tempo changes. Across our sample of syllables, both global and independent variability scale with average length while timing jitter does not, a pattern consistent with the Wing and Kristofferson (1973) model of sequence timing. We also find significant day-to-day drift in all three timing sources, but a circadian pattern in tempo only. In tests using artificially generated data, the model successfully separates out the different components with small error. The approach provides a general framework for extracting distinct sources of timing variability within action sequences, and can be applied to neural and behavioral data from a wide array of systems.

Multiple time scales in serial production of force: a tutorial on power spectral analysis of motor variability

We present a tutorial on a power spectral approach to variability in serial motor performance, describing as a case study two experiments on the form of the variance in two force production tasks. In Experiment 1 we examine grip force and load force in repetitive unimanual pulling; in Experiment 2, we describe repetitive bimanual pressing. In both experiments log-log plots of power spectral density of peak force of the responses in each stream against frequency (i.e. periodicity or repetition cycle defined with respect to the ordered succession of responses) were approximately linear with negative slopes which varied systematically with test conditions. We propose the two response streams in each experiment are associated with different levels of sustained attention and state a simple model involving summation of moving average processes on multiple time scales as a qualitative account of the changes in 1/f slope.

Adding Drift to the Decomposition of Simple Isochronous Tapping: An Extension of the Wing-Kristofferson Model

The Wing-Kristofferson model (A. M. Wing & A. B. Kristofferson, (1973a, 1973b) decomposes the variance of isochronous finger tapping into 2 components: a central clock component and a peripheral motor component. The method assumes that there is no drift in the intertap intervals. A new method is introduced that further decomposes the clock component drift and drift-free clock variance. The method was studied through simulation and empirical analyses. Clock variance was the most prominent, followed by drift, and then motor variance. Individual and group differences were larger for the motor and drift variances than for the drift-free clock variance, so that group differences observed in the past may have been partially due to the failure to fully remove drift. The authors argue that the methods presented and extensions thereon show great promise in extending a method in wide use since 1973.