Richard A. Heath

A nonlinear analysis of the temporal characteristics of handwriting

Motor skills provide us with an almost infinite variety of ways in which we can interact with the world. This paper considers the problem of how the psychomotor system translates a stable motor memory into an invariant spatial output within an infinitely variable biomechanical and environmental context. Initially the validity of a novel methodology, based on the concatenation of handwriting velocity data over several trials to form long time series, combined with singular value decomposition to reduce noise, was confirmed. The data analyzed were the horizontal and vertical velocity of the stylus as eight participants wrote the pseudo-word madronal on a computer graphics tablet. Nonlinear dynamic analysis techniques such as examination of delay portraits, as well as calculation of the correlation dimension and Lyapunov spectra were applied to test the hypothesis that handwriting velocity profiles are chaotic. The findings that the largest Lyapunov exponents were positive, the sums of Lyapunov spectra components were negative and the correlation dimensions were low and fractional supported this hypothesis. We conclude by proposing that the psychomotor actions found in handwriting are a product of a chaotic dynamic process whose initial conditions depend on the environmental and biomechanical context.

A general nonstationary diffusion model for two-choice decision-making

Abstract A general diffusion model for two-choice decision-making is proposed. This model can accommodate time-dependent and space-dependent diffusion process parameters, as well as time-dependent response thresholds. A tractable algorithm, based upon the work of Ricciardi and Durbin, is employed to compute the response conditioned decision time densities and applications of this algorithm are presented for the generalized cascade process model and the Ornstein-Uhlenbeck model. It is suggested that a suitable strategy for examining time-dependent information processing mechanisms, such as those operating when the relevant stimulus information is only available for a brief time period, is to use the response- signal RT deadline method to compute the time-dependent drift function which can then be used by the algorithm to compute predicted response conditioned decision time densities. Possible applications of these techniques in cognitive psychology are discussed.

Random-Walk and Accumulator Models of Psychophysical Discrimination: A Critical Evaluation

The accumulator model proposed by Vickers and the modified random-walk model proposed by Link and Heath are compared in their ability to account for confidence judgments in line-length discrimination tasks. The random-walk model proves to be a viable alternative to the accumulator model, and is able to account for the relationship between mean response time and confidence. The parameter estimation techniques available for the random-walk model are considered advantageous when compared with the accumulator model, because the predictions from the latter have been obtained with the use of computer simulation.

Category Norms for Australians

Responses to 28 category titles were, generated by 620 subjects sampled from the Riverina-Murray Institute of Higher Education, the University of Newcastle, NSW and a cross-section of the community. The response frequencies for items from each category correlated highly across the three samples. However, the correlations were significantly lower between the Riverina-Murray norms and norms from other cultures, implying that Australian norms should be used with Australian subjects. The categories could be represented by two dimensions which measured the ease with which responses are generated and the similarity between responses across subjects.

Can People Predict Chaotic Sequences

Previous studies suggesting that people predict chaotic sequences better than chance have not discriminated between sensitivity to nonlinear determinism and facilitation using autocorrelation. Since prediction accuracy declines with increases in the look-ahead window in both cases, a decline in prediction accuracy does not imply chaos sensitivity. To overcome this problem, phase-randomized surrogate time series are used as a control. Such series have the same linear properties as the original chaotic sequence but contain no nonlinear determinism, i.e. chaos. In the experimental task, using a chaotic Hénon attractor, participants viewed the previous eight days temperatures and then predicted temperatures for the next four days, over 120 trials. The control group experienced a sample from a corresponding phase-randomized surrogate series. Both time series were linearly transformed to provide a realistic temperature range. A transformation of the correlation between observed and predicted values decreased over days for the chaotic time series, but remained constant and high for the surrogate series. The interaction between the days and series factors was statistically significant, suggesting that people are sensitive to chaos, even when the autocorrelation functions and power spectra of the control and experimental series are identical. Implications for the psychological assessment of individual differences in human prediction are discussed.

Response Time and Temporal Order Judgement in Vision

Abstract Both response proportion and response time (RT) measures were obtained in a task requiring temporal order judgements (TOJ) of the illumination of two lights. The decrease in mean RT as the inter-stimulus interval increased enabled the deterministic decision rule for TOJ to be rejected. Although the data were not inconsistent with a decision process incorporating a threshold for temporal resolution, a model based on a random walk process accounted for important features of the data. The implications of these results for the commonly employed “perceived-order” method are discussed.

Detecting nonlinearity in psychological data: Techniques and applications

Modern graphical and computational techniques for detecting nonlinearity in psychological data sets are presented. These procedures allow researchers to determine the information complexity of temporal data, using physiological and psychological measurements, and to provide evidence for chaos in time series contaminated by measurement noise. Problems with noise reduction and appropriate experimental control, using surrogate time series, are discussed, and applications of the technology are illustrated, using response time, handwriting, and typing data sets. In an experimental application of appropriate nonlinear analysis procedures, the results of a time series prediction experiment confirm that some subjects are sensitive to chaos. In contrast to previous attempts demonstrating sensitivity to chaos, the experiment reported here employs surrogate series to control for linear stochastic aspects of the stimulus sequences, such as autocorrelation. Recommendations for the selection of appropriate software for performing nonlinear analyses are presented, including a comprehensive list of World-Wide Web sites offering such software.

A stochastic model for inter-keypress times in a typing task

A mathematical model for the inter-keypress times (IKT) in a typing task is proposed. The model, which includes a diffusion process terminated by a single response threshold, was evaluated using data obtained from typists. The differences in performance for successive cross-hand and within-hand keypresses were examined using IKT distributions and hazard functions, and it was shown that the empirical hazard functions could be fit by the theoretical hazard function derived from the convolution of normal and inverse Gaussian random variables. Some possible applications of the model for the evaluation of fatigue and strategic effects in typing are suggested.

A model for signal detection based on an adaptive filter

A model for the detection of brief stimuli based on a change detection algorithm and a random walk traversed by the residuals generated by an adaptive filter is proposed. A linear relationship between mean RT and response proportion measures obtained in a simulation of the model was consistent with data obtained in psychophysical discrimination tasks using human observers. In this way the role of the sensory system as a detector of change in ambient stimulation could be incorporated into a signal detection model.

The Ornstein-Uhlenbeck model for decision time in cognitive tasks: An example of control of nonlinear network dynamics

Abstract The Ornstein-Uhlenbeck (OU) model for human decision-making has been successfully applied to account for response accuracy and response time (RT) data in recent two-choice decision models. A variant of the OU model is shown to arise from the response dynamics of a nonlinear network consisting of randomly connected neural processing units. When feedback control of the network is effected by the stimulus onset, the average network response is an autocorrelated random signal satisfying the stochastic differential equation for the OU process. An alternative, more general, stimulus detection procedure is proposed which involves the use of an adaptive Kalman filter process to track any temporal change in autoregressive parameters. The predicted decision time distributions suggest that both the OU and the Kalman filter processes can serve as alternative models for RT data in experimental tasks.