Mission: Impossible? Modelling the Verbal Estimation of Duration

in Timing & Time Perception
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Three participants produced a large number of verbal estimates of tone durations in the range of 77–1183 ms. Data from this task were simulated by an ‘attractor model’, which used the idea of competition between ‘attractors’ (‘quantized’ values output as verbal estimates) which differed in weight, and distance from the stimulus duration to be estimated. To produce an estimate, all attractors competed for priority as output values, with the final value being decided probabilistically. The model embodied underlying scalar representations of time, in the form of mean accuracy and constant coefficient of variation. The model was able to reconcile such scalar properties of time with deviations from scalar properties often found in verbal estimation data, such as declining coefficients of variation with increasing duration value. The model furthermore showed that multiplicative and additive changes in underlying time representations should be translated veridically into behaviour, although the attractor competition process could distort patterns and absolute values of underlying variance.

Mission: Impossible? Modelling the Verbal Estimation of Duration

in Timing & Time Perception

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References

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Figures

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    Mean verbal estimates in ms (left panel), and coefficients of variation (right panel), plotted against stimulus duration for the three participants (P91, P93, and P95) used in the experiment.

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    The attractor set used in the initial simulations with the attractor model. Attractor value is indicated by location on the x-axis, attractor weight shown on the y-axis.

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    Left panel: Simulated mean verbal estimates using the attractor set shown in Fig. 1. The best-fitting regression line, and its slope, intercept, and r2 value are shown. Right panel: simulated coefficients of variation derived from the simulated results whose mean is shown in the left panel.

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    Left panel: Effects of varying the underlying coefficient of variation of the model, c, over values of 0.15, 0.25, and 0.35. Simulated coefficients of variation are plotted against stimulus duration. Right panel: simulations of verbal estimation of auditory stimuli, visual stimuli, and auditory stimuli preceded by clicks. Simulated mean verbal estimates are plotted against stimulus duration for the three conditions. See text for details.

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    Effects of additive changes on underlying duration values on simulated mean verbal estimates. For the simulation, the underlying duration values were reduced by 0 (normal) or by 10, 25, or 50 ms.

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    Simulated mean verbal estimates (left panel) and coefficients of variation (right panel) plotted against stimulus duration using the attractor set described in the text.

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    Simulated mean verbal estimates (left panel) and coefficients of variation (right panel) plotted against stimulus duration using the attractor set described in the text.

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    Upper panels: simulated mean verbal estimates; lower panels: simulated coefficients of variation, derived from simulations with the attractor sets described in the text.

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    Relative frequency of output values used by P91 (upper left panel), P93 (upper right panel), and P95 (lower panel) in estimates produced in the last ten sessions of the experiment.

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    Relative frequency of output values used for the 348 ms stimulus duration. Upper left panel: P91; upper right panel: P93; lower panel: P95.

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    Simulated mean verbal estimates for the three participants using the output frequencies shown in Fig. 10 as attractor values and weights. The line in each panel shows the means obtained in the experiment.

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    Simulated coefficients of variation using the output frequencies from Fig. 10 as the attractor set. The line shows coefficients of variation obtained in the experiment.

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    Simulation of relative frequency of output values used for the 348 ms stimulus duration. The dotted line shows data from the experiment.

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