Costo de Operación

One issue that arises from simulation 1 concerns the degree to which the randomness or otherwise of the sequences that the model generates are dependent upon the values of its parameters. A more detailed examination of the model’s parameter space is in order both to understand the mechanisms within the model that lead to deviations from expected values for the various measures and to ensure that the model cannot capture any pattern of behaviour (cf. Roberts & Pashler, 2000). This is the purpose of the simulation presented here. We consider the five key parameters relating to the operation of Working Memory, Monitoring, and Task Control discussed above, namely WM Decay Time, WM Update Efficiency, Monitoring Efficiency, Switch Rate, and Temperature.

7.1 Method

Five separate simulations were run, one for each of the key parameters. In each case, the value of the parameter was varied across a wide range, with 21 values chosen at equal intervals from the minimum to the maximum values. (For example, WM Decay Time was varied from 0 to 40 at intervals of 2, while Switch Rate was varied from 1.00 to 0.00 at intervals of 0.05.) Each simulation was run 36 times at each setting of the parameters to yield a sample of 36 simulated subjects for each point in parameter space. The means and standard deviations of all six indices of randomness were then calculated for each sample within each of the five simulations.

7.2 Results

Figure S1 shows how the values of the various measures of randomness (transformed to z- scores based on the mean and standard deviation of the baseline subjects) vary as a function of each parameter, when all other parameters are held at their values used in simulation 1. Panel a) of the figure shows the case of varying WM Decay Time. Several measures, particularly RNG, RR and AR, are insensitive to variation in WM Decay Time, while others – most notably R and TPI – are not. Thus when WM Decay Time is low (e.g., up to about 8 cycles), the model produces an R score that is one to two standard deviations above that of human subjects. As WM Decay Time increases, R decreases to the level of human subjects. TPI behaves in a similar fashion. The former reflects the role that a record of recent responses (held in Working Memory) plays in balancing response usage. Monitoring typically rejects putative responses that are known to have been produced recently (on the basis of their presence in Working Memory). Degrading Working Memory therefore results in an increasing R score, resulting ultimately in a score that is similar to chance when WM Decay Time is very low (4 or less). The high values of TPI when WM Decay Time is low also reflect chance performance on this measure. As one would expect, however, the deviation from baseline performance for all dependent measures is close to zero when WM Decay Time is near the value adopted in simulation 1 (i.e., 30 cycles).

Panel b) of the figure S1 shows the effect of decreasing WM Update Efficiency from its default value of 1.00 to its minimum value of 0.00. Again, the various measures of randomness are differentially sensitive to the manipulation, but RR and R are clearly highly sensitive to any departure from perfect updating. Indeed, the model only matches human performance on these measures when WM Update Efficiency is 1.00. The reason for the high rates of repeat responses at lower values is that when WM Update Efficiency is less than 1.00 there is a possibility that responses are generated without being recorded in Working Memory. In the absence of such a record, Monitoring has no way to inhibit putative responses (like repeats) that would normally be suppressed.

Figure S1: Effects of varying key parameters on each measure of randomness. Each panel shows the values of each measure of randomness as a function of the value of one parameter, with the measures of randomness in each case transformed to z-scores with respect to the data from the human subjects. This transformation a) allows all measures to be shown in a single graph and b) means that a value of zero corresponds to the group mean from the baseline subjects. Error bars represent one standard error.

The model’s behaviour is less sensitive to the efficiency of the Monitoring process, as shown in figure S1 panel c). There is a broad range (from about 0.75 to 0.50) where all dependent measures are close to the values observed in the baseline subjects. Some measures (R and TPI) increase slightly when Monitoring Efficiency falls below 0.50, while R also decreases slightly when Monitoring Efficiency is greater than 0.75.

The effects of varying the parameters related to Task Control are shown in figure S1 panels d) and e). The primary effect of decreasing Switch Rate is a decrease in TPI, due to the model failing to switch (and hence failing to switch between clockwise and counter- clockwise selection) sufficiently frequently, though at very low values of Switch Rate other measures (most notably R, RNG, RR and OA) also diverge from the values obtained from human subjects. In contrast, variation in Temperature affects all measures of randomness. When the temperature is substantially less than 1.00, inherent schema selection biases (e.g., resulting in a tendency towards adjacent or opposite responses) are strong, while when the temperature is substantially greater than 1.00 these biases are weak, leading most notably to high rates of repeat responses.

7.3 Discussion

These simulations demonstrate that behaviour of the model is: a) relatively insensitive to WM Update Rate, provided that parameter is more than about 15; b) highly sensitive to WM Update Efficiency, which must be very near 1.0 for baseline performance; c) reasonably constant over a wide range of Monitoring Efficiency; d) dependent upon Switch Rate, which must be above approximately 0.8 or higher for baseline performance; and e) sensitive to the Temperature of Task Control which must be near 1.0 for baseline performance. As perhaps one might expect, the various dependent measures sometimes co-vary as parameter values are altered, but the dependencies between the dependent measures are complex.

While the simulations reported in this section do not rule out the possibility that the model might be tuned to account for any pattern of measures across the six dependent measures (cf. Roberts & Pashler, 2000), they do demonstrate the model’s performance is not dependent on engineering the values of key parameters to specific values. With the exception of WM Update Efficiency, there is some freedom in the setting of parameter values needed to capture baseline performance. This is striking given that the simulations aim to fit the values of six dependent measures simultaneously.

Analysis of the model’s behaviour when parameters are varied is also instructive. Miyake and colleagues (2000) extracted two principal components from the indices of randomness calculated from their subject data: equality of response usage, which was reflected primarily in subjects’ R scores and held to reflect the efficacy of their Memory Monitoring and Updating executive function; and prepotent associates, which was reflected in TPI, RNG and adjacency measures and held to reflect the efficacy of their Response Inhibition executive function. Consistent with the former, in the current simulations, and with all other things being equal, very high values of Monitoring Efficiency result in lower values of R than more moderate values of Monitoring Efficiency, yet variation of this parameter (at the top end of its range) has no effect on other measures of randomness. The latter is less easily reconciled with the current model. However, prepotent associates tend to dominate responses when Temperature is substantially less than 1.0. Thus values of Temperature in the 0.7 to 0.3 range have a greater effect on several measures of prepotent associates (particularly RNG and AR). Whether this reflects ineffective inhibition processes or some other factor is unclear, though this issue is discussed further in relation to simulation 2 and in the General Discussion.