3.1 Description of the model
4.1.2 Parameter estimations for the double target condition
In the next step, I used the estimated drift parameters and residual times to predict the expected choice probabilities and mean reaction times for the double target condition.
Since the model had to be expanded in two decision criteria, one for each target position, I had to re-estimate the parameter for the decision criterion and the size of the bias parameter.3
Table 4.2: Parameters estimated on the double target condition
mi ld rv cs cp
β 1 2 1 1 1
Θ 16 13 14 14 12
Table 4.2 presents the estimated parameters for the bias and the decision criteria for five subjects. The decision criteria are smaller than in the single target condition and their magnitude is about equal for all subjects. For subject mi the distance between the bias coefficient and the decision criterion coefficient is the largest, since mi—unlike the other subjects—did not show strong hemispheric preferences. This is consistent with the estimation in the single target condition, in which subject mi did not show any bias at all. The predicted mean reaction times fit the observed pattern quite well for all subjects.
As it is shown for the subjectsmi and cp in Figures 4.3 and 4.5 (for all the remaining subjects, see Appendix B.2), some mean reaction times are considerably longer or shorter, in absolute figures than those predicted by the model. Furthermore, the fits for the means to un-accompanied stimuli are much poorer than for the accompanied stimuli.
One reason for this might be that there is generally much more scatter in the observed data points to un-accompanied stimuli than to accompanied stimuli since they are based
3For technical reasons I had to include one modification to the diffusion model described in Chapter 3:
The beginning of the process had to be set by the first visual stimulus that was presented, e.g., the visual stimulus at 24◦. In the model, this was achieved by the assumption of an additional time intervalι0. So if a visual stimulus at 24◦ appeared, the drift rate started inι0to raise towards the boundary. However, if the visual stimulus at 8◦ was presented first—which means thatonlystimuli at 8◦were presented—the drift rate in the time intervalι0 was set to zero.
subject mi: visual double stimuli
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8°V 8°AV-50 8°AV0 8°AV50 -8°V -8°AV-50 -8°AV0 -8°AV50
reactiontime[ms]
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8°V 8°AV-50 8°AV0 8°AV50 -24°V -24°AV-50 -24°AV0 -24°AV50
reactiontime[ms]
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-8°V -8°AV-50 -8°AV0 -8°AV50 24°V 24°AV-50 24°AV0 24°AV50
stimulus condition
reactiontime[ms]
gaze at a purely visual stimulus gaze at an accompanied stimulus gaze at an un-accompanied stimulus
gaze at a purely visual stimulus gaze at an
gaze at an
accompanied stimulus un-accompanied stimulus
predicted observed
Figure 4.3: Subject mi: Three double target conditions. Given are the predicted and observed mean reaction times and standard errors.
subject mi: visual double stimuli
0 0.5 1
8°V 8°AV-50 8°AV0 8°AV50 -8°V -8°AV-50 -8°AV0 -8°AV50
probability
0 0.5 1
8°V 8°AV-50 8°AV0 8°AV50 -24°V -24°AV-50 -24°AV0 -24°AV50
probability
0 0.5 1
-8°V -8°AV-50 -8°AV0 -8°AV50 24°V 24°AV-50 24°AV0 24°AV50
stimulus condition
probability
gaze at a purely visual stimulus gaze at an accompanied stimulus gaze at an un-accompanied stimulus
gaze at a purely visual stimulus gaze at an
gaze at an
accompanied stimulus un-accompanied stimulus
predicted observed
gaze at a purely visual stimulus gaze at an accompanied stimulus gaze at an un-accompanied stimulus
Figure 4.4: Subjectmi: Three double target conditions. Given are the predicted and observed probabil-ities.
subject cp: visual double stimuli
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8°V 8°AV-50 8°AV0 8°AV50 -8°V -8°AV-50 -8°AV0 -8°AV50
reactiontime[ms]
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8°V 8°AV-50 8°AV0 8°AV50 -24°V -24°AV-50 -24°AV0 -24°AV50
reactiontime[ms]
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-8°V -8°AV-50 -8°AV0 -8°AV50 24°V 24°AV-50 24°AV0 24°AV50
stimulus condition
reactiontime[ms]
gaze at a purely visual stimulus gaze at an accompanied stimulus gaze at an un-accompanied stimulus
gaze at a purely visual stimulus gaze at an
gaze at an
accompanied stimulus un-accompanied stimulus
predicted observed
gaze at a purely visual stimulus gaze at an accompanied stimulus gaze at an un-accompanied stimulus
Figure 4.5: Subject cp: Three double target conditions. Given are the predicted and observed mean reaction times and standard errors.
subject cp: visual double stimuli
0 0.5 1
8°V 8°AV-50 8°AV0 8°AV50 -8°V -8°AV-50 -8°AV0 -8°AV50
probability
0 0.5 1
8°V 8°AV-50 8°AV0 8°AV50 -24°V -24°AV-50 -24°AV0 -24°AV50
probability
0 0.5 1
-8°V -8°AV-50 -8°AV0 -8°AV50 24°V 24°AV-50 24°AV0 24°AV50
stimulus condition
probability
gaze at a purely visual stimulus gaze at an accompanied stimulus gaze at an un-accompanied stimulus
gaze at a purely visual stimulus gaze at an
gaze at an
accompanied stimulus un-accompanied stimulus
predicted observed
gaze at a purely visual stimulus gaze at an accompanied stimulus gaze at an un-accompanied stimulus
Figure 4.6: Subjectcp: Three double target conditions. Given are the predicted and observed probabili-ties.
on less observations. Figures 4.4 and 4.6 show the respective fits of the probabilities for subjects mi andcp (see Appendix B.2 for the whole sample). Reaction times are ordered according to the SOAs, i.e. an early presentation of the auditory stimulus accelerates the response. In contrast, this is not the case for choice probabilities. For example subjectmi did not select the accompanied stimuli more often if the auditory stimulus appeared 50 ms before the visual stimulus (SOA =−50 ms) than if it appeared at the same time (SOA = 0 ms) as the model would predict. A possible reason for this might be that the data base is too weak to reveal such a relationship. Just notice that one observation corresponds to a change in probability of 2%. Nevertheless, on some conditions the predicted probabilities deviate characteristically from the observed data for some conditions. If the accompanied stimulus appeared at 24◦ left or right of the fixation point, the model predicts much higher probabilities for all SOAs than could be observed.4 This means, the model can not account for a very strong preference for the inner stimulus; instead, it predicts choice probabilities for stimuli at 24◦ higher than observed. This might be due to the fact that I determined all parameters from the single stimulus conditions. Therefore, no spatial relationship between the two visual stimuli is included. In fact, context independence is one necessary requirement of my approach.