These graphs display the models fitted to each subject's data, while showing locations at which data was sampled. The model has three primary variables (spacing, envelope motion, and carrier strength) which we are concerned with; these variables can be considered to form a three-dimensional stimulus configuration space. The combination of these three variables determines the likelihood with which the observer will respond "clockwise" or "counterclockwise" to the given stimulus. Here we show the model's predictions over four planar sections through this three-dimensional space.
The upper figure (what I'm referring to as upper and lower shows up in the PDF on consecutive pages) shows model responses and observations over four sections. From upper right counterclockwise, we show how (a) model responses vary as a function of spacing and carrier strength, for stimuli with zero envelope motion, (b) as a function of spacing and envelope movement, for stimuli with zero carrier motion, (c) as a function of envelope motion and carrier strength, for stimuli with a fixed, narrow spacing, and (d) as a function of envelope motion and carrier strength (similarly to (c)), for stimuli with a fixed, wide spacing.
Each panel in the upper figure shows the model's predictions as a function of two of the three variables, leaving the other fixed; the value of the fixed variable is noted in the upper right corner of each panel. The shading represents the model's estimated probability of responding "clockwise" for that stimulus, with white representing a probability of 1 and black representing a probability of zero. Dotted contour lines are drawn at probabilities of 0.1, 0.3, 0.5, 0.7, and 0.9.
In the lower figure the four planar sections shown in the upper plot are replotted in perspective, showing the relation between the sections and their relation to the space of stimulus configurations. Shading and contour lines are as in the upper figure.
The upper figure also depicts the observer's responses. Circles plotted are drawn from subjects' responses, with their shading determined by the subject's response. Because a staircase procedure was used to select values of envelope motion, different numbers of trials were collected at each stimulus condition and a large number of stimulus conditions were used. For this graph we sort the set of stimulus conditions into regularly spaced bins, each represented here by a circle. The area of each circle is scaled in proportion to the number of trials collected in its bin.
Trials collected in one bin may take any value in the unseen dimension. For example, in the upper left panel, each circle represents a bin collecting trials in a small range of spacing and carrier strength, but across the entire range of envelope motion. The two panels on the right have the same axes, with spacing narrow for one and wider for the other; we divide the trials up into two groups so that circles in the upper left panel reflect trials with narrower spacings, and circles in the upper right panel reflect wider spacings, as indicated in the annotation at the upper right of each panel. For the other two plots, each circle represents a bin collecting stimuli over the entire range of the missing variable.
The shading of the circle reflects an average of the observers' responses falling within the bin; if the model fits exactly, the interior of each circle will match the exterior. Because the bin may collect stimulus conditions that vary in their expected rates of response, the shade of each circle is determined by the Pearson residual of the trials against the fitted model; we choose a shade that would give the same residual if all stimuli were located at the center of the bin. Thus if the interior of the circle is lighter than the background, it indicates that the observer gave more clockwise responses than the fitted model, aggregated over all stimulus configurations within the bin. (This amounts to a weighted average over the observer's responses in each bin.)