Definition of Loss Aversion (LA) and Correlation Between Measures.

<p><b>(a)</b> The local definition of LA focuses on the slopes of the value function on the either side of an inflection point between approach and avoidance (s+ and s- respectively), or gains and losses. Measures of s+ and s- are collected close to the origin (see green and purple boxes), where the scale of value will minimally bias assessments of risk. The slopes <b>(b)</b> s+ and <b>(c)</b> s- are schematized for two representative curves from one individual. <b>(d)</b> LA is computed by the absolute value of the ratio of s- to s+, and is summed over the 10% of the graph on either side of the origin or inflection point. LA from this graph is quite similar to that reported by Kahneman and Tversky [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0135216#pone.0135216.ref005" target="_blank">5</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0135216#pone.0135216.ref042" target="_blank">42</a>]. <b>(e)</b> Correlation of LA from the anticipatory phase of the PT-based task and from the RPT-based task, showing a significant effect after correction for multiple comparisons.</p

The Commonality of Loss Aversion across Procedures and Stimuli

<div><p>Individuals tend to give losses approximately 2-fold the weight that they give gains. Such approximations of loss aversion (LA) are almost always measured in the stimulus domain of money, rather than objects or pictures. Recent work on preference-based decision-making with a schedule-less keypress task (relative preference theory, RPT) has provided a mathematical formulation for LA similar to that in prospect theory (PT), but makes no parametric assumptions in the computation of LA, uses a variable tied to communication theory (i.e., the Shannon entropy or information), and works readily with non-monetary stimuli. We evaluated if these distinct frameworks described similar LA in healthy subjects, and found that LA during the anticipation phase of the PT-based task correlated significantly with LA related to the RPT-based task. Given the ease with which non-monetary stimuli can be used on the Internet, or in animal studies, these findings open an extensive range of applications for the study of loss aversion. Furthermore, the emergence of methodology that can be used to measure preference for both social stimuli and money brings a common framework to the evaluation of preference in both social psychology and behavioral economics.</p></div

Experimental Procedures and Resulting Value Functions.

<p><b>(a)</b> The PT-based experiment used two “gambles”, schematized by two spinners. One spinner showed two-thirds of its area as gains (+$10) and one-third as losses (-$8), leading to an expected outcome (i.e., referred to as actuarial outcome in Breiter et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0135216#pone.0135216.ref038" target="_blank">38</a>]) of +$4. The second spinner showed one-thirds of its area as gains (+$10) and two-thirds as losses (-$8), leading to an expected outcome of-$2. Each trial lasted 20 seconds, with 10s focused on the arrow spinning (anticipation phase) and 10s focused on the arrow stopping, and the win/loss flickering (outcome phase). Order of presentation between the PT-based experiment and RPT-based experiment was counterbalanced across subjects. <b>(b)</b> The RPT-based experiment used a keypress procedure [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0135216#pone.0135216.ref021" target="_blank">21</a>]: a picture would appear for 200ms, then be replaced by a fixation point for 1800ms. After 2000ms, the face would reappear, and if subjects did nothing, the face would stay up another 6000ms (e.g., default condition). Subjects could increase viewing time via a scalloping resistive function, getting close to maximum 1400ms. Alternatively, they could decrease viewing time with the same resistive function close to a minimum of 2000ms. The scalloping resistive function incrementally reduced the viewing time alteration achieved by each keypress, so subjects needed to exert effort to increase or reduce viewing times. Its mathematical formulation can be found in Kim et al. [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0135216#pone.0135216.ref021" target="_blank">21</a>], along with multiple control analyses about its impact on subject behavior. <b>(c)</b> The value function for the PT-based experiment mapped subjective ratings made during the anticipation phase of the experiment on the y-axis, and the actuarial amount of the spinner on the x-axis. For the outcome phase of this experiment, the value function mapped the subjective ratings made when the arrow stopped spinning against the gain or loss. <b>(d)</b> The RPT-based graph showed the mean intensity of keypressing to increase viewtime (K₊) or decrease viewtime (K_-) calibrated against the Shannon entropy of keypress patterns to increase (H₊) or decrease (H_-) viewtime. Solid and empty triangles stand for individual data points for the five categories of facial expressions.</p

Clinical characteristics of cervical dystonia patients.

*<p>subjects included in 2006 study using different analyses.</p><p>BFM: Burke Fahn Marsden dystonia rating scale.</p><p>Tsui: Tsui rating scale for cervical dystonia.</p><p>TW: Toronto Western Spasmodic Torticollis Rating Scale (TWSTRS) for cervical dyston.</p

Group differences for voxel-wise probabilistic diffusion tractography contrast (12 cervical dystonia patients versus 12 matched controls).

*<p>Met significance criteria (p<0.00011 [p<0.05 corrected, or t = 4.70] for t values, and 291 voxels for cluster threshold).</p><p>Negative t values indicate that tractography measures were reduced in cervical dystonia patients relative to control subjects. Positive t values indicate that tractography measures were elevated in cervical dystonia patients relative to control subjects. Note that all regions included in the cluster are reported; however, only one peak within the cluster was required to reach statistical significance (t>4.12). t values are reported for all regions exhibiting peaks of 3.5 or greater. L = left hemisphere; R = right hemisphere; wm = white matter.</p

Group differences for voxel-wise FA contrast (12 cervical dystonia patients versus 12 matched controls).

*<p>Met significance criteria (p<0.00022, [p<0.05, corrected, or t = 4.42] for t values, and 72 voxels for cluster threshold).</p>†<p>p value was within an order of magnitude of the corrected threshold (a trend).</p><p>Positive t values indicate FA values were elevated in cervical dystonia patients relative to control subjects; negative t values indicate FA values were reduced in cervical dystonia patients relative to control subjects. L = left hemisphere; R = right hemisphere; wm = white matter.</p

Regions of probabilistic diffusion tractography that were significantly different between cervical dystonia patients and controls.

<p>(A) shows reduced tractography from the left AL seed region, and (B) shows elevated tractography from the right pallidal seed region. Arrows point to the region through which we drew ROIs in our previous DTI study, which includes AL fibers. <i>A priori</i> segmented regions are shown as reference points: Pink = red nucleus; White = substantia nigra; Blue = pedunculopontine nucleus. MNI talairach coordinates are indicated for each two dimensional image. Lower images in each panel show three dimensional rendering of clusters; the image for the left AL includes the AL seed region in green, and the patient/control difference is shown in blue. t maps and three dimensional clusters are superimposed on the average FA map for all 24 subjects in the study for anatomical reference, and are thresholded at t = +/−2.07 (the threshold used to identify difference clusters, p<0.05, uncorrected, for df = 22). The color bars indicate the range of t values in each panel, from +/−2.07 to the peak t value for each contrast. Warm tones (red, orange, yellow) indicate regions in which cervical dystonia patients exhibited elevated tractography relative to control subjects. Cool tones (blues) indicate regions in which cervical dystonia patients exhibited reduced tractography relative to control subjects. Three dimensional images are shown in mono-color rather than graded/multi-color to illustrate location rather than significance. LH: left hemisphere; RH: right hemisphere.</p

Significant FA differences in cervical dystonia patients relative to control subjects.

<p>(A) Reduced FA in the left cerebellar white matter in patients. (B) Increased FA adjacent to and overlapping with the left substantia nigra in patients. MNI talairach coordinates are indicated for each image. t maps are superimposed on the average FA map for all 24 subjects in the study, and are thresholded at t = +/−2.5 here for illustrative purposes. The color bar indicates the range of t values in this figure for FA contrasts, from +/−2.5 to the peak positive and negative t values for this contrast. Warm tones (red, orange, yellow) indicate regions in which cervical dystonia patients exhibited elevated FA relative to control subjects. Cool tones (blues) indicate regions in which cervical dystonia patients exhibited reduced FA relative to control subjects. LH: left hemisphere; RH: right hemisphere.</p

Probabilistic diffusion tractography and overlap with <i>a priori</i> areas of evaluation (AOEs) used for the FA and MD contrasts.

<p>(A) Examples of tractography from the left ansa lenticularis (AL) seed region, averaged across control subjects (before contrasts were conducted), thresholded at 500 (samples). Note that tractography bifurcated at the level of the substantia nigra (see axial image). (B) Examples of tractography from the left pallidal seed region, averaged across control subjects (before contrasts were conducted), thresholded at 500. Like AL tractography, pallidal tractography bifurcated at the level of the substantia nigra (see axial image). There were also two projections to the thalamus, one superior and one more ventral (see sagittal image). (C) Intersection of tractography with segmentations of our <i>a priori</i> AOEs, including (in descending order) the ansa lenticularis (green), the substantia nigra (white), the red nucleus (pink), the pedunculopontine nucleus (blue), and the superior cerebellar peduncle (peach). Tractography maps are superimposed on the average FA map for all 24 subjects in the study. (D) Example of type Ib GPi neuron from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031654#pone.0031654-Parent1" target="_blank">[21]</a>, showing extensive arborization, including to the RN and PPN (reprinted with permission from The Journal of Comparative Neurology). MNI talairach coordinates are indicated for all images. LH: left hemisphere; RH: right hemisphere.</p

Voxel based morphometry in cervical dystonia.

<p>Voxel based morphometry demonstrated reduced gray matter local tissue volume in the posterior cingulate (A and B, blue voxels, shown at two significance thresholds, presented as family-wise uncorrected p-values), but no differences in the thalamus, in cervical dystonia (family-wise error corrected p = 0.9996). When the analysis was restricted to only those voxels in a thalamic mask (to minimize the loss of statistical power by multiple-comparisons correction; C, green voxels), no significant differences in local tissue volume were noted (p = 0.34). Significant voxels (A, B) and thalamic mask (C) overlie the mean gray matter structural image. Note that identical structural scans were used in VBM analyses and segmentation analyses (i.e., scans used in this figure were the same as those used for data in Figs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0155302#pone.0155302.g002" target="_blank">2</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0155302#pone.0155302.g003" target="_blank">3</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0155302#pone.0155302.g005" target="_blank">5</a>). VBM results were corrected using threshold-free cluster enhancement (TFCE). All axial and coronal views are from a single plane, indicated in MNI Talairach coordinates. Color bars at bottom indicate TFCE-corrected p-values for the images above. Abbreviations: pat = patients; ctrl = controls. R = Right hemisphere; L = Left hemisphere.</p