Figure 1.
Model-free clustering of an objective multi-round economic exchange game.
A) Depiction of Multi-Round Trust Task. A ten round task in which two players, an investor and a trustee, undergo repeated interactions. Adapted from previous publications [6], [7], [16], [20]. B&C) Our Approach. Following [23], we cluster investor-trustee dyads based on a regression of previous choices in the trust game. Specifically, we predict ratios of investment it in round t as a polynomial of past rounds of investment and return. The number of clusters, order of polynomial, and number of rounds back on which to base this dependence are all taken as free parameters in the model.
Figure 2.
Groups over-/under-represented in behavioral clusters.
We analyzed over-/under-representation of original groups in our clusters. Our approach is depicted in Figure 1 and detailed in Materials & Methods section. We used the most frequent value of a dyad's cluster assignment over all draws from the posterior to assign a type for this analysis. We computed the number of standard deviations over-/under-representation in the cluster as compared to that expected by chance. These values are shown for each cluster and each original group. ASD = Adolescents with Autism Spectrum Disorder [20]; ADHD = Children with Attention-Deficit/Hyperactivity Disorder; Per = Healthy individuals who met before playing the trust game [16]; Imp = Healthy individuals who played the trust game remotely with individuals from the California Institute of Technology [7]; BPD-M = Medicated individuals with Borderline Personality Disorder [6]; BPD-N = Non-medicated individuals with Borderline Personality Disorder [6].
Figure 3.
ADI-R C, repetitive interests score, correlates with assignment of dyads with ASD individuals to cluster 2.
For dyads with Adolescents with Autism Spectrum Disorder [20] assigned to cluster 2, in which they are over-represented, we analyzed the correlation of the (i) percent match of the dyad into cluster 2 from 30,000 draws from the posterior and (ii) the score on the Autism Diagnostic Interview-Revised [28] Repetitive Behavior subscale of the ASD individual playing in the trustee role. We found a correlation with and
.
Figure 4.
Interpersonal trust scale correlates with assignment of dyads with BPD trustees to cluster 3.
For dyads with Borderline Personality Disorder, Medicated and Non-Medicated [6], assigned to cluster 3, in which they are over-represented, we analyzed the correlation of the (i) percent match of the dyad into cluster 3 from 30,000 draws from the posterior and (ii) the score on the Interpersonal Trust Scale [29] of the BPD individual playing in the trustee role (self-report, lower score implies less trust). We found a correlation with and
(
).
Figure 5.
Characteristics of behavioral clusters.
A–D) Left Panel: Investor and Trustee Behavior in Behavioral Clusters. For each cluster, the corresponding number of dyads is shown in the title. Further, the corresponding mean investment ratios (red) and return ratios (black) are represented. Standard error of the mean is plotted, but is smaller than the markers used to denote means. Right Panel: Polynomial Coefficients Used to Predict Investment Ratios for Behavioral Clusters. Mean values of polynomial coefficients used to predict investment ratios for each cluster are shown. Specifically, the coefficients by the constant term (gray), return (red), and investment (green) ratios are shown.
Figure 6.
Agent-vs-agent validation of clustering scheme.
A) Depiction of agent-vs-agent trust task. Specifically, a k-nearest neighbors agent that samples healthy investor behavior plays the multi-round trust game against a -nearest neighbors agent that samples healthy or BPD trustee behavior for ten rounds [6]. B) Depiction of the space of sampled interactions. The sampling agent uses the records of investment and return from the trust game as played by either (i) healthy trustees, (ii) healthy investors, or (iii) BPD trustees depending on the specific agent used. The agent starts with a vector representing several immediate past choices for the game that is currently playing (this vector forms the center of the circle), and selects several records for which the corresponding vectors have the smallest Euclidean distance to the current vector (these vectors are inside the circle). C) The sampling agent finds the next investment (or return) ratios for all the closest recorded game trajectories. In Panel C, these ratios represent
. D) The agent then selects, with equal probability, one of these “next” ratios and returns it as the investment (or return) ratio for the game that is currently playing.
Figure 7.
Simulated data over-/under-represented in behavioral clusters.
The analysis detailed in Figure 2 was repeated with the Simulated Interactions. In Figure 2, Cluster 3 over-represents healthy individuals playing BPD trustees. Similarly, we compared the number of standard deviations by which in our analysis of simulated interactions, Cluster 3 over-represents simulated healthy-vs-BPD interactions by 7.19 standard deviations. On the other hand, Cluster 3 over-represents healthy-vs-healthy simulated interactions only by 0.46 standard deviations.