Figure 1
Decision-Making under Ambiguity Task. (a). Example Unambiguous Trial (left) and Ambiguous Trial (right). Participants chose one of two ‘urns’ from which to draw a token. The proportion of ‘X’s and ‘O’s varied between urns and across trials. The number above each urn (1–150) indicated the magnitude of electric shock that might be received if an ‘O’ was drawn. On 52% of trials (‘ambiguous trials’), a number of tokens in one urn (the ‘ambiguous urn’) were replaced by a “=” symbol. 10, 30, 40, 45, 46, 47, 48 or 49 of the 50 tokens were obscured. (b). Trial sequence and timing. Urn presentation (2.5–5.5s) was followed by a question mark (“?”) which indicated that participants could choose one of the two urns. Their decision was indicated by a square placed around the chosen urn magnitude. After a variable interval (2–6s), a token was randomly drawn from the chosen urn and displayed for 1.5s. There was a 3–6s interval prior to the next trial. Trial outcomes were stored across each block of five trials. At the end of the block, one outcome was selected at random; if an ‘O’ outcome was selected, this was delivered as an electric shock of corresponding magnitude (see Figure S1). During each block, stored outcomes were displayed by means of a summary histogram at the top of the screen (bins from left to right: ‘X’ outcome, ‘O’ outcome of magnitude 1–50, ‘O’ outcome of magnitude 51–100, ‘O’ outcome of magnitude 101–150).
Figure 2
Model-free analysis reveals high trait anxious individuals show greater avoidance of ambiguous urns as a function of missing information. (a) The proportion of ambiguous trials on which participants chose the unambiguous urn (i.e., avoided the ambiguous urn) is plotted against missing information, A, where A = 1– √ (n/50). Participants were divided into two groups using a median split on STAI trait anxiety (TA) scores for illustrative purposes. (b) Simple Information-Level Dependent Ambiguity Aversion (s-ILDAA) is defined as the slope of the regression of the proportion of ambiguous trials on which the unambiguous urn is chosen against missing information (i.e., the slope of the regression shown in Figure 2a). Larger values are indicative of greater avoidance of ambiguity as a function of missing information. Here, s-ILDAA values for each participant are correlated against STAI trait anxiety. In line with predictions, elevated trait anxiety was associated with increased avoidance of the ambiguous urn as a function of missing information, r (29) = 0.3168; p = 0.041, Pearson, one-tailed; rho(29) = 0.33, p = 0.036, Spearman, one-tailed. Note: Shaded regions represent +/– one standard error in the regression coefficients (obtained by resampling the data 10,000 times with replacement).
Figure 3
Model comparison results for the four main models. Panels a and b show penalized log-likelihood values for each model averaged across participants. In panel a, the results shown are for model comparison using the Bayesian information criterion (BIC); this penalizes models with a higher number of parameters more strictly than the Akaike information criterion (AIC). Results from model comparison using AIC are shown in panel b. Panels c and d show the results from Bayesian model selection (BMS; Stephan et al., 2009), see Methods. The BMS estimate of model prevalence, that is the population-level estimate of the proportion of participants best fit by each model, is given in Panel c. Panel d displays the protected exceedance probability for each model; this is the probability that each model is the most prevalent at the population level, i.e., that it is the most likely to explain behavior on the task. For trial-wise model fits see Figures S13 and S14.
Figure 4
Information-Level Dependent Ambiguity Aversion (ILDAA), as indexed by β3, is positively correlated with trait anxiety, rho (29) = 0.36, p = 0.023, Spearman, one-tailed. In model 3, the influence of missing information on selection of the unambiguous urn is captured by parameter estimates for β3; large positive values indicate greater ambiguity avoidance as a function of missing information. In this model, parameters are also included to control for the influence upon choice of difference between the two urns in outcome probability, outcome magnitude and categorical ambiguity (the presence or absence of ambiguity). The majority of participants showed increased avoidance of the ambiguous urn as level of missing information increased (this holds for all data points above the dotted line, 28/31 participants). The expected value of unambiguous and ambiguous urns was approximately matched across trials within information levels. Hence, rational behavior is associated with an ILDAA value of zero, or close to zero. Note: Shaded regions represent +/– one standard error in the regression coefficients (obtained by resampling the data 10,000 times with replacement).
Figure 5
Trait anxiety was linked to increased dACC and IFS activation as a function of missing information on trials where the ambiguous urn was subsequently chosen. (a). Left: Sagittal and axial views of the dorsal anterior cingulate (dACC) ROI. Right: We divided ambiguous trials according to whether participants chose the ambiguous or unambiguous urn (see Methods). The extent to which mean dACC activation, time-locked to urn presentation, varied as a function of level of missing information (A) was estimated for each participant for each trial type. The resulting z-score values are plotted against participant trait anxiety level (red circles: Ambiguous urn chosen trials; grey circles: Unambiguous urn chosen trials). Trait anxiety was positively correlated with dACC activation to missing information level on Ambiguous chosen trials, rho (29) = 0.48, p = 0.0061, pcorr = 0.031, but not on Unambiguous chosen trials, rho (29) = –0.09, p > 0.1. (b) Left: Sagittal and axial views of the left Inferior Frontal Sulcus ROI (IFS). Right: Z-scores for the mean left IFS response to level of missing information (A) at time of urn presentation are plotted against participant trait anxiety (red circles: Ambiguous urn chosen trials; grey circles: Unambiguous chosen trials). Trait anxiety was positively correlated with left IFS activation to missing information level on Ambiguous chosen trials, rho (29) = 0.60, p = 3.9e-4, pcorr = 0.0020, but not on Unambiguous chosen trials, rho (29) = –0.04, p > 0.1. Note. All correlations reported are Spearman, two-tailed. Shaded regions represent +/– one standard error in the regression coefficients (obtained by resampling the data 10,000 times with replacement).