Figure 1.
Schematic of the horizon and information conditions in the Horizon Task. In this task, participants play a series of 120 games, in a self-paced manner, lasting either 5 or 10 trials each, in which they choose between virtual slot machines, each of which pays out a reward in the form of points sampled from a Gaussian distribution whose mean is different for each option, varies from game to game, and is (initially) unknown to the subject. After four forced-choice trials, participants make either one or six free choices. The key manipulations in the Horizon Task are the number of free choices in each game (termed the “horizon”), which determines how valuable it is to explore, and the amount of information the participant has about each option (how many observed outcomes, from one to three). When the game is short (five total trials, one free choice; termed Horizon 1), exploration has no value since there is no opportunity to use new information in the future. When the game is long (10 total trials, 6 free choices; termed Horizon 6), it is often worth exploring at first to gain information that may be useful later on. The four forced-choice trials set up two information conditions: A) an unequal condition, or [1 3], in which subjects see one example from one bandit and three from the other, and B) an equal information, or [2 2], condition, in which subjects see two draws from each bandit. Thus, there are four combinations of horizons (1 vs. 6) and information (equal vs. unequal).
Table 1.
Demographic, cognitive, and clinical measures in the full sample of patients and controls
| Measure | Patients a | Controls b | Inferential statistic |
|---|---|---|---|
| Demographic | |||
| Age, years, M (SD) | 37.0 (10.1) | 36.4 (10.4) | t = 0.307 |
| Gender | 36 female, 72 male | 11 female, 22 male | χ 2 = 0.000 |
| Race | 53 C, 43 AFA, 4 AS, 7 M/O | 18 C, 13 AFA, 0 AS, 2 M/O | χ 2 = 1.372 |
| Subject education, M(SD) | 13.2 (2.1) | 15.1 (2.1) | t = 4.374*** |
| Parental education, M(SD) | 14.3 (2.9) | 14.0 (2.6) | t = 0.671 |
| Cognitive, M(SD) | |||
| WASI estimated IQ (four subtests) | 94.5 (14.1) | 111.5 (13.8) | t = 6.05*** |
| WRAT-Reading scaled score | 97.2 (14.8) | 109.7 (15.0) | t = 4.26*** |
| WTAR scaled score | 99.0 (17.5) | 110.9 (14.0) | t = 4.01*** |
| MATRICS composite score | 32.9 (12.7) | 51.3 (11.0) | t = 7.56*** |
| MATRICS domain scores | |||
| Processing Speed | 38.1 (12.5) | 53.1 (11.8) | t = 6.10*** |
| Attention/Vigilance | 39.9 (11.3) | 52.3 (11.2) | t = 5.53*** |
| Working Memory | 39.7 (10.4) | 51.9 (11.6) | t = 5.74*** |
| Verbal Learning | 37.7 (7.9) | 50.6 (8.8) | t = 8.01*** |
| Visuospatial Learning | 36.0 (12.3) | 45.5 (10.7) | t = 3.99*** |
| Reasoning/Problem Solving | 43.4 (10.8) | 49.6 (9.8) | t = 2.98** |
| Social Cognition | 41.9 (12.0) | 54.6 (8.0) | t = 5.70*** |
| Clinical, M(SD) | |||
| BPRS mean item score—all items | 1.7 (0.4) | ||
| BPRS mean item score—Psychosis c | 2.2 (1.2) | ||
| BPRS mean item score—Depression c | 1.9 (0.9) | ||
| SANS mean item score—all items | 1.5 (0.7) | ||
| SANS mean item score—Avolition/Anhedonia | 2.0 (0.9) | ||
Note. AFA = African American; AS = Asian; BPRS = Brief Psychiatric Rating Scale; C = Caucasian; MATRICS = Measurement and Treatment Research to Improve Cognition in Schizophrenia Consensus Cognitive Battery; M/O = mixed/other; SANS = Scale for the Assessment of Negative Symptoms; WASI = Wechsler Abbreviated Scale of Intelligence; WRAT-Reading = Wide-Ranging Achievement Test, Reading Subtest; WTAR = Wechsler Test of Adult Reading.
c From the factor analysis of McMahon et al. (2002).
Figure 2.
Graphical representation of the model. Each variable is represented by a node, with edges denoting the dependence between variables. Shaded nodes correspond to observed variables, that is, the free choices c Gshug , forced-trial rewards r Gshug , and forced-trial choices a Gshug . Unshaded nodes correspond to unobserved variables whose values are inferred by the model.
Figure 3.
Performance on the Horizon Task by diagnostic group. A) Proportions of optimal responses as a function of trial number for Horizon 1 (filled circles) and Horizon 6 (open circles) games. B, C) Model-free analysis of the first free choice as a function of horizon, with B showing proportions of high-information (information seeking) choices and C showing proportions of low-mean choices (indicative of behavioral variability).
Figure 4.
Percentages of information choices. A) Percentages of high-information choices at Horizon 1 plotted against those at Horizon 6, in patients (red crosses) and controls (blue circles). While most participants make more high-information choices at Horizon 6 than at Horizon 1, a subset of participants (predominantly schizophrenia patients) make few high-information choices in both horizon conditions. These individuals were said to be “ambiguity averse.” B) Percentages of low-mean-value choices at Horizon 1 plotted against those at Horizon 6, in patients (red crosses) and controls (blue circles).
Figure 5.
Comparison of experimental measures from the Horizon Task in ambiguity-averse (AA) and non-AA patients. A) Overall Horizon Task performance in AA and non-AA patients. B) Directed Exploration in AA and non-AA patients. C) Random Exploration in AA and non-AA patients.
Table 2.
Demographic, cognitive, and clinical measures in patient subgroups
| Measure | Non-AA patients a | AA patients b | Inferential statistic |
|---|---|---|---|
| Demographic | |||
| Age, years, M (SD) | 36.7 (10.3) | 38.3 (9.6) | t = 0.672 |
| Gender | 26 female, 59 male | 10 female, 13 male | χ 2 = 1.353 |
| Race | 47 C, 27 AFA, 3 AS, 7 M/O | 6 C, 16 AFA, 1 AS, 0 M/O | χ 2 = 11.489** |
| Subject education, M (SD) | 13.3 (2.1) | 13.0 (2.1) | t = 0.675 |
| Parental education, M (SD) | 14.6 (2.7) | 13.5 (3.4) | t = 1.611 |
| Cognitive, M (SD) | |||
| WASI estimated IQ (four subtests) | 96.1 (14.7) | 88.9 (10.0) | t = 2.721** |
| WRAT-Reading scaled score | 98.6 (15.5) | 91.8 (10.5) | t = 2.457* |
| WTAR scaled core | 101.0 (17.6) | 91.8 (15.6) | t = 2.268* |
| MATRICS composite score | 33.9 (13.2) | 29.1 (9.6) | t = 1.621 |
| MATRICS working memory | 41.0 (10.6) | 35.0 (8.1) | t = 2.527* |
| MATRICS processing speed | 38.6 (13.0) | 36.0 (10.3) | t = 0.895 |
| Clinical, M (SD) | |||
| BPRS mean item score—all items | 1.7 (0.4) | 1.7 (0.5) | t = 0.334 |
| BPRS mean item score—Psychosis | 2.1 (1.2) | 2.3 (1.2) | t = 0.663 |
| BPRS mean item score—Depression | 1.8 (0.9) | 2.1 (1.1) | t = 1.180 |
| SANS mean item score—all items | 1.5 (0.7) | 1.5 (0.6) | t = 0.184 |
| SANS mean item score—Avolition/Anhedonia | 2.0 (0.9) | 1.9 (0.7) | t = 0.557 |
Note. AA = ambiguity averse; AFA = African American; AS = Asian; BPRS = Brief Psychiatric Rating Scale; C = Caucasian; MATRICS = Measurement and Treatment Research to Improve Cognition in Schizophrenia Consensus Cognitive Battery; M/O = mixed/other; SANS = Scale for the Assessment of Negative Symptoms; WASI = Wechsler Abbreviated Scale of Intelligence; WRAT-Reading = Wide-Ranging Achievement Test, Reading Subtest; WTAR = Wechsler Test of Adult Reading.
Table 3.
Analyses of correlations between model-free and model-based measures of experimental behavior and clinical variables in patients in the Horizon Task
| Variable | BPRS overall mean | BPRS Psychosis item mean | BPRS Depression item mean | SANS overall mean | SANS Avolition/Anhedonia item mean |
|---|---|---|---|---|---|
| Model-based measures of performance | |||||
| Prior mean | 0.03 | 0.02 | −0.09 | 0.05 | 0.10 |
| Initial learning rate | −0.25** | −0.28 ** | −0.10 | −0.06 | −0.08 |
| Asymptotic learning rate | 0.08 | 0.09 | 0.03 | −0.03 | −0.03 |
| Model-free measures of information seeking/directed exploration | |||||
| Overall information seeking [Σp(high info)] | 0.01 | 0.01 | −0.04 | 0.02 | 0.06 |
| Directed exploration [Δp(high info)] | 0.06 | 0.03 | 0.12 | −0.05 | −0.06 |
| Model-based measures of information seeking/directed exploration | |||||
| Information weight (Horizon 1) | −0.02 | −0.01 | −0.14 | 0.04 | 0.08 |
| Information weight (Horizon 6) | 0.01 | 0.05 | 0.01 | −0.11 | −0.06 |
| Change in information weight | 0.02 | 0.08 | 0.16 | −0.19* | −0.15 |
| Model-free measures of behavioral variability/random exploration | |||||
| Overall behavioral variability [Σp(low mean)] | 0.17 | 0.23* | 0.02 | −0.01 | −0.02 |
| Random exploration [Δp(low mean)] | 0.29** | 0.39 *** | 0.19 | −0.03 | −0.03 |
| Model-based measures of behavioral variability/random exploration | |||||
| Reward weight (Horizon 1 [1 3]) | −0.03 | −0.10 | −0.04 | −0.01 | 0.04 |
| Reward weight (Horizon 6 [1 3]) | −0.04 | −0.17 | −0.09 | 0.13 | 0.14 |
| Reward weight (Horizon 1 [2 2]) | 0.09 | 0.11 | 0.08 | 0.11 | 0.12 |
| Reward weight (Horizon 6 [2 2]) | − 0.25* | −0.29** | −0.20* | 0.11 | 0.11 |
| Change in reward weight ([1 3]) | 0.01 | −0.01 | −0.09 | 0.14 | 0.12 |
| Change in reward weight ([2 2]) | −0.15 | −0.20* | −0.15 | −0.02 | −0.02 |
Note. Correlation values are Spearman coefficients. Correlations illustrated in Figure 6 are bolded. BPRS = Brief Psychiatric Rating Scale; SANS = Scale for the Assessment of Negative Symptoms.
Figure 6.
Relationships between cognitive and behavioral measures in patients. A) Composite Measurement and Treatment Research to Improve Cognition in Schizophrenia (MATRICS) scores correlated positively with overall information seeking in both patients and controls. B) Composite MATRICS scores correlated inversely with overall behavioral variability in both patients and controls. C) Verbal Learning scores from the MATRICS correlated positively with directed exploration scores in both patients and controls. D) Overall IQ estimates from the Wechsler Abbreviated Scale of Intelligence (WASI) correlated positively with prior mean, a model-based performance metric. Also in patients, ratings for psychotic symptoms correlated (E) positively with random exploration scores and (F) negatively with initial learning rate, a model-based indicator of the strength of prior beliefs. BPRS = Brief Psychiatric Rating Scale.
Table 4.
Correlations between measures of experimental behavior and cognitive variables in patients in the Horizon Task
| Construct | Overall Performance | Overall Information Seeking | Directed Exploration | Overall Behavioral Variability | Random Exploration |
|---|---|---|---|---|---|
| Variable | Prior mean | Σp(high info) | Δp(high info) | Σp(low mean) | Δp(low mean) |
| WASI estimated IQ (four subtests) | 0.385 *** | 0.387*** | 0.227* | −0.292** | 0.029 |
| WTAR scaled score | 0.248** | 0.223* | 0.210 | −0.317*** | 0.102 |
| MATRICS composite score | 0.303** | 0.351 *** | 0.212* | −0.300 ** | 0.001 |
| MATRICS domain scores | |||||
| Working Memory | 0.292** | 0.355*** | 0.186 | −0.211* | 0.079 |
| Processing Speed | 0.259** | 0.276** | 0.128 | −0.239* | −0.024 |
| Attention/Vigilance | 0.194* | 0.257** | 0.156 | −0.295** | −0.070 |
| Verbal Learning | 0.257** | 0.336*** | 0.232 * | −0.059 | 0.189* |
Note. Correlation scores are Spearman correlation coefficients; correlations illustrated in Figure 6 are bolded. MATRICS = Measurement and Treatment Research to Improve Cognition in Schizophrenia Consensus Cognitive Battery. WASI = Wechsler Abbreviated Scale of Intelligence; WTAR = Wechsler Test of Adult Reading.