Assessing the Validity of Three Tasks of Risk-Taking Propensity: Behavioral Measure and Computational Modeling

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1 Assessing the Validity of Three Tasks of Risk-Taking Propensity: Behavioral Measure and Computational Modeling Ran Zhou 1 (zhou.1500@osu.edu), Jay I. Myung 1 (myung.1@osu.edu), Carol A. Mathews 2 (carolmathews@ufl.edu), & Mark A. Pitt 1 (pitt.2@osu.edu) 1 Department of Psychology, The Ohio State University, Columbus, OH 43210, USA 2 Department of Psychiatry, University of Florida, Gainesville, FL 32610, USA Abstract Risk-taking propensity is a general personality disposition. Survey, behavioral, and modeling approaches have been used to study it. We compared three behavioral tasks (BART, C- ART, S-ART) and corresponding computational models to learn which aspects of risky behavior they measure by correlating task performance and parameter estimates with survey responses (impulsivity, sensation seeking, drug use). Results indicated that the BART was not correlated with any of the above domains, whereas behavioral measure from the two ART tasks correlated with impulsivity and sensation seeking. The parameter estimates from the two ART tasks, while having some validity, were weaker indices than the traditional behavioral measure of these tasks. Our findings provide insight into the use and design of these behavioral tasks and their corresponding computational models. Keywords: decision making under uncertainty; risk-taking propensity; computational cognition; parameter estimation; BART; ART Introduction People react differently towards choices involving uncertainty and risk, and this difference has been described as risk-taking propensity, which is hypothesized to be a general personality disposition (Slovic, 1964). However, accumulating evidence suggests that risk-taking propensity is a multidimensional concept, since people often exhibit different degrees of risk-taking across different decision domains (Weber, Blais, & Betz, 2002), which makes it difficult to assess with a single method of measurement. Psychometric approaches have traditionally been used to measure risk-taking propensity. Self-report methods are commonly used in studies of personality traits such as risktaking (e.g., Byrnes, Miller, & Schafer, 1999), but no single self-report instrument can fully capture its multidimensionality, and in practice, several instruments that examine various risk-related constructs such as impulsivity, sensation seeking, and naturalistic risk-taking behavior, are often needed. These constructs overlap with risk-taking propensity, but each accounts for unique variance in observed behavior, suggesting that none fully captures this domain (Hoyle, Fejfar, & Miller, 2000; Zuckerman, & Kuhlman, 2000). Another widely used psychometric approach is behavioral tasks. The Balloon Analogue Risk Task (BART; Lejuez et al., 2002) and the Angling Risk Task (ART; Pleskac, 2008) are two tasks that measure risk-taking propensity. Recently, researchers have taken this approach one step further by developing mathematical models of the cognitive processes thought to underlie task performance (Batchelder, 2016). Parameters of the models are thought to map onto specific mental constructs (e.g., impulsivity). Parameter estimates are obtained by fitting the proposed model to each participant's data, with the resulting parameter values obtained for each participant serving as an additional measure of the underlying cognitive processes. With various psychometric approaches available (survey data, behavioral measure, parameter estimates) for assessing specific propensities or personality traits, it is crucial for researchers to know what exactly the approaches are measuring, and which approach has better validity or reliability, in order to make sound inferences about the psychological characteristics underlying participants observed behavior. In this paper, we investigated three behavioral tasks that are commonly used in the study of risktaking propensity, namely the BART and two conditions of the ART, with the goal of comparing them and determining whether or not these tasks measure the same underlying construct, which of the three tasks is best at measuring riskrelated constructs, and whether the parameter estimates from computational models of these tasks perform as well as or better than the traditional behavioral measure. Behavioral Tasks The BART is a computerized task that simulates real-world decisions that involve balancing potential gains and losses (Lejuez et al., 2002), and it is one of the most commonly used laboratory-based measures of risk-taking behaviors. During the BART (Figure 1), participants have the choice of Pump or Collect. With each pump, if the balloon does not explode, 5 cents are added to a temporary bank. If the balloon explodes, however, all the money in the temporary bank is lost and a new trial is begun. If participants choose to collect rather than pump, the current trial ends, and all the money in the temporary bank is transferred to a permanent bank, which is counted towards the final total earning. There are 30 trials in total, and participants are instructed to try to earn as much money as possible at completion of the task. They are also told that the balloon on each trial has a probability of exploding, but they are not told what the probability is, nor whether the probability changes trial by trial or not. Many different types of studies have supported the validity of the BART. First, performance on the BART has been shown to correlate with risk-related constructs such as impulsivity and sensation seeking (e.g., Aklin et al., 2005), as well as real-world risky behaviors such as drug and alcohol use (e.g., Lejuez et al., 2003). Secondly, studies using selected participants from populations associated with high

2 risk propensity further supported the validity of the BART by showing that participants in high-risk groups, such as those with sleep deprivation or alcohol dependence, perform differently from participants in control groups with normal and healthy states (e.g., Acheson, Richards & de Wit, 2007). Figure 1: Screenshot of the BART. Although the literature provides strong support for the validity of the BART, the relationships between performance on the BART and risk-taking are not consistently found in all studies, and some have failed to find any significant correlation (p >.05) between performance on the BART and risk-related constructs (e.g., Aklin, et al., 2005; Lejuez et al., 2003). In attempting to explain the inconsistent findings, researchers have criticized the BART for being ill-defined for participants because this task lacks a clear description of the ongoing probabilistic process, making it difficult for researchers to understand how participants interpret the task and make choices (Pleskac, 2008). In order to address the problem of ambiguity with the BART, Pleskac (2008) developed a new class of tasks, namely the Angling Risk Task (ART), that allowed researchers to more clearly define the task for participants. The ART places participants in the context of a fishing tournament instead of asking them to pump up a balloon. In the cloudy day condition (C-ART, Figure 2), participants see red fish swimming in a shoal. For each trial, participants have the choice of Get Fish or Collect. If they press the Get Fish button, a fish is caught randomly from the shoal. A fish, once caught, shows as either yellow or red. Each red fish caught adds 5 cents to a temporary bank, whereas one yellow fish caught empties the temporary bank and start the next. As with the BART, the Collect button saves any money in the temporary bank towards a final total earning and ends the current trial. In the C-ART, participants know in advance that the fish-catching process is catch-and-release, meaning that the risk that they will catch a yellow fish is constant throughout the entire experiment, although they do not know what proportion of the fish are yellow, i.e., how large the risk is. In contrast, in the sunny day condition (S-ART, Figure 3), participants can see the exact numbers of yellow and red fish on the screen, and thus know in advance how large the risk is of catching a yellow fish. The currently available validity data for the ART, unfortunately, are relatively limited and somewhat inconsistent. Pleskac (2008) found that performance in the S- ART was correlated with self-reported naturalistic risktaking, namely risky use of drugs (r = 0.32, p <.01). However, Congdon et al. (2013) found that the correlation between the S-ART and self-reported risk-taking behavior was in the opposite direction (r =.53, p <.01). These results showed discrepancy not only within the ART itself, but also between the ART and the BART, which more consistently shows a positive correlation with risk-taking. One possible reason for the discrepant results across tasks is that the three tasks are not measuring the same underlying construct. Past studies have failed to provide tangible evidence regarding whether the differences in task design could change their predictive validity as little effort has been made to directly compare the tasks: Pleskac (2008) only compared conditions of the ART on their correlation to risky drug use, and Congdon et al. (2013) only compared the S-ART and the BART on their correlation to impulsivity. These researchers have tried to provide general guidance regarding the use of the tasks, but their findings described an incomplete picture. Figure 2: Screenshot of the Cloudy Day ART. Figure 3: Screenshot of the Sunny Day ART. In summary, the extant literature suggests that the cognitive processes underlying the BART, the C-ART and the S-ART might be distinct and independent from one another, but methodological differences between them cloud interpretation. No study has directly compared all three tasks, let alone replicated the Pleskac (2008) and Congdon et al. (2013) studies. Therefore, a more thorough comparison of the three tasks is needed, with the aim of resolving the observed discrepancies and developing a clear understanding of what aspects of risk-taking each task measures and how researchers can most effectively use each task. Computational Models In addition to behavioral measures such as number of pumps or amount of money earned that can be derived from the tasks described above, computational models have been developed

3 to interrogate the proposed underlying constructs, and we investigated whether these models could yield helpful parameter estimates compared to the behavioral measure. Here we review the computational models that were designed for the BART and ART tasks. We used the 4-parameter model that was advocated by Wallsten, Pleskac, and Lejuez (2005) for the BART. This model assumes that, on a given trial k, participants believe that there is a probability, denoted as pppppppppppppppp, that the balloon will burst on any pump, and pumping the balloon will not make it more likely to explode. Thus, they believe that the probability is stationary over pumps, but they will adjust this value based on what they learn from previous trials in this experiment. This probability is calculated as: pp kk bbbbbbbbbbbb = 1 αα+ kk 1 ii=0 nn ii ssssssssssssss μμ+ kk 1 pppppppppp ii=0 nn ii (0 < αα < μμ) (1) According to Eq. (1), participants start the task with a prior belief of 1 αα μμ that the balloon will explode on a pump. kk 1 ssssssssssssss kk 1 pppppppppp The quantities ii=0 nn ii and ii=0 nn ii represent the total number of pumps that did not end up with exploding in all trials prior to trial k, and the total number of all pumps in all trials prior to trial k. Given the probability that participants have in mind, the model further assumes that they also determine the number of pumps to make on trial k prior to the start of trial. This was called the optimizing number of pumps, denoted as ωω kk, and was calculated based on participants propensity for risktaking, γγ +, and pp bbbbbbbbbbbb kk : γγ + ωω kk = bbbbbbbbbbbb (γγ + 0) (2) ln(1 pp kk ) Given a fixed pp bbbbbbbbbbbb kk, individuals with a higher risk-taking propensity will have a higher number of pumps that they deem to be optimal compared to less risky individuals. The model further assumes that participants do not act solely based on the optimizing number of pumps they determined as calculated by Eq. (2), but that their response sensitivity, denoted as ββ, also has an influence on whether they will act rationally. The model thus calculates the actual probability that the participants will pump on trial k for a given pump opportunity l as: pp pppppppp kkkk = 1 1+ee ββ(ll ωω kk ) (ββ 0) (3) With more pumps on trial k, l increases, and the probability that the participants will actually pump decreases, until l reaches the optimizing number of pumps, ωω kk, then the probability is equal to.5. The response sensitivity parameter ββ can also be interpreted as the sensitivity towards participants prior evaluation of options (Wallsten, Pleskac, & Lejuez, 2005), since participants with higher ββ values will base their actions more on the optimizing number of pumps they had in mind. The C-ART is similar to the BART in that it also involves a learning component. The participants do not know the probability of losing, so they do not know a priori how easy it is for them to catch a yellow fish and have to learn from experience. This learning component makes it suitable to use the same 4-parameter model for the C-ART as for the BART. As for the S-ART, given that the participants are explicitly told the number of red and yellow fish, there is a minimal level of learning in this task, so a simplified 2-parameter model proposed by van Ravenzwaaij, Dutilh, and Wagenmakers (2011) is appropriate. This model assumes that participants belief about the probability of losing on each trial is constant over trials, and they do not learn from experience. The value of pp kk bbbbbbbbbbbb in Eq. (2) can now be substituted with the proportion of yellow fish in the shoal and does not change with trial k, so Eq. (1) is not needed. This 2- parameter model for the S-ART consists of Eq. (2) and (3) only, with parameters γγ + and ββ. The Current Study We undertook a comprehensive comparison of three tasks assessing risk-taking propensity, namely the BART, the C- ART, and the S-ART. The goal was to answer the following three questions: Do these tasks measure the same aspects of risk-taking? Which task is better at measuring selected riskrelated constructs? Do computational models help with making inferences from these tasks? The goals were achieved with a mixed design as illustrated in Table 1. There were four groups of participants. s BART, C-ART, and S-ART each completed only the corresponding behavioral task and self-report instruments. All completed all three behavioral tasks: the BART, the C-ART, and the S-ART, with the order of tasks randomized, and the same self-report instruments. The selfreport instruments were chosen to assess the tasks validity, measuring three constructs that are commonly found to be correlated with risk-taking propensity: impulsivity, sensation seeking, and past drug use. Table 1. Illustration of Experimental Design. BART C-ART S-ART All BART Once Once C-ART Once Once S-ART Once Once Self-report Once Once Once Once Note. Self-report includes all three self-report instruments completed in the same order. We note that in this design, data from All can be used to address each of the three goals outlined above. Correlation between performance on each of the tasks and each of the self-report instruments will tell us whether the tasks are measuring different aspects of risk-taking. The effect sizes of the correlations could suggest which task is better at a given aspect of risk-taking as measured by selfreport. By examining the correlation between model parameter estimates and each self-reported construct, we can see whether computational models contribute to making inferences from these tasks. In addition, by comparing performance on the same task across the two groups (e.g.,

4 BART and All s BART) we can examine whether completing additional tasks in the same session (as in the case in All) influences the validity of a task. Experiment Methods Participants. A total of 191 participants recruited from the Ohio State University ( BART = 43, C-ART = 40, S-ART = 41, All = 67). Materials and procedure. The self-report instruments we used in this experiment include the impulsivity subscale of the Eysenck Impulsiveness Scales (EIS; Eysenck, Pearson, Easting, & Allsopp, 1985), the Sensation Seeking Scale (SSS; Zuckerman, Eysenck, & Eysenck, 1978), and the Drug Abuse Screening Test (DAST-10; Skinner, 1982). The selfreport instruments were administered after completion of the behavioral tasks in the following order: EIS, SSS, DAST-10. Participants completed the behavioral tasks prior to the selfreport instruments. We used the adjusted score, which is the most commonly analyzed behavioral statistic in the BART (e.g. Lejuez et al., 2002), for each of the three tasks. For the BART, the adjusted score is defined as the average number of pumps excluding balloons that exploded. For the C-ART and the S-ART, it is calculated as the average number of casts excluding trials that ended up with a yellow fish caught. The adjusted score is considered an index of risk-taking propensity. Results 1. Behavioral performance statistics. We first examined the descriptive statistics of behavioral measure to see if the patterns fit past studies. The mean adjusted scores for each task is listed by group in Table 2. The first three rows of Table 2 show that for participants who only completed one task, S-ART had higher average adjusted scores than C-ART and BART. We compared these groups using a 2- sample t-test assuming unequal variances, and the results indicated that S-ART had higher adjusted score than BART (p =.02) and C-ART (p =.02), with no significant differences between BART and C- ART (p =.78). Similarly, the last row of Table 2 indicates that for participants in All, the S-ART had the highest average adjusted scores among the three tasks. A one-way repeated measures ANOVA on All s adjusted scores indicated a statistically significant difference between the tasks, F(2, 65) = 16.21, p <.01. A pairwise comparison post hoc test showed that All s S-ART had higher adjusted scores than C-ART (p <.01) and BART (p <.05). These results, taken together, suggest that participants pressed more for rewards in the S-ART than in the BART or the C-ART, which did not differ, meaning that participants may behave similarly in these two tasks. These patterns in behavioral measure were consistent with the findings of Congdon et al. (2013) and Pleskac (2008). Table 2. Mean (Standard Deviation) Adjusted Scores Adjusted scores BART C-ART S-ART BART (3.92) C-ART (2.93) S-ART (4.24) All (3.97) (4.62) (4.66) Note. Calculations are all based on a total of 30 trials. 2. Task validity comparison. The first goal of this study was to determine whether the three tasks measure the same aspects of risk-taking and if so, which task is best at measuring each aspect of risk-taking. This goal was achieved by calculating the correlation coefficients between each measure and self-reported constructs. We first calculated Pearson s r between the adjusted scores of each task and selfreported impulsivity (EIS), sensation seeking (SSS), and drug use (DAST-10). As shown in the first three rows of Table 3, the adjusted scores of each task positively correlated with each other, suggesting that participants behaved consistently to some extent in these tasks. The last three rows of Table 3 demonstrate that the adjusted score of the C-ART and the S- ART both had positive correlations with self-reported impulsivity and sensation seeking, and that the BART adjusted score did not correlate with any of the self-report measures. None of the tasks correlated with self-reported drug use. Results indicate that the three tasks are similar, but also suggest that they measure different aspects of risktaking, and the difference was likely to be statistically significant between the BART and two ART tasks. Table 3. Correlations Between the Adjusted Scores of the Behavioral Tasks and Self-Reported Measures in All. BART score C-ART score S-ART score 1. BART score 2. C-ART score.50*** 3. S-ART score.50***.62*** 4. EIS.10.25**.29** 5. SSS.15.46***.29** 6. DAST * p <.10, ** p <.05, *** p <.01 The second goal was to determine which task is better at measuring each aspect of risk-taking, and this was answered by comparing the absolute values of Pearson s r. The last three rows of Table 3 show that the C-ART was better than the S-ART at measuring sensation seeking as it had higher Pearson s r (.46) than the S-ART (.29), but the S-ART and the C-ART were similar in measuring impulsivity with Pearson s r of.29 and.25 respectively. Again, none of the tasks was significantly correlated with self-reported drug use. The third goal, to determine whether computational models are helpful over and above the behavioral measure, was achieved by checking if the model parameter estimates had at

5 least the same level of correlation to the self-report measures as adjusted scores. We correlated the estimated γγ + with selfreported impulsivity (EIS), sensation seeking (SSS), and drug use (DAST-10) using data from All, as summarized in Table 4. Both the C-ART and the S-ART had estimated γγ + that correlated with self-reported impulsivity, and the C-ART was also correlated with sensation seeking. Comparing the fourth and fifth rows of Table 4 to those of Table 3, it shows that the estimated risk-taking propensity parameter had a similar correlation with impulsivity as the adjusted scores in both the C-ART (r =.26) and the S-ART (r =.30). However, the estimated γγ + from the C-ART had a smaller correlation with sensation seeking (r =.30) than the adjusted score did, and the estimated γγ + in S-ART did not show a significant correlation. These results suggest that the risk-taking propensity parameter in the models may be not as informative as the behavioral measure. Table 4. Correlations Between the Estimated γγ + of the Tasks, and Self-Reported Measures in All. BART γγ + C-ART γγ + S-ART γγ + 1. BART γγ + 2. C-ART γγ +.24* 3. S-ART γγ +.29**.40*** 4. EIS.18.26**.30** 5. SSS.13.30** DAST-10.28** * p <.10, ** p <.05, *** p <.01 Further, we conducted the same analyses using data from BART, C-ART, and S-ART, and the results showed very similar patterns as All. BART s adjusted score and estimated γγ + did not correlate with any of the riskrelated constructs. C-ART s adjusted score and estimated γγ + had the same level of correlation with sensation seeking (both r = 0.47, p <.01). S-ART s adjusted score was correlated with sensation seeking (r = 0.34, p =.03) but the estimated γγ + was not (p =.21). These results indicate that the conclusions drawn from All s data were unlikely to be influenced by adding similar tasks in the same experimental setting. Discussion The purpose of this study was to compare three behavioral tasks assessing risk-taking propensity using both the standard behavioral measure and computed parameter estimates, with the ultimate goal of providing guidance on the use of these tasks and their corresponding computational models in assessing risk-taking propensity as an underlying construct. The first of the three questions the present experiment aimed to answer was whether the BART, the C-ART and the S-ART measure the same aspects of risk-taking. Our data suggest that they do not. From the task validity comparisons, it is clear that the behavioral measure of the two ART tasks was better at measuring impulsivity and sensation seeking than was the BART, which, in our experiment, did not show any correlation to the risk-related constructs. This departs from most of the past studies demonstrating the BART s validity on these constructs. One reason that our experiment did not reveal significant correlations between the BART and the self-reported risk-related constructs could be that in our experiment, the probability of losing in the BART (.05) was much higher than that commonly used in the past studies. Lejuez et al. (2002) used a losing probability of 1/128 (0.0078) at first trial, 1/127 at second trial, and so on until the balloon exploded. The relatively high probability of losing in the BART in our study may have made it less likely for the individuals with a high risk-taking propensity to stand out from others and it could be the reason why the BART in this experiment did not have strong validity. For the second question, which task is better at measuring the selected risk-related constructs, our results indicate that the two ART tasks were equally effective in measuring impulsivity and sensation seeking, with similar effect sizes, while the C-ART showed a slight advantage in measuring sensation seeking. We hypothesize that this difference may be due to the lack of learning in the S-ART, thereby decreasing the validity of the task. In the S-ART, participants are given the complete and full information they need to make a rational decision, and this could induce a higher level of rationality in making decisions in the task, thereby decreasing the risk-taking propensity in their behavior. The third question was whether computational models could help with making inferences from these behavioral tasks. It was interesting to note that in the two ART tasks, compared to adjusted scores, the estimated γγ + maintained similar levels of correlation with impulsivity, but not sensation seeking. This observation suggests that the risktaking propensity parameter in the models may be measuring impulsivity more than sensation seeking. A scatterplot in Figure 4 summarizes the correlation that the adjusted scores and estimated γγ + had with sensation seeking in both tasks. The left panel shows the correlation between adjusted scores and estimated γγ + in the C-ART and Sensation Seeking Scale score (SSS). The right panel shows the same for the S-ART. The adjusted score in both the C-ART and the S-ART had a positive but noisy correlation with SSS, as shown in the left graph of both panels. However, in the right graph of both panels, the correlation between estimated γγ + and SSS was similar but weaker. This suggests that the adjusted score and estimated γγ + have certain similarities in their ability to measure sensation seeking, but they may account for different variances among individuals, and finally, the variance that can be explained by the adjusted score is closer to what is measured by the self-report measures than the variance explained by estimated γγ + is.

6 Figure 4: Scatterplots of Adjusted Scores and Estimated γγ + (gplus) of the C-ART, S-ART and SSS. Conclusion This experiment is the first that examined the validity of three tasks of risk-taking propensity using both behavioral measure and parameter estimate. We compared the correlation of task performance and parameter estimates with self-reported impulsivity, sensation seeking, and drug use, and our results suggest that the S-ART is likely to be a better task in assessing impulsivity than either the BART or the C-ART, while if the target construct is sensation seeking, then the C- ART is likely the better choice, and if researchers are interested in naturalistic risky behavior, specifically drug use, then it is very likely that none of the tasks will suffice. Our findings also suggest that the standard behavioral measure derived from these tasks are likely to have higher validity than computationally derived parameter estimates. Although we did not find any clear superiority of parameter estimate over behavioral measure, our findings shed light on future directions of the use of computational models in these tasks. For example, in order to further test the models usefulness, we could choose self-report measures on other risk-related constructs to see if the parameter estimates are more strongly correlated with them, or manipulate certain experimental conditions such as using high-risk participants to determine whether they have higher risk-taking propensity as measured by the parameter estimates. Alternatively, it is possible that the parameters in these models do not reflect a general personality trait such as the one that the self-report instruments are thought to measure but instead are merely sensitive to a person s response under different circumstances. 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