Running head: Cognitive decision models in cocaine abusers. Cognitive modeling analysis of the decision-making processes used by cocaine abusers

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1 Cognitive Decision Models 1 Running head: Cognitive decision models in cocaine abusers Cognitive modeling analysis of the decision-making processes used by cocaine abusers Julie C. Stout, Jerome R. Busemeyer and Anli Lin Indiana University Steven R. Grant, Katherine R. Bonson National Institutes of Drug Abuse September 30, 2002 Send correspondence to: Dr. Julie C. Stout Department of Psychology, Indiana University 1101 East 10 th Street Bloomington IN phone: (812) jcstout@indiana.edu word count: 3401

2 Cognitive Decision Models 2 Abstract This article examines the theoretical basis of decision-making deficits exhibited by cocaine abusers using a laboratory decision-making task first described by Bechara, Damasio, Damasio, and Anderson (1994). A total of 12 male cocaine abusers and 14 controls performed the task, and the cocaine group performed significantly worse than the controls. A cognitive modeling analysis (Busemeyer & Stout, 2002) was used to estimate three parameters that measure importance of the cognitive, motivational, and response processes for determining the observed performance deficit. The results of this analysis indicated that motivational and choice consistency factors, but not learning/memory were mainly responsible for the decision-making deficit of the cocaine abusers in this task.

3 Cognitive Decision Models 3 Cognitive modeling analysis of the decision-making processes used by cocaine abusers Drug abusers choose the immediate rewards of using drugs despite negative longer-term consequences. Laboratory based decision tasks are being actively pursued as scientific tools to uncover how cognition and motivation interact with contingencies in the environment to create and sustain drug abuse in some individuals. For example, in the simulated gambling task first described by Bechara, Damasio, Damasio, and Anderson (1994), hereafter referred to as the card deck gambling task, participants select cards from four decks which have unknown contingencies. Participants are told to try to maximize their winnings, but because the contingencies of the decks are not made explicit, they must sample from the decks to learn the associations between particular decks and the win/loss outcomes. Several studies have shown that drug abusers perform more poorly on this gambling task than do comparison subjects, choosing relatively more from disadvantageous and less from advantageous decks (Bechara & Damasio, 2002; Bechara, Dolan, & Hindes, 2002; Grant, Contoreggi, & London, 2000). Other decision tasks, such as a betting and delay discounting (Kirby, Petry, & Bickel, 1999; Petry, Bickel, & Arnett, 1998; Rogers et al., 1999) have been used to isolate the conditions under which drug abusers show differences in decision behavior relative to controls. These decision tasks have also been used to suggest neurobiological substrates of drug abuse, and such work has generally supported the view that prefrontal cortical regions, especially the orbitofrontal cortex with its associated cortical and subcortical systems, may be important

4 Cognitive Decision Models 4 in drug abuse (Grant, Contoreggi et al. 2000; London, Ernst et al. 2000; Bechara and Damasio 2002). Decision tasks are complex and have unobservable components. Thus, failure to perform well on these tasks can be due to any of a number of causes. For example, poor performance on the gambling task may be due to poor learning of the contingencies, differences in the motivational significance of wins or losses, or even from an impulsive or erratic response style which can reduce the fidelity between one s knowledge about the contingencies and the selections that he or she makes. To uncover the sources of performance variations across decision tasks and across individuals, some studies use variations in the task design, for example reversing the patterns of wins and losses (Bechara, Dolan et al., 2002) to isolate possible explanations of choice behavior. Another approach is to use additional measures, such as indices of personality or cognitive ability, to identify individual differences that are associated with decision task performance (Petry, Bickel et al., 1998; Mazas, Finn et al., 2000; Bechara and Damasio, 2002; Bechara, Dolan et al., 2002). These approaches have been informative, but remain open to alternative interpretations because they rely on face validity rather than direct theoretical evidence. Mathematical psychologists are developing new theoretical tools that provide rigorous evidence for identifying the psychological processes underlying complex behaviors in cognitive tasks (Ratcliff, Thapar et al., 2001; Zaki and Nosofsky, 2001; Busemeyer and Stout, 2002; Reifer, Knapp et al., 2002). For this approach, simple mathematical models of a target task are developed and tested, and the parameters estimated from these cognitive models are used to describe the relative influences of task

5 Cognitive Decision Models 5 features on an individual s performance. Using this approach, individual difference measures of the relevant cognitive processes are extracted from the very same performance data that one desires to explain. This approach has been used for many years, for example, in signal detection theory, to estimate discriminability and bias from performance on detection tasks. Recently, we developed a cognitive model of decision-making that reveals the underlying psychological processes influencing performance on the card deck gambling task (Busemeyer & Stout, 2002). This initial application was limited to data collected from patients Huntington Disease, which is a progressive dementing illness. The purpose of this report is to provide new empirical tests of the model by evaluating it with data collected from cocaine abusers. For this study, we first fit candidate decision models to the data from individual subjects. Next we identified the best fitting model, and then we used that model to estimate the parameters for the individual subject data. The parameters of the model provide indices of the contribution of the psychological processes that explain the decision-making deficits exhibited by the drug abusers. These derived measures can also be used to determine the decisional characteristics that are most strongly associated with other individual difference variables, such as personality measures or indices of drug abuse severity. The remainder of this article is organized as follows. First we review the results of the empirical study comparing performance of cocaine abusers and controls on the simulated gambling task. Second, we apply our cognitive modeling approach to assess individual differences in this data. Finally, we compare the results obtained in our study

6 Cognitive Decision Models 6 of Huntington disease (Stout, Rodawalt, & Siemers, 2001) with the new results found with cocaine abuse populations. Method Participants and Procedure As part of a study in the NIDA Intramural Program, 14 control (age 30.0 ± 6.1, 100% male, estimated IQ ± 7.62) and 12 cocaine-abusing (age 36.9 ± 10.3, 79% male, 93.7 ± 10.3) individuals participated. The cocaine group was older (t(24) = -3.04, p <.01) and had lower IQs (t(24) = 3.22, p <.01) than did the control group. Exclusion criteria were history of significant medical illness or head trauma with loss of consciousness, Diagnostic and Statistical Manual (DSM) Axis I diagnosis other than Substance Abuse and Axis II diagnosis other than Borderline or Antisocial Personality Disorder. The cocaine group reported current regular cocaine abuse, and all had past experience with other drugs of abuse (stimulants, depressants, marijuana, opiates. One had a history alcohol abuse. IQ was estimated using the Shipley IQ Scale (Zachary, 1986). Participants were also in a PET study of the gambling task, although the Positron Emission Tomography (PET) results are not included in this report. The study was approved by the NIDA Institutional Review Board and all participants gave written informed consent. Procedure Participants were tested while seated in a comfortable chair in front of a computer monitor. Four card decks labeled (A, B, C, D) were displayed on the monitor, and participants were told to accumulate as much (play) money as possible by picking cards

7 Cognitive Decision Models 7 from the decks using the keyboard. Also on the display monitor, participants viewed levels of their winnings shown as stacks of coins. Decks differed with respect to the payoff for each card selection and the frequency and severity of penalties. Each selection from Decks A and B yielded $100, and each selection from Decks C and D yielded $50 per selection. These winnings were paired with losses on many cards such that Decks A and B were disadvantageous overall, leading to a net loss of $250 per 10 cards, whereas Decks C and D were advantageous overall, leading to a net gain of $250 overall. Decks A and C yielded lower frequency, larger magnitude losses, whereas Decks B and D yielded smaller, more frequent losses (for additional details, see Grant et al., 2000). Cognitive Modeling of Gambling Task To begin, we applied several dozen candidate formal cognitive models to the card task data. We then chose the model that maximized model fit indices across all participants data (a detailed example of this process is available in Busemeyer and Stout, 2002). Model fits were quantified for individual subjects by the difference, termed G 2, between the amounts of information accounted for in the cognitive model in comparison to a baseline model. The baseline model perfectly reproduces each individual s marginal choice probabilities, but it assumes a stationary multinomial process. Both the baseline model and the cognitive model have the same number of parameters (three). In order to improve over the baseline model, the cognitive model must account for the dynamic and sequential properties of each individual s data. Here, we present only the expectancyvalence model, which yielded the best fit for the data i. The expectancy - valence model yields three parameters that describe motivational, learning/memory, and choice

8 Cognitive Decision Models 8 consistency components of the data. Parameter values are estimated separately for each participant by solving for the parameter values that, according to the model, maximizes the likelihood of each participant's data. Thus, for each participant, the modeling process yields three theoretically derived parameter estimates of the three hypothesized psychological processes that influence choice behavior. These parameter estimates can be used as additional individual difference measures and correlated with other measures such as age, IQ, and severity of drug use. The mathematical details are given in the Appendix. The three individual difference parameters are described next. Definition of the motivational parameter, w: According to the expectancy-valence model, the decision maker experiences an affective reaction, called a valence, to the consequences (i.e., wins, losses) produced by each selection. Formally, this valence is represented by a weighted average (thus, w) of the losses and wins produced by the chosen deck. The motivational parameter indexes relative attention of the decision maker to the loss versus the win experienced with each selection. For example, cocaine abusers may persist in choosing from the disadvantageous decks because they are insensitive to the large losses produced by these decks. Such insensitivity to loss is indicated by smaller values of w. Definition of the learning/memory parameter, a: Based on past experience, the decision maker forms expectations about the consequences delivered by each deck. Whenever a deck is chosen, the newly experienced valence produced by that choice modifies the expectancy for that deck. Formally, the new expectancy for a deck is a weighted average of the previous expectancy and the new valence. The weight allocated to the newly experienced valence is denoted a, which is an updating rate parameter.

9 Cognitive Decision Models 9 Large values of a indicate strong recency effects and more rapid forgetting of past outcomes. Small values of a indicate the persistence of influences over longer spans of selections. For example, cocaine abusers may have a large learning rate which would cause them to forget the infrequently occurring large losses produced by these decks, and thus continue to choose disadvantageously. Consistency of choice behavior,?: The decision maker's choice on each trial is based not only on the expectancies produced by each deck, but also on the consistency with which the decision maker applies those expectancies when making the selections. This consistency is denoted θ. In effect, according to the expectency-valence model, the probability of choosing a deck is a ratio of the strength of that deck relative to the sum of the strengths of all the decks. Furthermore, the strength of a given deck is determined by the expectancy for that deck multiplied by the consistency parameter. When the consistency is very low, choices are random, reckless, impulsive, and independent of the expectancies; when consistency is very high, the deck that has the maximum expectancy will almost certainly be chosen on each trial. For example, cocaine abusers may fail to select a high proportion of advantageous cards because they respond unreliably to their expectations, and their choices are mostly random guesses, an effect that would lead to lower values on the consistency parameter, θ. Results Gambling Task Performance The control group gradually learned to choose from the advantageous decks, whereas the cocaine group chose nearly equally from the advantageous and disadvantageous decks (see Figure 1, jagged curves). This group effect remained after

10 Cognitive Decision Models 10 covarying out the effects of age and IQ. The cocaine group selected significantly fewer advantageous cards (analysis of covariance, F(1,22) = 7.8, MSE = 2.7, p =.01). Cognitive modeling results For comparison, Figure 1 shows the choice predictions derived from the expectancy-valence model with the observed proportion of choices (jagged curves). As can be seen in this figure, the expectancy-valence model tracks the observed trends fairly closely. The percentages of variance predicted by the model for the averaged results are 82% and 30% for the control and cocaine abuse groups respectively. For the individual analyses, a total of 81% of the participants (13 out of 14 controls, and 8 out of 12 cocaine abusers) produced improved fit statistics, indicating improved fit of the expectancy valence model over the baseline model ii. This percentage is significantly greater than expected by chance (z = 3.14, p <.01). All of the 5 subjects with poor model fits performed poorly on the task, choosing nearly equally from the advantageous and disadvantageous decks. A comparison of the groups on the three model parameters indicated group effects on the motivational and consistency, but not learning/memory parameters (see Table 1). Although the learning/memory parameter did not differ significantly across the two groups (t(17.41) = -.977, p =.34), the variance within groups differed (F = 6.77, p =.016, based on Levene's test for equality of variances). The variance was significantly larger for the cocaine abuse group, which produced both very low and very high learning/memory parameters. The motivational parameter was significantly lower for the cocaine abuse group than the controls (t(24) = 3.40, p =.002), indicating that the card selections of the cocaine abuse group were less influenced by losses than were controls. The consistency

11 Cognitive Decision Models 11 parameter for the cocaine abusers was significantly smaller than the control group (t(24) = 2.53, p =.018). This indicates that the card selections of the cocaine abusers were more erratic (i.e., less related to their overall expectancies of deck outcome). To ensure that these differences in parameters generated from the model were not explained by the group differences in age and IQ, we also computed an analysis of covariance, with age and IQ as the covariates. Results were similar, with a significant difference between the groups in the motivational parameter, a trend for a group difference in the choice consistency parameter, but no apparent difference in the learning/memory parameter. Association of model parameters with age and IQ Separate multiple regression analyses were performed to determine the magnitude of the independent effects of age and IQ on each of the model parameters. Neither age nor IQ had significant effects on the learning parameter. For the motivational parameter, although IQ was not significant, there was a marginal effect of age (β = -.42, t = -2.00, p =.057). For the consistency parameter, although age was not significant, there was a significant effect of IQ (β =.54, t = 2.72, p =.012). Utility of model parameters for predicting group membership A discriminant function analysis, used to determine the extent to which the three parameters could predict group membership, was statistically significant (Wilks Lambda =.506, chi square = 15.2, p =.002); all of the drug abuse participants were correctly classified; 11 of the 14 controls were correctly classified, so the overall rate of correct classification was 89%. The motivational parameter produced the largest standardized coefficient (.88), and the consistency parameter was next (.71), and the learning/memory parameter contributed very little (-.05).

12 Cognitive Decision Models 12 Discussion Basic Findings Cocaine abusers failed to learn to choose from the advantageous decks in the card deck gambling task, whereas controls rapidly learned to do so. The expectancy-valence model provided a better fit than a baseline model for 81% of the participants. The present study identified which of three possible psychological explanations were responsible for this deficit. The parameter estimates obtained from the expectancy-valence model yielded the following conclusions. First, the decision making of the cocaine abusers on the task was less responsive to losses than was the decision making of the controls. This suggests differences in motivational processes are a likely source of the differences in the decision-making styles of cocaine abusers, which is consistent with several major accounts in the drug abuse literature (Kirby, Petry et al., 1999; Grant, Contoreggi et al., 2000; London, Ernst et al., 2000; Bechara and Damasio, 2002; Bechara, Dolan et al., 2002). Second, the choices of the cocaine group were more random and less consistently related to expected payoffs than the choices made by the control group. This indicates that the response process also contributes to the decision-making differences between cocaine abusers and the control group. In contrast to the motivational processes and choice consistency, the learning/memory processes did not distinguish the drug abusers from the control group. Comparison with Previous Cognitive Modeling Results Busemeyer and Stout (2002) conducted cognitive modeling analyses of Huntington participants on the card deck gambling task. Huntington Disease is a progressive degenerative neurological disease that is associated with declines in cognitive

13 Cognitive Decision Models 13 function, particularly memory, executive, and attentional functions. The decision making deficit exhibited by the Huntington disease group was explained by the learning/memory parameter a (referred to as the updating rate in Busemeyer and Stout, 2002). Differences in performance were not associated with motivational influences, w, which did not differ between the Huntington and control groups. The results from the Huntington disease study are in sharp contrast with the present study, which points strongly to motivational differences as the source of the deficit in cocaine abusers. The findings in these studies have some external validity. For example, additional evidence points to learning/memory as a likely explanation for poor performance in Huntington s disease. These individuals have a dementing disease, and memory impairment is by definition an invariant of dementia. Also, in Stout et al. (2001), performance on the gambling task was associated with other measures of learning and memory. In contrast, the finding that motivation, or the attention given to losses relative to gains, is a stronger determinant in the decision process of the cocaine abusers is consistent with the conclusions from other studies of drug abusers (Petry, Bickel et al., 1998; Kirby, Petry et al., 1999; Bechara and Damasio, 2002; Bechara, Dolan et al., 2002) iii. Interestingly, choice consistency (which was referred to as the sensitivity parameter in Busemeyer and Stout (2002)) was lower for the clinical groups in both the Huntington and cocaine abuser study. This is consistent with the possibility that reduced consistency in choice behavior may be a less specific feature in neurobehavioral disorders. The comparison of the Busemeyer and Stout (Busemeyer & Stout, 2002) and the present study illustrates an important point about what can be gained from applying a formal model to decision data from clinical groups. That is, although the behavioral

14 Cognitive Decision Models 14 results from the cocaine abusers in the current study and the Huntington participants in the previous study appear similar, these performance deficits have different underlying theoretical explanations (i.e., motivational versus learning, respectively). Such differences can be revealed and systematically studied using a cognitive modeling approach. This may be particularly valuable in describing subgroups of clinical populations that show similar deficits with different underlying causes. For example, in the recent studies by Bechara et al (2002a; 2002b), two subgroups of drug abusers are identified by their performances on a variant of the card deck gambling task, one that is hypersensitive to reward, and another group that is indifferent to winning or losing. In such cases, cognitive modeling may be useful for revealing subgroups based on parameter estimates, and for explaining these subgroup differences in terms of psychological processes. The parameter estimates can also be studied in conjunction with other individual difference variables, such as personality features or the extent of drug use. Utility of Cognitive Modeling for Studies of Drug Abuse Understanding psychological processes using cognitive modeling provides a means for building a bridge between neurophysiology and behavior (these connections are developed in more detail in Stout, Bechara, Busemeyer, and Lin, in progress). Without our cognitive modeling analysis, it would not be possible to discern whether the performance deficits in cocaine abusers in this study were due to learning/memory or motivational processes. If our results had indicated that learning/memory was responsible for the performance deficit, that finding would lead to the investigation of neurophysiological mechanisms of learning and memory. Instead, our cognitive modeling

15 Cognitive Decision Models 15 analysis identifies a motivational source for the behavioral deficit. This finding leads to investigations of the brain s reward systems, an area of intense research focus in current studies of drug abuse.

16 Cognitive Decision Models 16 References Bechara, A., & Damasio, H. (2002). Decision-making and addiction (part I): Impaired activation of somatic states in substance dependent individuals when pondering decisions with negative future consequences. Neuropsychologia, 40(10), Bechara, A., Dolan, S., & Hindes, A. (2002). Decision-making and addiction (part II): Myopia for the future or hypersensitivity to reward. Neuropsychologia, 40(10), Busemeyer, J. R., & Stout, J. C. (2002). A contribution of cognitive decision models to clinical assessment: Decomposing performance on the Bechara gambling task. Psychological Assessment, 14. Grant, S., Contoreggi, C., & London, E. D. (2000). Drug abusers show impaired performance in a laboratory test of decision making. Neuropsychologia, 38(8), Kirby, K. N., Petry, N. M., & Bickel, W. K. (1999). Heroin addicts have higher discount rates for delayed rewards than non-drug using controls. Journal of Experimental Psychology: General, 128, Petry, N. M., Bickel, W. K., & Arnett, M. (1998). Shortened time horizons and insensitivity to future consequences in heroin addicts. Addiction, 93(5), Rogers, R. D., Everitt, B. J., Baldacchino, A., Blackshaw, A. J., Swainson, R., Wynne, K., Baker, N. B., Hunter, J., Carthy, E., London, M., Deakin, J. F. W., Sahakian, B. J., & Robbins, T. W. (1999). Dissociable deficits in the decision-making cognitive of chronic amphetamine abusers, opiate abusers, patients with focal damage to prefrontal

17 Cognitive Decision Models 17 cortex, and tryptophan-depleted normal volunteers: Evidence for monoaminergic mechanisms. Neuropsychopharmacology, 20, Stout, J. C., Rodawalt, W. C., & Siemers, E. R. (2001). Risky decision making in Huntington's disease. Journal of the International Neuropsychological Society, 7, Zachary, R. A. (1986). Shipley Institute of Living Scale. Los Angeles: Western Psychological Services.

18 Cognitive Decision Models 18 Appendix This appendix summarizes the main assumptions of the expectancy - valence model of performance for the Bechara task. First we introduce some notation. The two advantageous decks are labeled D 1 and D 2, and the two disadvantageous decks are labeled, D 3 and D 4. The time index, t, is used to denote the trial number, that is the total number of cards selected by a particular decision maker at some point during training. The deck chosen on trial t is denoted D(t), so that for example D(t) = D 2 if the second advantageous deck is chosen on trial t. The reward or gain received by choosing deck D is denoted R(D), i.e., R(D) = $50 for advantageous choices, and R(D) = $100 for disadvantageous choices. The loss received from choosing deck D on trial t is denoted L(D(t)), e.g., if a disadvantageous deck is chosen on trial t=9 and a loss of $1250 occurs, then L(D(9)) = -$1250. Motivational Process. According to the expectancy-valence model, the gains and losses experienced after making a choice produce an affective reaction in the decision maker called a valence. The valence experienced after choosing deck D on trial t, denoted v(t), is represented as a weighted average of the gains or rewards, denoted R(D(T), and losses, denoted L(D(T)) : v(t) = [(1-w) R(D(t)) + w L(D(t))]. (1a) The motivation parameter, 0 < w < 1, allows for the possibility that different amounts of attention are given to the losses as compared to the gains.

19 Cognitive Decision Models 19 Learning/memory Process. The decision maker learns expectancies about the valences produced by choosing each deck during training. The expected valence for deck D i on trial t is denoted Ev[D i t]. These expectancies are updated by an adaptive learning mechanism. If deck D i is chosen on trial t, and the valence v(t) is experienced, then the expectancy for this deck is updated as follows: Ev[D i t] = (1-a) Ev[D i t-1] + a v(t). (1b) If deck D i was not chosen, then its expectancy remains unchanged. This learning model produces expectancies that are a weighted average of the past valences. The learning/memory rate parameter, 0 < a < 1, determines how much weight is given to past experience. Consistency of Choice Process. The choice made on each trial is a probabilistic function of the expectancies associated with each deck. The probability of choosing deck D i is an increasing function of the expectancy for that deck, and a decreasing function of the expectancies for the other decks. This principle is captured by the following ratio of strengths rule for choice probabilities (cf. Luce, 1959): Pr[ D i e t + 1] = 4 e j= 1 Ev[ Di t] θ ( t ) Ev[ Dj t] θ ( t ) (1c) The parameter θ(t) = (t/10) c in Equation (1c) is called the sensitivity parameter (and the coefficient c of this power function must be estimated from the data). As the sensitivity parameter increases in magnitude, the choices become more strongly dependent on the expectancies.

20 Cognitive Decision Models 20 The expectancy-valence model was compared to a baseline model, which is a statistical rather than a cognitive model. The baseline model assumes that a multinomial process generates choices with constant probabilities across trials. The probability of choosing from deck D 1 is denoted p 1, the probability of choosing from deck D 2 is denoted p 2, the probability of choosing from deck D 3 is denoted p 3, and finally the probability of choosing from deck D 4 is p 4 = 1 - (p 1 +p 2 +p 3 ). Like the cognitive model described above, the baseline model has three parameters that must be estimated from the data, p 1, p 2, and p 3. Unlike the cognitive model, this model simply assumes that the choices are independently and identically distributed across trials. Nevertheless, the baseline model is a strong competitor because it can perfectly reproduce the marginal choice probabilities, pooled across trials. Thus, a cognitive model can only perform better than this model if it succeeds in explaining how choices change over training as a function of trial-by-trial feedback. The parameters that maximize the log likelihood for each model and person were used to make model comparisons (see Busemeyer and Stout, 2002, for details about the maximum likelihood estimation procedure). The cognitive model was compared with the baseline model by computing differences in log likelihood as follows: G 2 = 2(L Cognitive - L Baseline ) (2) G 2 is a measure of improvement of the expectancy-valence model over the baseline model. If the two models being compared were nested, so that one was a special case of the other, then G 2 would be chi-square distributed with degrees of freedom equal to the difference in the number of parameters. However in this case, the models are not nested and they contain the same number of parameters, so that standard chi square tests are not

21 Cognitive Decision Models 21 applicable. Furthermore, standard non-nested model comparison measures, such as the Akaike information criterion (AIC) or the Schwartz Bayesian information criterion (BIC) produce exactly the same result as Equation (2), because there are no differences in number of parameters. Nevertheless we can continue to use the G 2 statistic as a descriptive index of model performance. Positive values of the G 2 statistic indicate that a given cognitive model performs better than the baseline model. For the control group, the mean improvement in G 2 was equal to (med = 51.13, std = 55.71); and for the cocaine abuse group, the mean was 5.27 (med = 6.36, std = 14.57). A total of 81% of the participants (13 out of 14 controls, and 8 out of 12 cocaine abusers) produced positive G 2 improvement statistics, which is significantly different from chance according to a z-test (z = 3.14, p <.01). A larger improvement was observed for the control group because this group has a larger training effect (see endnote ii). We compared dozens of other cognitive models with the expectancy valence model. In particular, we compared the heuristic strategy-switching model and the Bayesian Expected Utility model (described in Busemeyer & Stout, 2002) with the expectancy valence model. The mean G 2 for the Heuristic Strategy Learning model was and for the control and drug abuse groups, respectively. The mean G 2 for the Bayesian Expected Utility model was and for the control and drug abuse groups, respectively. Note that if the G 2 for cognitive model A exceeds the G 2 for cognitive model B, then cognitive model A performs better than cognitive model B for a particular individual. Clearly, the expectancy valence model produces a better average fit than either of these two alternative cognitive models.

22 Cognitive Decision Models 22 Author Notes Julie C. Stout, Jerome R. Busemeyer, and Anli Lin, Department of Psychology, Indiana University; Steven R. Grant and Katherine R. Bonson, Brain Imaging Center, Intramural Program at NIDA. Dr. Grant is now with the NIDA Program Office; Dr. Bonson is now at the Controlled Substances Program of the U.S. Food and Drug Administration. This research was supported by NIDA grant DA-R and by the Intramural Research Program of the National Institute of Drug Abuse. Requests for reprints should be directed to Julie Stout at

23 Cognitive Decision Models 23 Footnotes i In particular, we rigorously compared the three models discussed previously in Busemeyer and Stout (2002), called the heuristic strategy switching model, the Bayesian Expected Utility model, and the Expectancy Valence model. The latter was the best fitting model for the present data, and it was also the best fitting model for the data analyzed in Busemeyer and Stout (2002). ii The reader may question the lower percentage predicted for the drug abuse group. This necessarily follows from the fact that there is no learning curve for this group. All there is to explain are sequential dependencies over trials, so there is much less signal in the noise. We have conducted computer simulations using the same parameters for each group as we found in this paper. In the simulations, of course, all of the data is generated by the model. But the same difference in percentage predicted appears in the simulated data because of the reduced signal to noise ratio for the drug abuse group. iii More recently, we (Stout, Bechara, Busemeyer, & Lin, in progress) conducted cognitive modeling analyses of Bechara's data obtained from orbital frontal cortex damaged patients, and the results match those obtained from the cocaine abusers.

24 Cognitive Decision Models 24 Table 1: Summary of Parameter Estimates from the Expectancy Valence Model Attention Weight Update Rate Sensitivity Mean 1 Med Std Mean 2 Med Std Mean 3 Med Std Control Drug t(24) = 4.3, p = t(24) = -1.02, p = t(24) = 2.53, p =.018.

25 Cognitive Decision Models 25 Figures Figure 1. The left and right panels of Figure 1 display the results for the control and drug abuse patients, respectively. Each panel shows the proportion of participants choosing from the advantageous decks as a function of the number of cards selected. The jagged curve represents the actual data and the smooth curve represents the predictions of the model. Both curves are have been linearly filtered by a moving average window of size 7.

26 Cognitive Decision Models 26 Figure 1 Figure 1

27 Cognitive Decision Models 27 i In particular, we rigorously compared the three models discussed previously in Busemeyer and Stout (2002), called the heuristic strategy switching model, the Bayesian Expected Utility model, and the Expectancy Valence model. The latter was the best fitting model for the present data, and it was also the best fitting model for the data analyzed in Busemeyer and Stout (2002). ii The reader may question the lower percentage predicted for the drug abuse group. This necessarily follows from the fact that there is no learning curve for this group. All there is to explain are sequential dependencies over trials, so there is much less signal in the noice. We have conducted computer simulations using the same parameters for each group as we found in this paper. In the simulations, of course, all of the data is generated by the model. But the same percentage predicted appears in the simulated data because of the reduced signal to noise ratio for the drug abuse group. iii More recently, we (Stout, Bechara, Busemeyer, & Lin, in progress) conducted cognitive modeling analyses of Bechara's data obtained from orbital frontal cortex damaged patients, and the results match those obtained from the cocaine abusers.