Supporting Information: Expectancy-Valence Modeling

The Expectancy Valence (EV) model is a computational model analyzing trial-by-trial choice-behavior (Busemeyer and Stout 2002). Specifically, it distills the performance in the IGT (and similar tasks) into three underlying components characterizing the cognitive-motivational profile of the decision-maker.

1) Weight to gains vs. losses: The evaluation of wins and losses experienced after making a choice is called a valence, denoted u(t), and is calculated as a weighted average of gains and losses from the chosen option in trial t.

u(t) = w×win(t) - (1- w) ×loss(t) / (1)

The parameter w determines the subjective weight to gains versus losses (0 ≤ w ≤ 1). In the IGT, giving high weight to gains can lead to more choices from the disadvantageous decks, which produce larger gains.

2) Influence of recent vs. past outcomes: The valences produced by deck j are summarized by an accumulated subjective value for each deck, called an expectancy, and denoted Ej(t). A Delta learning rule is used for updating the expectancy after each choice from the selected deck j:

Ej(t) = Ej(t-1) + f×[u(t) – Ej(t-1)] / (2)

The recency parameter, f, describes the degree to which the expectancies reflect the influence of the most recent outcomes or more distant past experience (0 ≤ f ≤ 1). In the IGT, high recency can result in disadvantageous choices due to discounting or forgetting of infrequent negative outcomes.

3) Sensitivity of responses to expectancies is measured by the choice consistency parameter. Using Luce’s rule:

/ (3)

Where Pr[Gj(t)] is defined as the probability that deck j will be selected on trial t by the model. The term q (t) controls the consistency of choice probabilities and expectancies, where: q (t) = (t/10) c and c is the choice consistency parameter. When the value of the parameter c is very high, the deck with maximum expectancy will almost certainly be chosen on each trial. When the value of c is low, choices are inconsistent and more random. The parameter c is constrained between -5 and 5, covering the range between expectancy-based and nearly random choices (Busemeyer and Stout 2002).

Model fit was evaluated in relation to a deterministic baseline model. In this model the predicted proportions for each trial are set according to the overall deck proportions. The baseline model thus has three parameters according to the proportion of the choices of decks A, B, and C (and deck D’s is calculated accordingly). We estimated the three parameters and calculated the model fit for each participant, using a method outlined elsewhere (Busemeyer and Wang 2000; Yechiam and Busemeyer 2005). The fit index is a difference score obtained by comparing the log likelihood score of the learning model and the baseline model used:

G2 = 2×[ LLmodel – LLbaseline]. / (4)

We then averaged the parameter values across each group. The averages and standard deviations of the model parameters in each group are presented in Table S1. For the IGT, while the model fit was adequate compared to the baseline model, no significant differences were found among groups.

For the FPGT the model fit was not adequate and we therefore focus on the analysis of the differences in overall deck selections (included in the article’s results section), which in this task captures trial ahead choices better than the Expectancy-Valence learning model.

Table S1: Mean model fit and estimated parameters of the EV model, by group. Standard deviations are in parentheses.

ADHD / Non-ADHD
MPH / Placebo / MPH / Placebo
Model fit, G2 / 10.47 (12.68) / 6.21 (13.14) / 15.91 (28.63) / 7.06 (19.31)
Weight to gain, w / 0.65 (0.44) / 0.62 (0.42) / 0.57 (0.27) / 0.55 (0.23)
Recency, f / 0.47 (0.31) / 0.49 (0.28) / 0.33 (0.47) / 0.25 (0.38)
Consistency, c / 1.18 (2.70) / 0.70 (1.77) / 1.52 (1.89) / 1.16 (1.44)


References:

Busemeyer JR, Stout JC (2002) A contribution of cognitive decision models to clinical assessment: Decomposing performance on the Bechara gambling task. Psychol Assess 14:253-262.

Busemeyer JR, Wang Y-M (2000) Model comparisons and model selections based on generalization criterion methodology. J Math Psychol 44:171-189.

Yechiam E, Busemeyer JR (2005) Comparison of basic assumptions embedded in learning models for experience based decision-making. Psychon B Rev 12:387-402.