Cognitive model decomposition of the BART: Assessment and application

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Abstract

The Balloon Analogue Risk Task, or BART, aims to measure risk taking behavior in a controlled setting. In order to quantify the processes that underlie performance on the BART, Wallsten, Pleskac, and Lejuez (2005) proposed a series of mathematical models whose parameters have a clear psychological interpretation. Here we examine a 2-parameter simplification of Wallsten et al.’s preferred 4-parameter model. A parameter recovery study shows that — with plausible restrictions on the number of participants and trials — both parameters (i.e., risk taking γ+ and response consistency β) can be estimated accurately. To demonstrate how the 2-parameter model can be used in practice, we implemented a Bayesian hierarchical version and applied it to an empirical data set in which participants performed the BART following various amounts of alcohol intake.

Section snippets

The BART models

The BART models by Wallsten et al. (2005) are cognitive decision models inspired by the Expectancy–Valence model (Busemeyer & Stout, 2002) for the famous Iowa Gambling Task (Bechara, Damasio, Tranel, & Damasio, 1997). In their article, Wallsten et al. presented a total of 10 models that make different assumptions about the details of the decision process (for an overview see Wallsten et al. (2005), p. 870, Table 2). As a basis of our discussion we use Wallsten et al. ’s “Model 3”, a

Bayesian parameter estimation

In previous work, parameter estimation for the 4-parameter BART model was carried out by means of individual subject maximum likelihood (Wallsten et al., 2005).2 This means that the model was applied to each participant’s data separately, and that inference concerned the parameter point values that make the observed data most likely.

Here we estimate the parameters of the BART model in a Bayesian way. In Bayesian inference, the researcher

Parameter recovery simulations

In this section we examine parameter recovery of the 2-parameter simplification of the BART model. In this model, pbelief is fixed to the value of pburst. This way, the only parameters left to estimate are γ+ and β. We generated data for a grid of values for parameters γ+ and β. We did so by plugging in the parameter values into Eqs. (3), (4), to calculate the probability that DM will pump on trial k for pump opportunity l, pklpump. We generated pumps and cashes based on these probabilities,

Experiment

In this section we will present an application of a hierarchical version of the 2-parameter model to empirical BART data. In a within-subjects design, we administered three different doses of alcohol to every participant, each measured in blood alcohol content, or BAC, in grams per liter: a placebo condition (BAC = 0), a tipsy condition (BAC = 0.5) and a drunk condition (BAC = 1). After consumption, each participant completed a 20 min version of the BART.

We expected that a higher dose of

Concluding comments

The first goal of this paper was to increase our knowledge about how the BART models can be applied to empirical data. In order to do so, we have assessed parameter recovery for a simplified version of the BART model by Wallsten et al. (2005) with 4, 3, and 2 parameters, of which the results for the 4- and 3-parameter versions of the model are reported online. Our second goal was to test the effects of alcohol on performance on the BART task in an experimental setting. We have created a

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