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5.4.1 Deck Selection Profiles

Experiment 3 was completed by analysing the same data presented in Ex- periment 1, but implemented a reduced parameter version of the EVM. For this reason, the deck selection profiles of the 25 participants are exactly the same as those presented in Section 5.2.2.

5.4.2 Posterior Distributions

The following figures are the sampled posterior distributions for the pa-

Figure 5.25: Sampled posterior distributions (with mixing) for Participants 01 through 04

.

Figure 5.26: Sampled posterior distributions (with mixing) for Participants 05 through 08

Figure 5.27: Sampled posterior distributions (with mixing) for Participants 101 to 104

.

participants completing the IGT in Experiment 1. These are pairwise plots in which the two upper diagonal panels are a reflection of the two lower diagonal panels. Across the central diagonal, the mixing for each of the two

parameters (W and φ) are presented. This is the mixing for all five MCMC

chains concatenated together such that the first 2,000 samples correspond to the first chain, the second 2,000 samples to the second chain and so on.

Figure 5.28: Sampled posterior distributions (with mixing) for Participants 105 to 108

.

Figure 5.29: Sampled posterior distributions (with mixing) for Participants 109 to 111

Figure 5.30: Sampled posterior distributions (with mixing) for Participants 201 to 203

.

Figure 5.31: Sampled posterior distributions (with mixing) for Participants 301 to 304

Figure 5.32: Sampled posterior distributions (with mixing) for Participants 401 to 404

.

Figure 5.33: Sampled posterior distributions (with mixing) for Participants 405 to 407

Chapter 6

Quantifying performance on

the Balloon Analogue Risk

Task.

6.1

Introduction

When using any sort of model of behaviour, the goal is to link the param- eters of the model with the underlying cognitive processes that give rise to observed behaviour. This is usually with the view to use the parameter es- timates to either infer something about an individual’s cognitive processes or gain some sort of representative, average estimate of the cognitive per- formance for a group of individuals. Empirical models, which are driven by the patterns in the data rather than mechanistic models of how the data has arisen, may not be able to provide any clear links back to the cognitive processes underlying observed behaviour. Mechanistic models, which are developed based on the theories surrounding the cognitive processes which give rise to observable behaviour, are therefore often favoured over their empirical counterparts. However, there is also a possibility that mechanistic models based on complex models of cognitive processes have been incorrectly specified or specified in such a way that the observed behaviour can not be described by a unique combination of the model parameters. This inabil- ity to specify parameters was exactly what we observed in Chapter 4 when considering the Expectancy Valence Model (EVM) of the Iowa Gambling

Task (IGT). The solution presented in Chapter 4 was to simplify the model, allowing for a less complex description of the individual’s behaviour, but the question of whether this a true measurement of an individual’s behaviour remains. Given the IGT requires such a complex system of cognitive pro- cesses to produce behaviour, it may be the case that it is just not possible to tease apart those cognitive processes by modelling the single observed be- haviour of deck choice. Perhaps then, the solution is to look for a cognitive task which relies on a less complex system of cognitive processes to produce behaviour; instead of expecting one task to answer multiple questions about cognitive deficits, simplify our expectations and test one (or two) cognitive processes at a time.

The Balloon Analogue Risk Task (BART) is theorised to assess risk seeking behaviour alone (Lejuez et al., 2002), making the BART a relatively simple task compared to the IGT. In this way, modelling the cognitive pro- cesses underlying performance on the BART should be less complex than for the IGT. The following chapter will investigate whether using this cogni- tively less demanding task makes it easier to decompose behaviour using a less complex mechanistic model than the EVM of the IGT. The van Raven- zwaaij et al. (2011) two-parameter BART (2pB) model of behaviour will be assessed with the main aim being to ascertain if parameter estimates can be gained with enough accuracy to be useful at the level of the individual. A new, empirical model of behaviour on the BART, the Basic Response Model (BRM), is constructed based solely on the patterns in the observed data and is proposed as an alternative to the 2pB model. The BRM is then extended to a more complex model, using our understanding of par- ticipants behaviour on the task rather than our observations in the data, as a second potential alternative to the fully mechanistic 2pB model. The Run Dependent Response Model (RDRM), is therefore an example of the

fusion between mechanistic and empirical models. Whether the BRM and RDRM may have any use in modelling cognitive deficiencies at the level of the individual will also be explored.

The focus on the accuracy of the considered models at the level of the individual has particular importance in a clinical context. Clinically, the goal of psychological assessment is to ascertain if an individual may have some cognitive deficit requiring treatment or support of some kind. It is not unreasonable to think that individuals presenting for assessment may have cognitive deficits that give rise to behaviour outside of, or more extreme than, what is considered normal. In these cases the models used to measure possible cognitive deficits need to be able to accurately identify behaviours away from the normal range of results, in the extreme edges of performance. When measuring group performance, these extreme performers are labelled as outliers and their results are often ignored or averaged out in various statistical ways to lessen their impact on the overall results (see Chapter 4 for examples). However, for a model to be of clinical use, these outliers must be able to be measured as accurately as any other performer in the group. For this reason, this chapter will be a focus on the ability of the considered models to accurately identify performance away from normal, in the extreme.