Implications of Visual Attention Phenomena for Models of Preferential Choice

Abstract

We use computational modeling to examine the ability of evidence accumulation models to produce the reaction time (RT) distributions and attentional biases found in behavioral and eye-tracking research. We focus on simulating RTs and attention in binary choice with particular emphasis on whether different models can predict the late onset bias (LOB), commonly found in eye movements during choice (sometimes called the gaze cascade). The first finding is that this bias is predicted by models even when attention is entirely random and independent of the choice process. This shows that the LOB is not evidence of a feedback loop between evidence accumulation and attention. Second, we examine models with a relative evidence decision rule and an absolute evidence rule. In the relative models a decision is made once the difference in evidence accumulated for 2 items reaches a threshold. In the absolute models, a decision is made once 1 item accumulates a certain amount of evidence, independently of how much is accumulated for a competitor. Our core result is simple-the existence of the late onset gaze bias to the option ultimately chosen, together with a positively skewed RT distribution means that the stopping rule must be relative not absolute. A large scale grid search of parameter space shows that absolute threshold models struggle to predict these phenomena even when incorporating evidence decay and assumptions of either mutual inhibition or feedforward inhibition.

Keywords: attention; choice models; drift diffusion; eye-tracking; gaze cascade.

Figure 1

Empirically measured late onset bias during (a) preferential binary choice between faces (Shimojo et al., 2003); (b) multiattribute choice between 2 apartments each with 5 numerical attributes (Mullett and Tunney, 2016), and (c) choices between two risky gambles (Stewart, Hermans, & Matthews, 2015). Note that whereas a and b are plotted against time, c is plotted by discrete fixations.

Figure 2

Average LOB for absolute threshold model (a) and relative threshold model (c). Also, shown are the patterns of LOB broken down by length of deliberation time (RTs) for absolute (b) and relative (d). See the online article for the color version of this figure.

Figure 3

Average LOB for absolute threshold model (a) and relative threshold model (c) when attention is modeled as having a probabilistic bias on evidence accumulation. The results show no qualitative differences compared to the deterministic rule, even when the patterns of LOB are separated by RTs for both absolute (b) and relative (d). Note the change in scale from Figure 2. See the online article for the color version of this figure.

Figure 4

The LOB is plotted for the absolute threshold rule when attention is exogenously biased toward the currently preferred item. See the online article for the color version of this figure.

Figure 5

Average LOB for absolute threshold model with mutual inhibition (a) and the LOBs from the same model when simulations are split into deciles by RT. See the online article for the color version of this figure.

Figure 6

The average LOB for an absolute threshold rule with feedforward inhibition when I = 1 (a) and when I = 0.5 (c). This shows that when inhibition is high, such a model can produce the LOB, and mimic the relative threshold rule. In addition, when split into deciles by RT, the model with full inhibition shows gradual increase in bias across all trial lengths (b), whereas when I = 0.5, the bias is flat within each RT decile (d). See the online article for the color version of this figure.

Figure 7

The LOB plots estimated by the grid search of parameters for the relative threshold rule. Columns list different values for the threshold T, and rows correspond to values of attention bias A.

Figure 8

The RT distributions estimated by the grid search of parameters for the relative threshold rule. Columns list different values for the threshold T, and rows correspond to values of attention bias A.

Figure 9

The top row of panels shows the average LOB produced by increasing the threshold parameter in a model with full mutual inhibition. The second row shows the RT distributions for the same models. The lower two rows show the effect of increasing the threshold parameter when inhibition is set to zero.

Figure 10

The LOB and RT distributions produced by different levels of decay within a mutual inhibition model. Blank subplots occur for parameter values where too few decisions were made within the imposed deadline of 30s and therefore results cannot be plotted.

Figure 11

The LOB and RT distributions produced by different levels of attention bias within a mutual inhibition model.

Figure 12

The LOB and RT distributions produced by different levels of inhibition within a mutual inhibition model.

Figure 13

The LOB and RT distributions produced by different thresholds within a feedforward inhibition model.

Figure 14

The LOB and RT distributions produced by different rates of decay within a feedforward inhibition model. Blank subplots occur for parameter values where too few decisions were made within the imposed deadline of 30s and therefore results cannot be plotted.

Figure 15

The LOB and RT distributions produced by different levels of attention bias within a feedforward inhibition model.

Figure 16

The LOB and RT distributions produced by different inhibition parameter values within a feedforward inhibition model.

Figure A1

A histogram showing the distribution of fixation durations measured in Mullett and Tunney (2016) and sampled from during real-time simulations.

Figure B1

This shows the LOB for an input inhibition model. Plot a shows the average LOB for a value of I = 0.8 and plot b shows the LOBs separated by decile of reaction times. Plots c and d show the same for a model where I = 0.9. See the online article for the color version of this figure.