Aims and findings

This document attempts to fit a drift-diffusion model to the performance data from Keefe & Zald, 2020. In this study, subjects performed a simple discrimination task in which they attempted to discriminate the direction of a turned landscape target within an RSVP stream of landscape distractors. Either shortly before (Lags 1, 2, 8) or after (Lags -2 and -1) the target, a critical distractor was presented. This critical distractor was either a neutral image of people in everyday settings or an emotional distractor of opposite-sex couples in erotic situations. In a departure from the typical EAB paradigm, subjects were asked to report the direction of the turned target as quickly as possible - and their responses were constrained to the duration of the RSVP presentation. This study found that subjects were less accurate following emotional vs. neutral distractors at short (-1, 1, 2) lags, as has been demonstrated in previous studies of the EAB. Novelly, the study demonstrated that these decrements in accuracy were accompanied by increased RT and decreased ratings of target vividness in correct trials at the lags where a significant EAB was observed. This demonstrates that the EAB is a graded, and not discrete phenomenon.

Given these results, we argue that our findings are consistent with an Interactive Race Model in which the emotional distractor doesn’t just “outrace” the target to a threshold for perception, but also interferes with evidence accumulation of the target. However, we don’t attempt to formally model the paradigm. This document attempts to do just that using a drift diffusion model, which estimates the rate of evidence accumulation (i.e., drift rate or v) for the target towards a threshold for response. In addition to this drift rate parameter, the model also attempts to estimate the distance between the thresholds for each of the 2AFC responses (i.e, a) and the duration of time that is not spent making the perceptual decision (i.e., non-decision time or Ter). If our account of distractor interference with target processing is correct, then we would expect for the effects of the emotional distractor to be best described by a change in drift rate. Conversely, if the distractor leads subjects to adopt a more conservative criterion or disrupts motor processes, then we would expect to see changes in the distance of the thresholds or non-decision time, respectively.

Accordingly, I fit the data using an EZ Diffusion Model (Wagenmakers, Van der Maas, Raoul, & Grasman, 2007) to the data. I started by making a few descriptive plots of the distribution of RTs to make sure that (1) the data is right-skewed, (2) there are no large differences between conditions that may interfere with model fitting, and (3) there are no differences between response times to different targets. Then, I fit the data and plotted each of the parameters in the conditions of interest. Each of these parameters was estimated for each subject in each lag x emotion condition, and these parameter estimates were then submitted to an ANOVA. What I find is that only the drift-rate parameter demonstrates the interaction between lag and emotion that characterizes the EAB. This suggests that the EAB is indeed the result of interference with information accumulation about the target.

Note: all error bars are within-subject SEM. Trials with RTs of less than 200 ms or greater than 2 SDs above the mean were excluded. Conditions with perfect accuracy were adjusted using the convention that I typically use with d’: adjusting as if the subject would have gotten 1 trial incorrect in twice as many trials.

RT Distributions

RT split by lag, emotion, and accuracy

RT split by only by lag and emotion

RT split by clockwise and counter-clockwise targets

CW indicates clockwise targets and CCW indicates counterclockwise targets.

DDM Fitting

In each figure, the violin plot outlines the full distribution of the values obtained from fitting the EZ-Diffusion model to each subject. The central point indicates the mean of the parameter estimates, with within-subject SEM error bars (Cousineau, 2005).


Drift Rate

Boundary separation

Non-decision time

Statistics

Drift rate ANOVA

Effect DFn DFd SSn SSd F p p<.05 ges partial_eta_squared
(Intercept) 1 19 4.627 0.230 381.466 0 * 0.895 0.953
lag 4 76 0.132 0.152 16.529 0 * 0.196 0.465
Emotion 1 19 0.066 0.036 34.676 0 * 0.109 0.646
lag:Emotion 4 76 0.048 0.123 7.416 0 * 0.081 0.281

Drift rate t-tests

lag t_val p_val lower_conf_int upper_conf_int cohen_d
-2 0.8004884 0.4284208 -0.0210416 0.0485609 0.2531367
-1 2.1221822 0.0406958 0.0014978 0.0655338 0.6710929
1 4.5989818 0.0000461 0.0392071 0.1008652 1.4543257
2 5.1857922 0.0000074 0.0436646 0.0995856 1.6398915
8 -0.3417899 0.7346406 -0.0508230 0.0361952 -0.1080835


Boundary separation ANOVA

Effect DFn DFd SSn SSd F p p<.05 ges partial_eta_squared
(Intercept) 1 19 3.526 0.007 9504.329 0.000 * 0.985 0.998
lag 4 76 0.021 0.020 19.522 0.000 * 0.282 0.507
Emotion 1 19 0.000 0.005 0.042 0.840 0.000 0.002
lag:Emotion 4 76 0.000 0.021 0.212 0.931 0.004 0.011


Non-decision time ANOVA

Effect DFn DFd SSn SSd F p p<.05 ges partial_eta_squared
(Intercept) 1 19 175.297 0.925 3600.004 0.000 * 0.989 0.995
lag 4 76 15.429 0.628 466.712 0.000 * 0.888 0.961
Emotion 1 19 0.015 0.071 4.005 0.060 0.008 0.174
lag:Emotion 4 76 0.011 0.320 0.668 0.616 0.006 0.034

Conclusions

I fit an EZ Diffusion Model (Wagenmakers et al., 2007) to the data from the Keefe & Zald, 2020 in order to investigate the mechanisms of emotional attentional capture in the EAB paradigm. What I find is that only drift rate (i.e., the rate of information accumulation about the target) demonstrates the interaction between lag and emotion that characterizes the EAB, suggesting that emotional distractors disrupt information accumulation about the target.

Modeling considerations

We only have RT data from the subset of trials in which subjects gave a response to the target following the presentation of the target and preceding the end of the end of the RSVP stream. The choice to restrict responses to the duration of the RSVP presentation was made in order to encourage subjects to respond as quickly as possible, but comes at the expense of a significant proportion of data. While we analyze the non-response rate in our manuscript, that information doesn’t really help us here. I’m concerned that this arrangement compromises the validity of the Drift-Diffusion Model given that we don’t have information about the longer-duration responses that might have emerged.

Additionally, I don’t believe that a DDM necessarily dictates the type of mutual interference that is proposed by the Usher and McClelland Interactive Race Model that we refer to in our manuscript. While that type of interference could best characterize the change in drift rate that we see here in target information accumulation, it doesn’t necessitate mutual interference as the main mechanism of change in drift rate. We could fit that type of leaky accumulator model specifically, but that level of modeling is comfortably beyond my expertise at the moment. Nevertheless, I was able to fit our data easily thanks to the R code that Wagenmakers et al. (2007) included in their paper. I have no more than a conceptual understanding of the mathematics behind it, admittedly.