Abstract: PURPOSE: The Simon, flanker, or Stroop effect on the current trial is influenced by the preceding trial type, with larger congruency effect following congruent trials than following incongruent trials, which is termed congruency sequence effect (CSE, Gratton et al., 1992). The conflict adaptation account (Gratton et al., 1992) and feature integration account (Hommel et al., 2004) are used to explain the CSE. Given that the diffusion model for conflict tasks (DMC, Ulrich et al., 2015) has provided a quantitative account of the mechanisms underlying decisions in conflict tasks, and it has not been applied to the congruency sequence effect (CSE). The present study expands analysis of the reaction time (RT) distributions reflected by delta plots to the CSE, and then extends the DMC to simulate the results, we refer to this model as the CSE-DMC. This model has the assumptions of the DMC that the controlled and automatic processes accumulate differently and independently, and adds two other assumptions: (1) feature integration influences only the controlled processes; (2) following incongruent trials the automatic processes are reduced, as more attention is paid to the task-relevant attribute (or target) and less to the task-irrelevant attribute (or distractor). These assumptions are inspired by the conflict adaptation and feature integration accounts and the previous findings.
METHODS: Studies 1 to 3 analyzed and modeled the data from a spatial Simon task, an arrow-based Simon task and a flanker task, respectively. For each study, we used Vincentile analysis to analyze the RT distributions for CSE. Then, we fit them with the CSE-DMC to examine whether it can fit the data well and better than that of two variants, the FI-DMC and CA-DMC models that only add one aforementioned assumption. We coded the trial sequences: a congruent trial followed by another congruent one (cC) and by an incongruent trial (cI); an incongruent trial followed by a congruent (iC) trial and by an incongruent trial (iI). Then the conditional accuracy function (CAF) and conditional duration function (CDF) were created. After that, a repeated-measures analysis of variance (ANOVA) was performed on accuracy, with bin, preceding congruency, and current congruency as within-subject variables, and another was performed on RT, with percentile, preceding congruency, and current congruency as within-subject variables. The CSE-DMC and the other Models were fitted separately to the CAFs and the CDFs for each task with four conditions (cC, cI, iC, iI), each has 5 CAF bins and 5 CDF quantiles. Predictions of each model were generated using Monte Carlo simulations with a step size of 1 ms, and a constant diffusion constant of for the superimposed process. The G2 was used to fit each model to the data. 100,000 trials were simulated for each condition and minimization cycle. The G2 criterion was minimized with the Nelder-Mead SIMPLEX method. Model selection for the CSE was made by computing a BIC statistic that penalizes models according to their number of free parameters.
RESULTS: RT distributions: On accuracy the Simon effects following congruent trials or incongruent trials became smaller across the RT distribution as RT increased, whereas the arrow-based Simon and flanker effects have similar RT distributions for each CSE condition. On RT, with increasing RT, (1) the spatial Simon effect was almost unchanged following congruent trials but initially became smaller and finally reversed following incongruent trials; (2) the arrow-based Simon effects increased following both congruent and incongruent trials, but more so for the former than the latter; (3) the flanker congruency effect varied quadratically following congruent trials but increased linearly following incongruent trials. Model fitting: The CSE-DMC could fit the data well and provided a better fit with the data than the other models, regardless of the task types.
CONCLUSIONS: the congruency effects following congruent and incongruent trials are different on mean RT and RT distributions, which could be a consequence of the automatic and controlled processes of conflict stimulus activation on the current trial being influenced differently by the prior trial. We provided evidence for this supposition by showing that the hypothesized computational mechanisms underlying these processes can be instantiated within the CSE-DMC.

Key words: diffusion model for conflict tasks, congruency sequence effect, Simon effect, flanker effect