Abstract Many models of response time that base choices on the first evidence accumulator to win a race to threshold rely on statistical independence between accumulators to achieve mathematical tractability (e.g., Brown and Heathcote, 2008; Logan et al., 2014; Van Zandt et al., 2000). However, it is psychologically plausible that trial-to-trial fluctuations can cause both positive correlations (e.g., variability in arousal, attention or response caution that affect accumulators in the same way) and negative correlations (e.g., when evidence for each accumulator is computed relative to a criterion). We examine the effects of such correlations in a racing accumulator model that remains tractable when they are present, the log-normal race (LNR Heathcote and Love, 2012). We first show that correlations are hard to estimate in binary choice data, and that their presence does not noticeably improve model fit to lexical-decision data (Wagenmakers et al., 2008) that is well fit by an independent LNR model. Poor estimation is attributable to the fact that estimation of correlation requires information about the relationship between accumulator states but only the state of the winning accumulator is directly observed in binary choice. We then show that this problem is remedied when discrete confidence judgments are modeled by an extension of Vickers’s (1979) “balance-of-evidence” hypothesis proposed by Reynolds et al. (submitted). In this “multiple-threshold race” model confidence is based on the state of the losing accumulator judged relative to one or more extra thresholds. We show that not only is correlation well estimated in a multiple-threshold log-normal race (MTLNR) model with as few as two confidence levels, but that it also resulted in clearly better fits to Ratcliff et al.’s (1994) recognition memory data than an independent mode. We conclude that the MTLNR provides a mathematically tractable tool that is useful both for investigating correlations between accumulators and for modeling confidence judgments.

中文翻译：

---

相关赛车证据累加器模型

摘要 许多基于第一个证据累加器以赢得阈值竞赛的响应时间模型依赖于累加器之间的统计独立性以实现数学易处理性（例如，Brown 和 Heathcote，2008 年；Logan 等人，2014 年；Van Zandt 等人., 2000)。然而，从心理学上来说，试验间的波动可以导致正相关（例如，以相同方式影响累加器的唤醒、注意力或反应谨慎的可变性）和负相关（例如，当计算每个累加器的证据时）相对于标准）。我们研究了这种相关性在存在时仍然易于处理的赛车累加器模型中的影响，即对数正态种族（LNR Heathcote 和 Love，2012）。我们首先表明在二元选择数据中很难估计相关性，并且它们的存在并没有显着提高模型对词汇决策数据的拟合（Wagenmakers 等人，2008 年），该数据非常适合独立的 LNR 模型。糟糕的估计归因于这样一个事实，即相关性的估计需要有关累加器状态之间关系的信息，但在二元选择中只直接观察到获胜累加器的状态。然后我们表明，当离散置信度判断通过 Reynolds 等人提出的 Vickers (1979)“证据平衡”假设的扩展建模时，这个问题得到了解决。（提交）。在这个“多阈值竞赛”模型中，置信度基于相对于一个或多个额外阈值判断的失败累加器的状态。我们表明，不仅在多阈值对数正态种族 (MTLNR) 模型中可以很好地估计相关性，只有两个置信水平，而且它也明显更好地拟合了 Ratcliff 等人 (1994) 的识别内存数据多于独立模式。我们得出结论，MTLNR 提供了一种数学上易于处理的工具，对于研究累加器之间的相关性和对置信度判断建模都很有用。