Correlated racing evidence accumulator models

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.