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Correlated racing evidence accumulator models


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Reynolds, A, Kvam, PD, Osth, AF and Heathcote, A ORCID: 0000-0003-4324-5537 2020 , 'Correlated racing evidence accumulator models' , Journal of Mathematical Psychology , doi: 10.31219/

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Many models of response time that base choices on the first evidence accumulator to win arace to threshold rely on statistical independence between accumulators to achieve mathematicaltractability (e.g., Brown & Heathcote, 2008; Logan et al., 2014; Van Zandt et al., 2000).However, it is psychologically plausible that trial-to-trial fluctuations can cause both positivecorrelations (e.g., variability in arousal, attention or response caution that aect accumulatorsin the same way) and negative correlations (e.g., when evidence for each accumulator is computedrelative to a criterion). We examine the eects of such correlations in a racing accumulatormodel that remains tractable when they are present, the log-normal race (LNR Heathcote &Love, 2012). We first show that correlations are hard to estimate in binary choice data, and thattheir presence does not noticeably improve model fit to lexical-decision data (Wagenmakerset al., 2008) that is well fit by an independent LNR model. Poor estimation is attributableto the fact that estimation of correlation requires information about the relationship betweenaccumulator states but only the state of the winning accumulator is directly observed in binarychoice. We then show that this problem is remedied when discrete confidence judgments aremodelled by an extension of Vickers’ (1979) “balance-of-evidence” hypothesis proposed byReynolds et al. (submitted). In this “multiple-threshold race” model confidence is based onthe state of the losing accumulator judged relative to one or more extra thresholds. We showthat 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 toRatcli et al.’s (1994) recognition memory data than an independent mode. We concludethat the MTLNR provides a mathematically tractable tool that is useful both for investigatingcorrelations between accumulators and for modelling confidence judgments.

Item Type: Article
Authors/Creators:Reynolds, A and Kvam, PD and Osth, AF and Heathcote, A
Journal or Publication Title: Journal of Mathematical Psychology
Publisher: Academic Press Inc Elsevier Science
ISSN: 0022-2496
DOI / ID Number: 10.31219/
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